The 2022-23 bracket, and the entry that wins the pool

The entry

Against 9 other entries in a room that reads the table, loosely, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 0.0 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 5.8% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 27.62% for this bracket; the 27.64% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 27.64% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 26.73% for an entry that never wins a tiebreaker and 28.63% for one that always does — it finishes level with 1.1 others 1.90% of the time — so the whole tiebreaker is worth 1.90 points at the outside. Chalk has more riding on it: 26.73% to 28.63% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 10 in the pool, whoever holds the winning score had the Cup winner in 48% of 20,000 tournaments this April (50% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 77.7% in the tournaments its champion (Carolina Hurricanes) wins and 18.32% in the rest, so 54% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 27.62% it claimed and not the 27.64% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 10 people choosing between 128 things land on each other more often than 10 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 16.48% of the time here, and 18.6% of that arrives as a tie shared with 1.4 other people holding the same bracket — against 9.4% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 22.6% against the main bracket's 24.7%, and it is the better of the two in 2 of 7. Chalk averages 21.7%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 28.12%, the model's chalk 20.22% and the room's own bracket 14.10%. The entry would have been a live contender for first in 4 of 7 Aprils, chalk in 4 and the room's bracket in 5. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 9 other entries in a room that reads the table, as the crowd did, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 2.7 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 4.1% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 30.42% for this bracket; the 30.80% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 30.80% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 29.83% for an entry that never wins a tiebreaker and 31.85% for one that always does — it finishes level with 1.1 others 2.02% of the time — so the whole tiebreaker is worth 2.02 points at the outside. Chalk has more riding on it: 29.24% to 31.31% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 1 of 15 series, which is fewer decisions than it looks: it advances Tampa Bay Lightning where chalk advances Boston Bruins, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 12.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 10 in the pool, whoever holds the winning score had the Cup winner in 48% of 20,000 tournaments this April (50% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 77.7% in the tournaments its champion (Carolina Hurricanes) wins and 18.32% in the rest, so 54% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 30.42% it claimed and not the 30.80% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 1 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 10 people choosing between 128 things land on each other more often than 10 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 15.98% of the time here, and 21.2% of that arrives as a tie shared with 1.4 other people holding the same bracket — against 14.4% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 23.5% against the main bracket's 25.6%, and it is the better of the two in 1 of 7. Chalk averages 21.9%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 38.02%, the model's chalk 19.80% and the room's own bracket 10.86%. The entry would have been a live contender for first in 4 of 7 Aprils, chalk in 4 and the room's bracket in 4. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 9 other entries in a room that reads the table, tightly, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 2.7 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 3.3% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 35.87% for this bracket; the 36.64% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 36.64% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 35.59% for an entry that never wins a tiebreaker and 37.80% for one that always does — it finishes level with 1.2 others 2.21% of the time — so the whole tiebreaker is worth 2.21 points at the outside. Chalk has more riding on it: 34.59% to 37.02% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 1 of 15 series, which is fewer decisions than it looks: it advances Tampa Bay Lightning where chalk advances Boston Bruins, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 12.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 10 in the pool, whoever holds the winning score had the Cup winner in 48% of 20,000 tournaments this April (50% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 77.7% in the tournaments its champion (Carolina Hurricanes) wins and 18.32% in the rest, so 54% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 35.87% it claimed and not the 36.64% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 10 people choosing between 128 things land on each other more often than 10 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 15.67% of the time here, and 25.2% of that arrives as a tie shared with 1.5 other people holding the same bracket — against 21.1% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 25.6% against the main bracket's 28.3%, and it is the better of the two in 1 of 7. Chalk averages 23.0%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 39.84%, the model's chalk 21.06% and the room's own bracket 8.36%. The entry would have been a live contender for first in 4 of 7 Aprils, chalk in 4 and the room's bracket in 4. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 9 other entries in a room that believes the model, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 2.8 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The search itself reported 16.63% for this bracket; the 16.56% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 16.56% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 15.10% for an entry that never wins a tiebreaker and 18.16% for one that always does — it finishes level with 1.2 others 3.06% of the time — so the whole tiebreaker is worth 3.06 points at the outside. Chalk has more riding on it: 15.23% to 18.11% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 2 of 15 series, which is fewer decisions than it looks: it advances Winnipeg Jets and Seattle Kraken where chalk advances Los Angeles Kings, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 2.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 10 in the pool, whoever holds the winning score had the Cup winner in 48% of 20,000 tournaments this April (50% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 77.7% in the tournaments its champion (Carolina Hurricanes) wins and 18.32% in the rest, so 54% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 16.63% it claimed and not the 16.56% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 10 people choosing between 128 things land on each other more often than 10 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 13.00% of the time here, and 32.3% of that arrives as a tie shared with 1.6 other people holding the same bracket — against 8.2% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 12.9% against the main bracket's 15.2%, and it is the better of the two in 0 of 7. Chalk averages 12.7%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 5.11%, the model's chalk 8.46% and the room's own bracket 8.46%. The entry would have been a live contender for first in 3 of 7 Aprils, chalk in 3 and the room's bracket in 3. