Half point backtest: the key-number model against history
A half point is worth what the number it crosses is worth: the share of games that land on exactly 3, on 7, on an odd hockey total, on a one-run win. The half point calculator prices every move with one key-number model per league, fitted to the market’s no-vig price. In October 2026 we scored those models against closing lines and final scores, league by league, along the calculator’s own code path. The short answer: the NFL model was already close, college football’s key numbers reached only half as far as the data, hockey and baseball needed a different shape altogether, and soccer needed a model of its own.
The short answer: what the backtest found in each league, and what changed
- NFLWhat history saidClose to history; a little low at 3 and 7 (1 to 3 cents a half point) and through 2 and 6 since 2015. No refit beat it on held-out seasonsWhat changed on viggedUnchanged
- College footballWhat history saidThe key numbers reached only half as far as the data, and totals had noneWhat changed on viggedKeys to 45 on spreads and 30 to 85 on totals, with 3 and 7 weighted far more heavily
- NBAWhat history saidUsable as it was; a retuned entry was no better on 2023–26What changed on viggedUnchanged, to be re-run after the 2025–26 season
- College basketballWhat history saidFewer one-point games than the curve says, in every eraWhat changed on viggedA smaller one-point key and a slightly narrower curve
- WNBAWhat history saidSpreads too narrow, with a hole at one point; totals too narrow on 2025–26What changed on viggedWider margins with keys at 0, 1 and 2; wider totals, shown as approximate
- NHLWhat history saidThe wrong shape: most totals end odd, and empty-net goals make three-goal wins commonWhat changed on viggedA key for every goal, on margins and on totals
- MLBWhat history saidThe wrong shape: most totals end odd, and home teams win by exactly one run far more often than away teamsWhat changed on viggedOdd totals weighted up; run-line keys that tell home from away
- Soccer (big five)What history saidNo model: the NFL fallback put the draw at 0.1%What changed on viggedA model of its own for the Premier League, La Liga, Serie A, the Bundesliga and Ligue 1
To price a move on your own numbers, the half point calculator runs the shipped model for every league below.
What the key-number model is
Every spread and total is a bet on where the final lands, and the model behind the calculator describes the landing spot in two parts. A bell curve, centered on the market’s expectation and as wide as the league’s margins usually spread, says roughly where the final will fall. A table of key numbers then says how much more, or less, often the final lands on each exact number than the curve alone allows: in the NFL, 3 and 7 carry the biggest weights, because a field goal and a touchdown decide so many games, and 0 almost none, because ties are rare. Each league has its own curve width and its own keys, on margins and on totals.
To price a move, the calculator fits the curve to the market first. Both prices on the line are de-vigged (power method) to get the chance that the favorite covers, pushes left out, and the curve’s center slides until the model gives that same chance. The model then reads off win, push and loss at every nearby number, and the break-even price on the new number is the one that leaves the bet’s expected value where it was. The same model prices the middles page, the board’s best-line ranking and alternate lines, so a model that is wrong about where finals land is wrong in several places at once.
How we tested it
The test follows the calculator’s path, one game at a time. For each game in a league’s history we take the closing line, de-vig the closing prices to the chance of covering (or use 50% where an archive keeps lines but no prices), fit the model’s center to that chance, and read off the model’s probability for every possible final. That distribution is scored against the final score of that same game only, so nothing from later games leaks in, and the scores add up over thousands of games into one number for how well the model’s shape matches where finals land. Comparing shares, how often the final sat on 3, on an odd total, on a one-run margin, against what the model predicted says where the shape is off.
Every retune was fitted on early seasons and judged on later ones it had never seen. College football’s new keys, fitted on 2006 to 2014 alone, matched 2015 to 2025 on all 17 key numbers. MLB’s keys were fitted on 2014 to 2019 and held on 2021 to 2025. Soccer’s model was fitted on the 2019/20 to 2022/23 seasons and checked on 2023/24 to 2025/26 and, separately, on 2005 to 2019. The NFL and NBA entries were challenged by refits the same way and kept, because no refit beat them out of sample. Every share quoted here comes with a 95% range in square brackets (a Wilson interval, or for a half point’s value in cents a resampling of the games). The scripts swap candidate entries into the model in memory and never change the shared code, so the figures here come from exactly the code the calculator runs, and a second pass re-ran and reviewed each league before anything shipped.
