The Statball Lab

Baseball is the hardest major sport to predict — the best team loses a third of its games, and the worst wins a third. The Model is Statball's attempt at the ceiling: an Elo system tuned over 212,003 games, layered with short-term form, rest, streaks, and park context, trained and tested the only honest way — walking forward through time, so every one of its 169,939 scored predictions was made about games strictly in its future. It calls 56.8%, against 53.9% for the home-team heuristic and 56.4% for Elo alone.

The number that matters more than accuracy is calibration: when the model says 60%, does the home team win 60% of the time? Across every probability bucket the average gap is 0.2 points — and the confidence tiers cash exactly as promised: its 70–100%-confidence picks hit 70.5% across 3,673 games. For scale on what's possible at all: a deliberately-cheating benchmark that knows every team's *final* season record and every starter reaches only 59.6%. Baseball's randomness sets the ceiling; the skill is in knowing which side of it you're on. Try the model on the model page, where the same ratings price the live slate.

Every forecast the model makes gets scored, which means every team gets a forecastability rating: how badly did this club scramble the model? The all-time champion of chaos is the 1950 Cubs — Brier score 0.258 over 153 games, the largest era-adjusted gap between how predictable they should have been and how predictable they were. Whatever that season was, the math couldn't hold onto it.

The mirror side: the most predictable team-season the model ever scored was the 2024 White Sox (0.193) — a club so true to its own signal that watching it was, statistically, optional.

Convert each decade's home-win rate into the Elo points it's worth and home field becomes a single line you can watch fall. It peaked at 37 points in the 1930s, when travel was brutal, parks were idiosyncratic, and umpires answered to the crowd. It's 23 points now. Standardized parks, charter flights, replay review — every modernization shaved a little off the most dependable edge in baseball.

This is also why the model treats home advantage as a parameter rather than a constant: a model that still prices home field at its dead-ball value would be systematically wrong in the modern game, and the calibration curve would show it.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games the Red Sox in the 1920s scored 1.11 runs per game below that baseline, over 1,542 games (4.04 actual vs 5.15 expected) — scoring the calendar and the venue can't explain.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 1,000,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.15. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character by the Red Sox.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games the Yankees in the 1930s scored 0.86 runs per game above that baseline, over 1,541 games (6.29 actual vs 5.43 expected) — scoring the calendar and the venue can't explain.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 1,000,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.19. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character by the Yankees.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games the Brooklyn Dodgers in the 1950s scored 0.85 runs per game above that baseline, over 1,239 games (5.23 actual vs 4.38 expected) — scoring the calendar and the venue can't explain.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 1,000,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.18. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character by the Brooklyn Dodgers.

Flip the perspective and the residual mining measures defense: what opponents managed against a club beyond every known factor. Here, opponents against the Phillies in the 1920s scored 0.75 runs per game above the fully-adjusted baseline across 1,534 games (5.95 actual vs 5.20 expected) — and that baseline already includes the ballpark, the era, and the franchise's own long-run defensive character.

The effect survives FDR control across 3,762 subgroups, a 1,000,000-shuffle permutation test at p<0.001, and carries a bootstrap 95% interval of ±0.19. Whatever was happening on that side of the ball, it wasn't the park and it wasn't the schedule.

Flip the perspective and the residual mining measures defense: what opponents managed against a club beyond every known factor. Here, opponents against the Cubs in the 2000s struck out 1.00 strikeouts per game above the fully-adjusted baseline across 1,618 games (7.93 actual vs 6.92 expected) — and that baseline already includes the ballpark, the era, and the franchise's own long-run defensive character.

The effect survives FDR control across 3,762 subgroups, a 300,000-shuffle permutation test at p<0.001, and carries a bootstrap 95% interval of ±0.14. Whatever was happening on that side of the ball, it wasn't the park and it wasn't the schedule.

The engine repeated its whole procedure with winning as the target instead of scoring — era, calendar, ballpark, home field, and the long-run quality of both clubs all absorbed before mining. What's left is pure over- or under-performance, and this pocket has the most of it: the Pirates in the 1900s won at a rate +14 points above that fully-informed baseline (0.634 against an expected 0.497, over 1,354 games). That's roughly 22 extra wins per 162 games.

It cleared Benjamini–Hochberg false-discovery control across 3,455 candidate subgroups and a 1,000,000-shuffle permutation test at p<0.001, with a bootstrap 95% interval of ±3 points. Sequencing, one-run margins, bullpen timing — something in how those games unfolded broke their way beyond anything the rosters explain.

The engine repeated its whole procedure with winning as the target instead of scoring — era, calendar, ballpark, home field, and the long-run quality of both clubs all absorbed before mining. What's left is pure over- or under-performance, and this pocket has the most of it: the Cardinals in the 1900s won at a rate −13 points below that fully-informed baseline (0.381 against an expected 0.512, over 1,347 games). That's roughly 21 missing wins per 162 games.