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 29 other entries in a room that reads the table, loosely, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 3.4 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 1.0% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 13.53% for this bracket; the 13.13% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 13.13% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 12.47% for an entry that never wins a tiebreaker and 13.83% for one that always does — it finishes level with 1.1 others 1.35% of the time — so the whole tiebreaker is worth 1.35 points at the outside. Chalk has more riding on it: 12.56% to 14.03% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 2 of 15 series, which is fewer decisions than it looks: it advances Winnipeg Jets where chalk advances Los Angeles Kings, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 11.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 30 in the pool, whoever holds the winning score had the Cup winner in 69% of 20,000 tournaments this April (76% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 51.1% in the tournaments its champion (Carolina Hurricanes) wins and 6.52% in the rest, so 68% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 13.53% it claimed and not the 13.13% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 3 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 30 people choosing between 128 things land on each other more often than 30 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 5.55% of the time here, and 32.4% of that arrives as a tie shared with 1.5 other people holding the same bracket — against 15.2% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 10.1% against the main bracket's 11.0%, and it is the better of the two in 3 of 7. Chalk averages 9.1%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 4.58%, the model's chalk 3.93% and the room's own bracket 0.76%. The entry would have been a live contender for first in 4 of 7 Aprils, chalk in 3 and the room's bracket in 1. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 29 other entries in a room that reads the table, as the crowd did, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 3.4 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 0.5% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 16.37% for this bracket; the 15.81% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 15.81% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 15.04% for an entry that never wins a tiebreaker and 16.67% for one that always does — it finishes level with 1.1 others 1.63% of the time — so the whole tiebreaker is worth 1.63 points at the outside. Chalk has more riding on it: 14.99% to 16.61% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 2 of 15 series, which is fewer decisions than it looks: it advances Winnipeg Jets where chalk advances Los Angeles Kings, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 11.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 30 in the pool, whoever holds the winning score had the Cup winner in 69% of 20,000 tournaments this April (76% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 51.1% in the tournaments its champion (Carolina Hurricanes) wins and 6.52% in the rest, so 68% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 16.37% it claimed and not the 15.81% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 30 people choosing between 128 things land on each other more often than 30 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 5.03% of the time here, and 36.3% of that arrives as a tie shared with 1.7 other people holding the same bracket — against 18.4% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 11.7% against the main bracket's 12.1%, and it is the better of the two in 3 of 7. Chalk averages 9.3%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 2.83%, the model's chalk 5.07% and the room's own bracket 0.63%. The entry would have been a live contender for first in 3 of 7 Aprils, chalk in 2 and the room's bracket in 1. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 29 other entries in a room that reads the table, tightly, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 2.7 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 0.3% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 21.91% for this bracket; the 22.06% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 22.06% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 21.07% for an entry that never wins a tiebreaker and 23.14% for one that always does — it finishes level with 1.1 others 2.07% of the time — so the whole tiebreaker is worth 2.07 points at the outside. Chalk has more riding on it: 20.43% to 22.43% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 1 of 15 series, which is fewer decisions than it looks: it advances Tampa Bay Lightning where chalk advances Boston Bruins, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 12.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 30 in the pool, whoever holds the winning score had the Cup winner in 69% of 20,000 tournaments this April (76% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 51.1% in the tournaments its champion (Carolina Hurricanes) wins and 6.52% in the rest, so 68% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 21.91% it claimed and not the 22.06% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 2 to 3 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 30 people choosing between 128 things land on each other more often than 30 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 4.54% of the time here, and 43.5% of that arrives as a tie shared with 2.0 other people holding the same bracket — against 31.7% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 14.5% against the main bracket's 15.7%, and it is the better of the two in 4 of 7. Chalk averages 10.4%. The second chance is the easier competition here, which is not the intuition — fewer picks sounds like less room to be different, and it is really less room for everybody else.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 14.44%, the model's chalk 8.25% and the room's own bracket 0.60%. The entry would have been a live contender for first in 3 of 7 Aprils, chalk in 2 and the room's bracket in 1. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 29 other entries in a room that believes the model, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 25.1 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The search itself reported 4.98% for this bracket; the 4.52% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 4.52% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 4.13% for an entry that never wins a tiebreaker and 4.95% for one that always does — it finishes level with 1.2 others 0.81% of the time — so the whole tiebreaker is worth 0.81 points at the outside. Chalk has more riding on it: 4.01% to 5.16% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 4 of 15 series, which is fewer decisions than it looks: it advances Winnipeg Jets and Boston Bruins where chalk advances Los Angeles Kings and Carolina Hurricanes, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 4.