The 2017-18 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 -0.4 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 10.1% 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 24.63% for this bracket; the 24.70% 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 24.70% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 23.79% for an entry that never wins a tiebreaker and 25.67% for one that always does — it finishes level with 1.1 others 1.88% of the time — so the whole tiebreaker is worth 1.88 points at the outside. Chalk has more riding on it: 23.82% to 25.85% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators where chalk advances Winnipeg Jets, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 8.

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 52% 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 74.1% in the tournaments its champion (Boston Bruins) wins and 14.89% in the rest, so 50% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 24.63% it claimed and not the 24.70% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 3.48% of the time here, and 28.4% of that arrives as a tie shared with 1.6 other people holding the same bracket — against 8.1% 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 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 -0.4 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 7.7% 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 24.44% for this bracket; the 24.52% 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 24.52% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 23.55% for an entry that never wins a tiebreaker and 25.55% for one that always does — it finishes level with 1.1 others 1.99% of the time — so the whole tiebreaker is worth 1.99 points at the outside. Chalk has more riding on it: 23.64% to 25.66% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators where chalk advances Winnipeg Jets, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 8.

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 52% 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 74.1% in the tournaments its champion (Boston Bruins) wins and 14.89% in the rest, so 50% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 24.44% it claimed and not the 24.52% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 3.05% of the time here, and 32.8% of that arrives as a tie shared with 1.6 other people holding the same bracket — against 10.3% 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 4.8 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 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 25.62% for this bracket; the 26.28% 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 26.28% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 25.25% for an entry that never wins a tiebreaker and 27.37% for one that always does — it finishes level with 1.1 others 2.11% of the time — so the whole tiebreaker is worth 2.11 points at the outside. Chalk has more riding on it: 24.76% to 27.21% 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 — 5.2 expected points at these lengths against 4.5 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 Minnesota Wild where chalk advances Winnipeg Jets, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 10.

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 52% 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 74.1% in the tournaments its champion (Boston Bruins) wins and 14.89% in the rest, so 50% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 25.62% it claimed and not the 26.28% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 2.61% of the time here, and 39.2% of that arrives as a tie shared with 1.7 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 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 2.4 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 search itself reported 15.89% for this bracket; the 15.39% 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 15.39% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 14.24% for an entry that never wins a tiebreaker and 16.68% for one that always does — it finishes level with 1.2 others 2.44% of the time — so the whole tiebreaker is worth 2.44 points at the outside. Chalk has more riding on it: 14.09% to 16.79% 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 — 5.3 expected points at these lengths against 4.6 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 Columbus Blue Jackets and Nashville Predators where chalk advances Pittsburgh Penguins, Winnipeg Jets and San Jose Sharks, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 3.

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 52% 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 74.1% in the tournaments its champion (Boston Bruins) wins and 14.89% in the rest, so 50% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 15.89% it claimed and not the 15.39% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 14.32% of the time here, and 32.7% of that arrives as a tie shared with 1.5 other people holding the same bracket — against 8.4% 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 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 -0.4 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 2.4% 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 10.70% for this bracket; the 10.82% 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 10.82% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 10.26% for an entry that never wins a tiebreaker and 11.42% for one that always does — it finishes level with 1.1 others 1.16% of the time — so the whole tiebreaker is worth 1.16 points at the outside. Chalk has more riding on it: 9.96% to 11.08% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators where chalk advances Winnipeg Jets, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 8.

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 77% 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 45.5% in the tournaments its champion (Boston Bruins) wins and 4.04% in the rest, so 69% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 10.70% it claimed and not the 10.82% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 0.69% of the time here, and 34.5% of that arrives as a tie shared with 1.7 other people holding the same bracket — against 9.7% 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 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 -0.4 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 1.6% 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 10.72% for this bracket; the 10.96% 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 10.96% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 10.29% for an entry that never wins a tiebreaker and 11.69% for one that always does — it finishes level with 1.2 others 1.40% of the time — so the whole tiebreaker is worth 1.40 points at the outside. Chalk has more riding on it: 10.13% to 11.43% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators where chalk advances Winnipeg Jets, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 8.

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 77% 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 45.5% in the tournaments its champion (Boston Bruins) wins and 4.04% in the rest, so 69% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 10.72% it claimed and not the 10.96% 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 2 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 0.55% of the time here, and 43.3% of that arrives as a tie shared with 1.6 other people holding the same bracket — against 15.0% 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 8.0 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 0.8% 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 13.32% for this bracket; the 14.13% 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 14.13% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 13.55% for an entry that never wins a tiebreaker and 14.76% for one that always does — it finishes level with 1.1 others 1.21% of the time — so the whole tiebreaker is worth 1.21 points at the outside. Chalk has more riding on it: 11.72% to 13.33% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators and Pittsburgh Penguins where chalk advances Winnipeg Jets and 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 8.