It cleared Benjamini–Hochberg false-discovery control across 3,455 candidate subgroups and a 1,000,000-shuffle permutation test at p<0.001, with a bootstrap 95% interval of ±3 points. Sequencing, one-run margins, bullpen timing — something in how those games unfolded broke against them beyond anything the rosters explain.

Flip the perspective and the residual mining measures defense: what opponents managed against a club beyond every known factor. Here, opponents against the Tigers in the 1940s struck out 0.88 strikeouts per game above the fully-adjusted baseline across 1,554 games (4.40 actual vs 3.52 expected) — and that baseline already includes the ballpark, the era, and the franchise's own long-run defensive character.

The effect survives FDR control across 3,762 subgroups, a 300,000-shuffle permutation test at p<0.001, and carries a bootstrap 95% interval of ±0.12. Whatever was happening on that side of the ball, it wasn't the park and it wasn't the schedule.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games at Memorial Stadium in the 1950s homered 0.40 home runs per game below that baseline, over 932 games (0.45 actual vs 0.86 expected) — a power surge (or outage) the era and the ballpark can't account for.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 300,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.04. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games the Reds in the 1970s walked 0.53 walks per game above that baseline, over 1,611 games (3.81 actual vs 3.29 expected) — plate discipline moving independently of era and identity.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 300,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.11. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character by the Reds.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games at Ebbets Field in the 1950s homered 0.32 home runs per game above that baseline, over 1,214 games (1.22 actual vs 0.89 expected) — a power surge (or outage) the era and the ballpark can't account for.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 300,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.06. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character.

Manager effects are famously hard to separate from roster effects — a skipper handed a juggernaut looks like a genius. This residual is built to resist that: the franchise's own long-run quality, the era, the parks, and every opponent's strength are subtracted before a tenure is measured. On what remains, the Orioles under Earl Weaver (1968–1986) ran +8 points of win percentage above the same club's baseline over 2,519 games — roughly 13 wins a season found somewhere between the lineup card and the bullpen phone.

The usual caveat applies with force: a tenure isn't a controlled experiment, and rosters change within it. But the size of the sample, the FDR correction across every tenure tested, and a permutation bar of one-in-a-thousand mean this isn't small-sample noise. Whatever it measures — tactics, culture, or a front office moving in lockstep — it moved with the manager.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games the St. Louis Browns in the 1910s committed 0.24 errors per game above that baseline, over 1,516 games (1.97 actual vs 1.73 expected) — glove work far off the franchise's own standard.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 300,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.08. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character by the St. Louis Browns.

The baseline model already knows the era, the month, day or night, home or road — and the long-run identity of the franchise, the ballpark, and the opponent. Mining what's left across 3,762 slices of history, this pocket stands out: games the White Sox in the 1930s in daylight committed 0.16 errors per game above that baseline, over 1,521 games (1.31 actual vs 1.15 expected) — glove work far off the franchise's own standard.

Statistical footing: Benjamini–Hochberg FDR under 1% across every candidate, a 300,000-shuffle permutation test at p<0.001, bootstrap 95% CI ±0.06. With multiple-comparison artifacts paid for, what remains is a real, sustained departure from character by the White Sox.

From every parsed line score, the engine flagged wins that required erasing a three-run deficit somewhere along the way — the games that were, at some inning boundary, statistically lost. In the 1990s, 11.6% of Athletics wins were that kind of win, against an era norm of 8.1% (773 wins). No other franchise-decade departs from its era as far upward.

A comeback share isn't the same thing as being good — it measures the *shape* of winning, not the amount. This pocket cleared FDR and a 200,000-shuffle permutation test at p<0.01, so the shape is real: these teams played from behind and got up off the canvas at a rate the era around them never matched.

Take every nine-inning game where the home team came to bat in the bottom of the ninth trailing, and just count. Down one run, the home side wins 12.9% of the time (17,999 games). Down two, 5.4%. Down three, 2.2%. The ninth-inning miracle every fan carries in memory is memorable precisely because the base rate is this brutal.

The stranger result is what didn't change. Split the century at 1960 and the curve barely moves — the largest gap at any deficit is 0.8 points, within noise on a permutation test. Livelier balls, relief specialists, the designated hitter, the pitch clock: none of it has moved the arithmetic of trailing in the ninth. It's as close to a physical constant as the sport has.

Everything about run-scoring has changed since 1901 — the ball, the mound, the bullpen, the strike zone. The value of the *first* run hasn't. The team that scores it wins 66.9% of decided games, and the decade-by-decade line is nearly flat: the entire spread across twelve decades is 4.0 points. Dead-ball, live-ball, steroids, pitch clock — the first punch has been worth the same the whole time.

Which is a genuinely odd kind of stability. In a 10-run era the first run should matter less than in a 3-run era, and at the margins it does; but the compensating forces (more scoring means more chances to answer, and also more first-scorer runs that come in crooked-number innings) cancel almost perfectly. The engine went looking for eras that broke the rule and found none worth reporting.

Read enough line scores and the ninth inning starts to look strange. In 49.2% of nine-inning games the bottom half simply doesn't happen — the home team already leads, so the rulebook deletes it. And when it *is* played, it's played under selection: only games where the home side trails or is tied get one, which means the batting team is disproportionately behind and desperate.