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 30 in the pool, whoever holds the winning score had the Cup winner in 69% of 20,000 tournaments this April (76% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 51.1% in the tournaments its champion (Boston Bruins) wins and 6.52% in the rest, so 68% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 4.98% it claimed and not the 4.52% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 30 people choosing between 128 things land on each other more often than 30 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 3.56% of the time here, and 54.0% of that arrives as a tie shared with 2.0 other people holding the same bracket — against 11.6% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 4.3% against the main bracket's 4.7%, and it is the better of the two in 3 of 7. Chalk averages 3.7%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 10.05%, the model's chalk 0.38% and the room's own bracket 0.38%. The entry would have been a live contender for first in 2 of 7 Aprils, chalk in 1 and the room's bracket in 1. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 99 other entries in a room that reads the table, loosely, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 3.4 expected points and roughly 1.0× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 0.1% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 5.20% for this bracket; the 5.02% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 5.02% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 4.70% for an entry that never wins a tiebreaker and 5.38% for one that always does — it finishes level with 1.2 others 0.69% of the time — so the whole tiebreaker is worth 0.69 points at the outside. Chalk has more riding on it: 4.66% to 5.42% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 2 of 15 series, which is fewer decisions than it looks: it advances Winnipeg Jets where chalk advances Los Angeles Kings, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 11.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 100 in the pool, whoever holds the winning score had the Cup winner in 87% of 20,000 tournaments this April (94% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 24.0% in the tournaments its champion (Carolina Hurricanes) wins and 2.29% in the rest, so 74% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 5.20% it claimed and not the 5.02% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 100 people choosing between 128 things land on each other more often than 100 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 1.35% of the time here, and 61.6% of that arrives as a tie shared with 2.2 other people holding the same bracket — against 14.8% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 4.1% against the main bracket's 4.6%, and it is the better of the two in 2 of 7. Chalk averages 3.4%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 0.04%, the model's chalk 0.08% and the room's own bracket 0.00%. The entry would have been a live contender for first in 0 of 7 Aprils, chalk in 1 and the room's bracket in 0. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 99 other entries in a room that reads the table, as the crowd did, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 6.0 expected points and roughly 1.1× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 0.1% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 7.05% for this bracket; the 6.70% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 6.70% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 6.31% for an entry that never wins a tiebreaker and 7.14% for one that always does — it finishes level with 1.2 others 0.83% of the time — so the whole tiebreaker is worth 0.83 points at the outside. Chalk has more riding on it: 5.80% to 6.82% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 3 of 15 series, which is fewer decisions than it looks: it advances Tampa Bay Lightning and Winnipeg Jets where chalk advances Boston Bruins and Los Angeles Kings, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 12.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 100 in the pool, whoever holds the winning score had the Cup winner in 87% of 20,000 tournaments this April (94% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 24.0% in the tournaments its champion (Carolina Hurricanes) wins and 2.29% in the rest, so 74% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 7.05% it claimed and not the 6.70% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 100 people choosing between 128 things land on each other more often than 100 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 1.10% of the time here, and 65.9% of that arrives as a tie shared with 2.4 other people holding the same bracket — against 15.4% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 5.2% against the main bracket's 5.7%, and it is the better of the two in 2 of 7. Chalk averages 3.5%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 0.01%, the model's chalk 0.30% and the room's own bracket 0.00%. The entry would have been a live contender for first in 0 of 7 Aprils, chalk in 1 and the room's bracket in 0. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 99 other entries in a room that reads the table, tightly, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 6.0 expected points and roughly 1.1× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The third box is the bracket the room itself mostly submits, and it finishes first 0.0% of the time: the crowd's own pick is the worst of the three, because it is the one with the most company. The search itself reported 11.68% for this bracket; the 11.31% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 11.31% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 10.72% for an entry that never wins a tiebreaker and 11.97% for one that always does — it finishes level with 1.2 others 1.25% of the time — so the whole tiebreaker is worth 1.25 points at the outside. Chalk has more riding on it: 9.46% to 10.89% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.8 expected points at these lengths against 4.4 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 3 of 15 series, which is fewer decisions than it looks: it advances Tampa Bay Lightning and Winnipeg Jets where chalk advances Boston Bruins and Los Angeles Kings, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 12.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 100 in the pool, whoever holds the winning score had the Cup winner in 87% of 20,000 tournaments this April (94% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 24.0% in the tournaments its champion (Carolina Hurricanes) wins and 2.29% in the rest, so 74% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 11.68% it claimed and not the 11.31% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 2 picks away, and every one of them backs the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 100 people choosing between 128 things land on each other more often than 100 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 0.81% of the time here, and 78.4% of that arrives as a tie shared with 3.1 other people holding the same bracket — against 54.5% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 7.7% against the main bracket's 8.4%, and it is the better of the two in 3 of 7. Chalk averages 4.0%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.1 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 0.01%, the model's chalk 1.85% and the room's own bracket 0.00%. The entry would have been a live contender for first in 0 of 7 Aprils, chalk in 1 and the room's bracket in 0. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.