What the backtest found, league by league
NFL: close, and a little low at 3 and 7
The NFL model needed no change. Of 1,164 games that closed at −3 since 1999, 9.2% [7.7, 11.0] landed on exactly 3 against the model’s 8.5%, and at a −7 close 6.8% [4.9, 9.4] of 497 games landed on 7 against the model’s 5.4%. Both times the model sits inside the range on the low side, so a half point onto or off 3 or 7 may be worth 1 to 3 cents more than the calculator shows, and since 2015 the same has been true of half points through 2 and 6. A refit that trims the far keys (9, 17 to 19, 21, 24 and 28) scored a hair better on the seasons it was fitted to and no better on the rest, so the entry stays as it is.
College football: the keys reached only half as far as the data
College football was the biggest miss among the football models. Its keys stopped at 21 on spreads (3, 7, 10, 14, 17 and 21) and it had none on totals, while college games land on 24, 28, 31, 35 and beyond far more often than a plain curve allows, and totals have key numbers of their own from 30 to 85. College scores also spread wider than NFL scores: a −3 close lands on exactly 3 in 6.0% [4.7, 7.7] of 965 games, against 9.2% in the NFL. The shipped entry writes out every margin to 45 and most totals from 30 to 85, with 3 and 7 weighted far more heavily than before, and it sits inside history’s range on every published row (the table below). The cost shows up in prices: at a 50/50 main, buying from +3 to +3.5 now breaks even at −115 rather than −110, and +7 to +7.5 at −113 rather than −108.
NBA, college basketball and the WNBA: a hole at one point
The NBA model held up: a retuned entry scored no better on the 2023 to 2026 seasons, so it stays, to be re-run after the 2025–26 season. College basketball and the WNBA both showed a hole at one point, with one-point finals coming up less often than the curve said, for college in every era, so each now carries a one-point key below 1. College basketball’s curve came in a little narrower; the WNBA’s, too narrow on spreads, went wider on margins and on totals, where the width is a hedge between the 2025–26 season and earlier ones and the calculator marks the result as approximate. These three ran on closing-line archives licensed for research use only, so their history figures are not published here. The changes are small at the main, about a cent on a −110 half point, and larger only on far alternate lines.
NHL: the wrong shape, not the wrong width
Hockey broke the bell curve. A tie is an even total and one goal settles it, so every game that reaches overtime or a shootout ends on an odd total, and a one-goal win in regulation is odd too; most NHL totals end odd. Empty-net goals then turn one-goal leads into two- and three-goal wins in the last minute, so the favorite’s margin has bumps of its own. A curve spreads its chance evenly over neighboring numbers, which is why the old entry gave 5 and 6 the same 17% at a 5.5 close. The shipped entry has a key for every goal on margins and on totals: at a 5.5 close it puts 23% on 5 and 11% on 6, and on the puck line at 1.5 it puts more on a three-goal win (19%) than on a two-goal win (14%), where the old curve had them the other way round. In the calculator, over 5.5 bought to 5 now breaks even at −187 rather than −152, and sold to 6 at +128 rather than +151. The check ran on closing lines from 2007–08 to November 2022, an archive licensed for research only, so its figures are not published; the shipped entry lands close to history on both sides of the main. Because the puck line’s keys drift from era to era, the calculator moves it only from ±1.5 toward the moneyline, and moves totals at most two goals, with anything past one goal marked approximate.
MLB: odd totals, and the home team bats last
Baseball has the same two problems, with causes of its own. A total is odd exactly when the margin is odd, and the one-run game is the most common margin in baseball, so totals end odd far more often than even. In Pinnacle’s 2016 closing lines, 12.1% [9.4, 15.4] of the 454 games that closed at 7.5 ended on exactly 7 runs and 9.5% [7.1, 12.5] on exactly 8; the old curve split them almost evenly, and the shipped entry, with odd totals weighted up, says 11.1% and 7.6%. On the run line, the home team bats last: it stops batting the moment it leads after the top of the ninth, and a walk-off ends the game as the winning run scores, so home teams win by exactly one run far more often than away teams do. In 2016, 17.1% [15.3, 19.0] of 1,584 home favorites at −1.5 won by exactly one run, against 12.9% [10.8, 15.4] of 835 away favorites. The old model could not tell home from away and put about 10% on a home one-run win; the shipped entry carries signed keys, so a home win by one is a different number from an away win by one, and says 17.6% and 12.0%. Fitted on 2014 to 2019, the keys held on 2021 to 2025 (retail lines licensed for research only). In the calculator, over 7.5 bought to 7 now breaks even at −129 rather than −123, and a home favorite’s −1.5 bought to −1 is worth more than an away favorite’s, which is why the calculator asks which team you are on.