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 77% 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 45.5% in the tournaments its champion (Pittsburgh Penguins) wins and 4.04% in the rest, so 69% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 13.32% it claimed and not the 14.13% 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 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 0.41% of the time here, and 54.2% of that arrives as a tie shared with 2.1 other people holding the same bracket — against 26.5% 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 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: 2.4 expected at these lengths, 2.4 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 2017-18 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 10.5 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 5.04% for this bracket; the 4.76% 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 4.76% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 4.23% for an entry that never wins a tiebreaker and 5.37% for one that always does — it finishes level with 1.2 others 1.15% of the time — so the whole tiebreaker is worth 1.15 points at the outside. Chalk has more riding on it: 4.21% to 5.52% 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 — 5.3 expected points at these lengths against 4.6 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 5 of 15 series, which is fewer decisions than it looks: it advances Tampa Bay Lightning, Columbus Blue Jackets and Nashville Predators where chalk advances Boston Bruins, Pittsburgh Penguins and Winnipeg Jets, and a club backed in the first round is backed again in every round it survives. It differs from the table's bracket in 5.

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 77% 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 45.5% in the tournaments its champion (Tampa Bay Lightning) wins and 4.04% in the rest, so 69% of what it has rides on one series it prices at 16.8%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 5.04% it claimed and not the 4.76% 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 6 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 4.18% of the time here, and 58.1% of that arrives as a tie shared with 2.1 other people holding the same bracket — against 12.8% 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 4.3% 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 8.0 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 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 4.07% for this bracket; the 4.13% 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 4.13% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 3.84% for an entry that never wins a tiebreaker and 4.44% for one that always does — it finishes level with 1.1 others 0.60% of the time — so the whole tiebreaker is worth 0.60 points at the outside. Chalk has more riding on it: 3.67% to 4.26% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators and Pittsburgh Penguins where chalk advances Winnipeg Jets and 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 8.

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 96% 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 39.6% in the tournaments its champion (Pittsburgh Penguins) wins and 0.37% in the rest, so 93% of what it has rides on one series it prices at 11.6%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 4.07% it claimed and not the 4.13% 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 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 0.18% of the time here, and 49.7% of that arrives as a tie shared with 2.3 other people holding the same bracket — against 12.8% 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 8.0 expected points and roughly 1.3× 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 4.75% for this bracket; the 4.82% 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 4.82% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 4.55% for an entry that never wins a tiebreaker and 5.12% for one that always does — it finishes level with 1.1 others 0.56% of the time — so the whole tiebreaker is worth 0.56 points at the outside. Chalk has more riding on it: 3.31% to 3.98% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators and Pittsburgh Penguins where chalk advances Winnipeg Jets and 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 8.

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 96% 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 39.6% in the tournaments its champion (Pittsburgh Penguins) wins and 0.37% in the rest, so 93% of what it has rides on one series it prices at 11.6%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 4.75% it claimed and not the 4.82% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 0.13% of the time here, and 59.0% of that arrives as a tie shared with 2.4 other people holding the same bracket — against 19.6% 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 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 8.0 expected points and roughly 1.6× 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 0.2% 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 6.97% for this bracket; the 6.88% 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 6.88% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 6.50% for an entry that never wins a tiebreaker and 7.27% for one that always does — it finishes level with 1.1 others 0.77% of the time — so the whole tiebreaker is worth 0.77 points at the outside. Chalk has more riding on it: 4.04% to 4.88% 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 — 5.3 expected points at these lengths against 4.6 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 Nashville Predators and Pittsburgh Penguins where chalk advances Winnipeg Jets and 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 8.

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 96% 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 39.6% in the tournaments its champion (Pittsburgh Penguins) wins and 0.37% in the rest, so 93% of what it has rides on one series it prices at 11.6%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 6.97% it claimed and not the 6.88% 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 4 picks away, and 2 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 0.08% of the time here, and 81.0% of that arrives as a tie shared with 3.3 other people holding the same bracket — against 32.0% 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: 2.5 expected at these lengths, 2.4 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 2017-18 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 14.0 expected points and roughly 1.3× its chance of winning. Expected points is a quantity you can lead the field in and never finish first in. The search itself reported 1.73% for this bracket; the 1.70% 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 1.70% above splits every tie evenly, which is what an entrant with no view on that number should expect. The two ends are 1.47% for an entry that never wins a tiebreaker and 1.95% for one that always does — it finishes level with 1.2 others 0.48% of the time — so the whole tiebreaker is worth 0.48 points at the outside. Chalk has more riding on it: 1.03% to 1.67% 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 — 5.3 expected points at these lengths against 4.6 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 Columbus Blue Jackets and Nashville Predators where chalk advances Pittsburgh Penguins, Winnipeg Jets and 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 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 96% 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 39.6% in the tournaments its champion (Columbus Blue Jackets) wins and 0.37% in the rest, so 93% of what it has rides on one series it prices at 11.6%. A small pool is a different game — with 10 in it the winner had him 50% of the time and this entry finishes first 14.9% 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.

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 1.73% it claimed and not the 1.70% 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 Tampa Bay Lightning, Boston Bruins, Washington Capitals, Pittsburgh Penguins, Nashville Predators, Winnipeg Jets, Vegas Golden Knights, San Jose Sharks already through. Its deadline is the first Game 2 of round two, and 4 of the 4 second-round openers were in hand: Boston Bruins 6–2 Tampa Bay Lightning, Pittsburgh Penguins 3–2 Washington Capitals, Winnipeg Jets 4–1 Nashville Predators and Vegas Golden Knights 7–0 San Jose Sharks. 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 1.08% of the time here, and 96.3% of that arrives as a tie shared with 4.8 other people holding the same bracket — against 21.3% 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, 2.1 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 2017-18 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.