The entry

Against 99 other entries in a room that believes the model, this is the bracket with the best chance of finishing first, out of all 32,768 coherent ones, chosen with 8 of the 8 openers in hand.

The trade is visible in those first two boxes. The entry gives up 35.0 expected points and roughly 1.4× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The search itself reported 1.77% for this bracket; the 1.69% above is the same bracket scored against rooms and tournaments it never saw, and the difference between them is the winner's curse rather than a rounding error.

And a tie is not quite a coin. The pool settles a tie for first on the number of goals scored in the Final, and 1.69% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 1.52% for an entry that never wins a tiebreaker and 1.88% for one that always does — it finishes level with 1.1 others 0.35% of the time — so the whole tiebreaker is worth 0.35 points at the outside. Chalk has more riding on it: 1.01% to 1.52% on the same rooms, because a bracket the room also submits is a bracket that ties.

This entry's two is the pair this bracket was choosing between, which after the first round is whoever it had itself advanced — so the chalk column often names a club that is not in it, because chalk advanced someone else. The table is the room's own bracket, the club it prefers at each series, in italics where this entry parts from it. That is what coherence means, and it is why fifteen series with sixteen clubs in them come to 2¹⁵ brackets and not more: every pick after the first round is a choice between two clubs the entry itself put there. The percentage beside a club is its chance of winning that series across every path it could take there, as it stood at the deadline — a marginal, not a head-to-head, except in the first round where the two are the same thing, and where the score beside the pair is the opener that was in hand. Games is the length to write beside a first-round pick: the model's most likely length for that club to win in, from the state at the deadline, with its chance and, where the answer is not six, six's. It is three points a series if the winner is also right — 4.7 expected points at these lengths against 4.3 writing six everywhere — and over seven Aprils from the deadline the model's own answer collected 5.1 of 24 and "six" collected 6.0, 0.6 standard errors apart. Write either; it is 5.9% of the board and nothing here can tell them apart. Worth is the points that series pays, under this pool's own rule: 10, 25, 50, 100 a series by round, which puts 53% of the board in the last three of the fifteen. That is why a pool is won and lost on the champion pick. This entry differs from the model's chalk in 4 of 15 series, which is fewer decisions than it looks: it advances Florida Panthers where chalk advances Boston Bruins and Carolina Hurricanes, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 4.