Soccer: a model of its own for the big five
Soccer had no model at all. A request for a big five league fell back to the NFL entry, which put the draw, the single most common result in soccer, at 0.1%. The new entry was fitted on the 2019/20 to 2022/23 seasons of the Premier League, La Liga, Serie A, the Bundesliga and Ligue 1 and checked on 2023/24 to 2025/26, the seasons in the table, and separately on 2005 to 2019. On the later seasons it says 29.5% of even-priced draw no bet lines push, against 29.6% [26.1, 33.5] of the 587 that did, and 25.2% of even-priced 2.5-goal totals land on exactly 2 goals, against 25.0% [23.0, 27.0] of 1,781. It misses in one place: a favorite at a handicap of 1 wins by exactly one goal, a push, 28.4% of the time against the model’s 25.9%, and favorites of 1.5 goals or more win by exactly one or two goals more often than the curve says. So the calculator marks moves onto or off a handicap of 1 as approximate and prices no sells off a handicap of 1.5 or more. It prices half and whole goals only, a goal either way, and 2.5-goal totals, in those five leagues; quarter lines, other totals, MLS, Liga MX and the Champions League wait for data. The price change is the largest in the study: away +0.5 bought to +1 at a 50/50 main breaks even at −200, where the fallback said −105.
The model against history, in one table
| What was counted | Model | History (95% range) | Games |
|---|---|---|---|
| NFL | |||
| Games closing −3 that landed on exactly 3 | 8.5% | 9.2% (7.7–11.0) | 1,164 games, 1999–2026 |
| Games closing −3.5 that landed on exactly 3 | 8.4% | 9.8% (7.8–12.3) | 692 games, 1999–2026 |
| Games closing −7 that landed on exactly 7 | 5.4% | 6.8% (4.9–9.4) | 497 games, 1999–2026 |
| What the half point −3 → −2.5 is worth | 18.5¢ | 20.2¢ (16.7–24.7) | 1,164 games, 1999–2026 |
| College football | |||
| Games closing −3 that landed on exactly 3 | 6.8% | 6.0% (4.7–7.7) | 965 games, 2006–2025 |
| Games closing −7 that landed on exactly 7 | 6.0% | 5.9% (4.4–7.9) | 725 games, 2006–2025 |
| Games closing −7 that landed on exactly 9 | 0.9% | 0.8% (0.4–1.8) | 725 games, 2006–2025 |
| Totals closing 55 that landed on exactly 55 | 3.9% | 3.9% (2.4–6.2) | 411 games, 2006–2024 |
| MLB | |||
| Totals closing 7.5 that ended on exactly 7 runs | 11.1% | 12.1% (9.4–15.4) | 454 games, 2016 |
| Totals closing 7.5 that ended on exactly 8 runs | 7.6% | 9.5% (7.1–12.5) | 454 games, 2016 |
| Home favorites at −1.5 that won by exactly 1 run | 17.6% | 17.1% (15.3–19.0) | 1,584 games, 2016 |
| Away favorites at −1.5 that won by exactly 1 run | 12.0% | 12.9% (10.8–15.4) | 835 games, 2016 |
| Soccer (big five) | |||
| Handicap 0 (draw no bet) that pushed: a draw | 29.5% | 29.6% (26.1–33.5) | 587 games, 2023/24–2025/26 |
| Favorites at −0.5 whose match ended in a draw | 27.5% | 28.3% (25.6–31.2) | 992 games, 2023/24–2025/26 |
| Even-priced 2.5-goal totals that ended on exactly 2 goals | 25.2% | 25.0% (23.0–27.0) | 1,781 games, 2023/24–2025/26 |
History: closing (or near-closing) lines and final scores, overtime, shootouts and extra innings included (soccer after 90 minutes and stoppage time); nflverse’s NFL lines are its closing-time lines, not one named book’s. The model column is worked out live from the model the calculator uses, at a −110 / −110 close. The range is where history’s figure would fall 95 times in 100 by chance alone (for the half point’s value, in cents of break-even price, a resampling of the games): a model figure inside it is as close as these games can tell. College football’s keys were fitted on 2006–2025; fitted on 2006–14 alone, the same method matched 2015–25 on all 17 key numbers. MLB’s were fitted on 2014–19 (2016 included) and held on 2021–25; soccer’s on 2019/20–2022/23, and the rows here are later seasons of the big five only.
At 3 and 7 NFL games have landed a little more often than the model says, so half points there may be worth 1 to 3 cents more than the calculator shows. The NBA, WNBA, college basketball and NHL models were checked the same way (and the last three retuned), but on line archives licensed for research use only, so their figures are not published here; nor are MLB’s 2021–25 retail lines.
- NFL lines and scores: nflverse (Lee Sharpe) (CC BY 4.0; figures aggregated by vigged)
- College football lines and scores: cfbfastR-data / SportsDataverse (CC BY 4.0; figures aggregated by vigged), from CollegeFootballData.com; 2006–19 lines originally collected from Sportsbook Review.
- MLB 2016 closing lines: the pinnacle.data R package (GPL-3; figures aggregated by vigged).
- The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at www.retrosheet.org.
- Football results and odds: Football-Data (www.football-data.co.uk)
What changed on vigged
Each retune moves prices toward history. The first table gives the break-even price of the side bought, at a 50/50 main, before and after, for the moves each change affects most; the second the model’s chance that a final lands exactly on a middle number, which is what the middles page prices. The football and basketball models also price alternate lines and the board’s best-line ranking, so those moved with them.
| League | Move | Before | Shipped |
|---|---|---|---|
| College football | +3 → +3.5 | −110 | −115 |
| College football | +7 → +7.5 | −108 | −113 |
| College football | +3 → +10 | −222 | −243 |
| College football | over 54.5 → 64.5 | +276 | +264 |
| College basketball | +6.5 → +7 | −108 | −109 |
| College basketball | +6.5 → +13.5 | −288 | −307 |
| WNBA | +4.5 → +5 | −109 | −108 |
| WNBA | over 163.5 → 173.5 | +321 | +286 |
| NHL | over 5.5 → 5 | −152 | −187 |
| NHL | over 5.5 → 6 | +151 | +128 |
| MLB | over 7.5 → 7 | −123 | −129 |
| MLB | over 8.5 → 9 | +122 | +128 |
| Soccer | away +0.5 → +1 | −105 | −200 |
| League | Middle number | Before | Shipped |
|---|---|---|---|
| College football | 3, at a 3 close | 4.7% | 6.8% |
| College football | 7, at a 3 close | 3.6% | 5.8% |
| College football | total 55, at 54.5 | 2.5% | 3.9% |
| College basketball | 1, at a 5.5 close | 3.5% | 3.0% |
| WNBA | 1, at a 4.5 close | 3.8% | 2.3% |
| NHL | total 5, at 5.5 | 17.0% | 23.3% |
| NHL | total 6, at 5.5 | 17.0% | 10.9% |
| NHL | favorite by 2, at 1.5 | 18.9% | 13.8% |
| NHL | favorite by 3, at 1.5 | 14.4% | 19.2% |
| MLB | total 8, at 8.5 | 9.2% | 7.6% |
| MLB | total 9, at 8.5 | 9.2% | 10.9% |
| MLB | home win by exactly 1, at −1.5 | 10.3% | 17.7% |
Alongside the retunes: a price the model cannot reach now says so instead of returning a number from the edge of the search; each new league moves a number only as far as its model was checked (the NHL puck line from ±1.5 toward the moneyline, NHL totals two goals, MLB totals 1.5 runs, soccer a goal either way); moves the model is less sure of are marked approximate; and the live list on the calculator page and the game pages now include NHL and MLB odd totals and the run line’s one-run game, from pregame markets only, because the model is a pregame model.
What the data could not settle
- The NFL’s far keys: a trim of 9, 17 to 19, 21, 24 and 28 was no better out of sample, so it was not applied.