Do you need the champion? Measured rather than assumed, tournament by tournament, in the room as the crowd was measured to be. With 100 in the pool, whoever holds the winning score had the Cup winner in 87% of 20,000 tournaments this April (94% averaged over the 7 Aprils; by size of pool, 50% of 10, 76% of 30 and 94% of 100). This entry's chance of first place is 24.0% in the tournaments its champion (Florida Panthers) wins and 2.29% in the rest, so 74% of what it has rides on one series it prices at 21.5%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 18.3% of the time without him — but at a hundred the pool is decided by the Final and the other fourteen series decide who among the holders takes it. Over the 7 Aprils played the entry had him 0 of 7 times, chalk 0 and the table's bracket 0, and 4.4% of the league's ESPN crowd did this April.

Is it a peak, or a plateau?

The best single bracket means nothing without the shape of the rest. If thousands sit within a whisker of it, the optimiser has found the luckiest estimate on a flat surface rather than a real maximum. Every one of the 32,768 coherent brackets, by its chance of finishing first — these are the search's own estimates, so the top of this distribution is the 1.77% it claimed and not the 1.69% the entry earned out of sample:

The brackets immediately behind it are near-copies rather than rivals, which is the other half of the same point: the 4 behind it are 1 to 5 picks away, and 3 of them back the same champion.

The second chance

The same pool runs a second competition with its own prize. Once the first round is over and the second-round matchups are set, an entrant may submit a fresh bracket covering rounds two, three and four — 25, 50 and 100 a series, the eight settled ones worth nothing. It does not replace the original entry; both run. So this is the same model at a later moment, choosing seven picks from 128 coherent brackets rather than fifteen from 32,768, with Florida Panthers, Toronto Maple Leafs, Carolina Hurricanes, New Jersey Devils, Seattle Kraken, Dallas Stars, Vegas Golden Knights, Edmonton Oilers already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Florida Panthers 4–2 Toronto Maple Leafs, Carolina Hurricanes 5–1 New Jersey Devils, Seattle Kraken 5–4 Dallas Stars (OT) and Vegas Golden Knights 6–4 Edmonton Oilers. The entry is priced from there.

A smaller pool of brackets is a more crowded one. 100 people choosing between 128 things land on each other more often than 100 choosing between 32,768, so the room's own favourite is submitted many times over and its wins are split rather than won outright. The room's own bracket finishes first 0.90% of the time here, and 95.0% of that arrives as a tie shared with 4.2 other people holding the same bracket — against 18.4% of the fifteen-pick bracket's first places, in this same room. That is the crowding this whole page is about, and it is the stronger of the two here.

Across all 7 postseasons, in this same room: the second-chance entry averages 1.4% against the main bracket's 1.6%, and it is the better of the two in 1 of 7. Chalk averages 1.0%. Against a room that read the model it was the easier competition, because the room crowded onto the model's favourites; against the room as measured it is not, and the two are worth about the same. Enter both.

Games is the length to write beside each second-round pick, the model's most likely length for that club to win in from the state at this deadline — the 12 points this competition pays for calling the length of the four second-round series, on a board of 312: 2.3 expected at these lengths, 2.0 writing six. The same bonus in the first round was measured over seven Aprils and the model's answer could not be told from "six games" in every box; write either.

And against what actually happened

The tournament the entry was priced against is simulated. This one is not: both entries are scored against the real 2022-23 postseason, over every room that might have turned up. A figure near zero means what it says — somebody in almost every room did better, which is what happens when the club that won was not on either bracket.

Across all 7 postseasons, in this same room: the optimised entry averages 0.00%, the model's chalk 0.00% and the room's own bracket 0.00%. The entry would have been a live contender for first in 0 of 7 Aprils, chalk in 0 and the room's bracket in 0. Both are far below what the simulated tournaments promised, because a real April contains upsets the model priced low — and seven of them is seven, not a hundred and five.