- The NBA: a retuned entry with a wider curve and keys at 0, 1 and 2 was no better on 2023 to 2026. It gets re-run after the 2025–26 season.
- WNBA totals: the shipped width is a hedge, and 2026 points wider still. Refit after 2027.
- The NHL puck line: its keys drift by era, the archive stops in November 2022, and the current era’s totals of 6 and 6.5 have the thinnest evidence. The plan is a refit each season from vigged’s own closing archive.
- MLB totals: a different curve family (negative binomial) scored a little better in the tails. Optional, not applied.
- Soccer: quarter lines, totals other than 2.5, and MLS, Liga MX and the Champions League need data first; the one-goal win at a handicap of 1 waits for more seasons.
- History rows for the NBA, college basketball, the WNBA and the NHL need a source whose terms allow a published figure.
Data sources
vigged ran this backtest in October 2026 against the key-number code that prices the half point calculator and the middles page. Lines and scores come from public archives:
- nflverse: NFL lines and scores 1999–2026, with closing prices from 2006 (CC BY 4.0)
- cfbfastR-data, SportsDataverse’s republication of CollegeFootballData.com: college football lines and scores 2006–2025 (CC BY 4.0). Its 2006–19 lines were originally collected from Sportsbook Review, and rows filled from unlicensed exports are left out of the published figures
- the pinnacle.data R package: Pinnacle’s MLB 2016 closing lines (GPL-3), with scores from Retrosheet; MLB retail lines for 2014–21 and 2021–25 were used for research only
- Football-Data (football-data.co.uk): results and odds for 22 European divisions, of which the page shows the big five
- NBA, college basketball, WNBA and NHL: closing-line archives licensed for research use only, so their figures stay in the backtest
The credit each source asks for is under the table above. None of vigged’s own live odds feed was used. For what a half point is worth on your own numbers, go to the half point calculator; for how the no-vig price the model is fitted to is built, see de-vig methods compared.
Frequently asked questions
What is a half point backtest?
A check of the model that prices half points against what games did. Every closing line in a league’s history is run through the same model the half point calculator uses, which gives a chance for every final margin or total, and those chances are scored against the final score of that same game. The shares the model predicts (games landing on 3, on an odd total, on a one-run win) are then compared with the shares that happened.
How accurate is the half point calculator?
On every published row of the model-against-history table, the model’s figure sits inside the range history’s figure could take by chance alone, and a test in vigged’s code fails if a model change ever moves one outside. The NFL model runs a little low at 3 and 7, so a half point there may be worth 1 to 3 cents more than the calculator shows. The other leagues were retuned where history disagreed, then checked on seasons they were not fitted to.
Why do hockey and baseball totals land on odd numbers so often?
Because a tie is an even total and one goal or one run settles it. Every NHL game that goes to overtime or a shootout ends on an odd total, and a one-goal win in regulation is odd too. In baseball a total is odd exactly when the margin is odd, and the one-run game is the most common margin there is. A bell curve spreads its chance evenly over neighboring totals; the shipped models weight the odd ones up.
Why does the MLB run line depend on which team is the favorite?
Because the home team bats last. When it leads after the top of the ninth the game ends, and a walk-off ends it the moment the winning run scores, so home teams win by exactly one run far more often than away teams. In Pinnacle’s 2016 closing lines, 17.1% of home favorites at −1.5 won by exactly one run, against 12.9% of away favorites. The model carries separate keys for each, and the calculator asks which team you are on.
Which leagues changed after the backtest?
College football got key numbers out to 45 on spreads and 30 to 85 on totals. College basketball and the WNBA got a smaller one-point key, and the WNBA wider margins and totals. The NHL got a key for every goal, MLB odd-total keys and run-line keys that tell home from away, and soccer’s big five leagues a model of their own. The NFL and NBA models held up and were left alone.
Why are some leagues missing from the history table?
Licensing. The NFL, college football, MLB 2016 and soccer figures come from sources whose terms allow a published aggregate, with the credit each asks for. The NBA, college basketball, WNBA and NHL checks ran on closing-line archives licensed for research use only, as did MLB’s 2021 to 2025 retail lines, so those models were retuned the same way but their figures stay off the page.
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