The result is the only half-inning whose statistics describe a different game. Home eighth innings average 0.52 runs; played home ninths average 0.43, and 49.2% of all home wins end them early with a walk-off. Every 'ninth inning scoring' stat you've ever seen carries this truncation inside it — the inning isn't quieter or louder than the others so much as it's incomplete by design.

Most of this site mines what happened *in* games. This scan mines whether the games happened at all. For every franchise, the engine compared the days and times of its home schedule against what the rest of the league was doing in exactly the same seasons, then ranked every cell by how many games are simply missing. The winner isn't close: the Cubs played 959 night home games where the league's behavior predicts 3920 — a deficit of about 2,961 games, 47 standard deviations from random.

The engine doesn't know why; it only counts. History does know: Pennsylvania's blue laws banned Sunday baseball until 1934, which is why Philadelphia's and Pittsburgh's Sunday columns are craters — and the same scan's night-game version finds Wrigley Field, which didn't install lights until 1988, as the sport's great missing-nights anomaly. Legislatures and light towers, recovered from nothing but a century of datestamps.

Describe every team-season since 1901 by seven numbers — runs scored and allowed, home runs, strikeouts, walks, errors, winning percentage — each as a distance from that same season's league average. Then let an isolation forest, an algorithm built to find points that don't belong, rank all of them by how hard they are to isolate as normal. The winner: the 1927 Yankees — home runs +2.9σ versus that season's league, strikeouts +2.4σ versus that season's league, walks +2.3σ versus that season's league.

The list matters as much as the winner: the rest of the top five are the 2025 Rockies, the 1976 Reds, the 1962 Mets, the 1991 Tigers. The algorithm can't tell a dynasty from a disaster and has never heard of any of these clubs. It only sees geometry, and these are the five profiles sitting farthest outside the shape of their own eras.

Describe every qualifying batter-season since 1914 by six numbers — singles, doubles, triples, home runs, walks and strikeouts, each per plate appearance and each measured against that same season's league — and let an isolation forest rank which profiles are hardest to pass off as a normal hitter. The most anomalous season ever played belongs to Babe Ruth, 1921: home runs +6.5σ from that season's hitters, walks +4.1σ from that season's hitters, singles -3.3σ from that season's hitters.

The rest of the top five: Babe Ruth (1919), Babe Ruth (1920), Babe Ruth (1923), Babe Ruth (1922). The algorithm knows no names and no narratives — it sees 16,450 dots in six dimensions and reports the ones floating farthest from the cloud. That the dots it picks tend to have famous stories attached is the whole point: extremity this measurable usually forces its way into history one way or another.

Teams usually change slowly — a trade here, an aging arm there. To find the exceptions, the engine measured every franchise's statistical identity each season (seven stats, each relative to that year's league) and computed the distance between every pair of back-to-back seasons: 2,606 transitions. The largest jump in history belongs to the Philadelphia Athletics, 1914 to 1915 — 8.4 standard deviations of accumulated change.

The biggest movers: runs allowed moved +4.4σ, errors moved +4.4σ, winning percentage moved -4.2σ. The engine has no idea what happened in that offseason. The history books do — and recovering documented upheavals blind, from geometry alone, is precisely the validation that makes the rest of this page worth believing.

A dynasty is usually defined against the league. This one is defined against the mirror: with each franchise's own hundred-year character subtracted from the baseline, a positive season means a club outplayed *itself*. The longest such run in history is the Orioles, 1968 through 1985 — 18 consecutive seasons above their own identity, averaging +8 points of win percentage the whole way. Sustained overachievement is far harder than a hot season; residuals want to return to zero, and for 18 years these teams refused.

The record has a shadow twin. The longest run *below* self belongs to the Pirates, 1993 to 2012: 20 straight seasons of a franchise underperforming its own history. One list is a monument to front offices compounding advantages; the other is what institutional decay looks like when you subtract every excuse.

When a team gets better, when do fans actually show up? The engine paired every franchise's change in winning percentage with its change in home attendance — the same season and one season later — across 2,244 transitions. The answer: improvement moves the gate immediately (r = 0.46), with the lagged effect nearly absent (r = 0.06).

Word of a winner travels faster than the offseason: walk-up sales and bandwagons move the gate in real time, and by the next spring the effect has mostly already happened.

Nearly every stat in baseball drifts with the decades, so nearly every pair looks correlated. Correlate the year-over-year *changes* instead and the fakes disappear — and the engine deliberately excludes mechanically-linked pairs so only non-obvious couplings can surface. The strongest survivor: home runs and walks move together, r = 0.47 across a century of season-to-season swings.

That held against a 100,000-shuffle permutation null with false-discovery control across every pair tested. When one of these lurches in a given winter, the other lurches with it — a season-level rhythm connecting two numbers the box score files on opposite pages.

Baseball history is usually periodized by narrative — dead ball, live ball, expansion. The engine periodizes it by arithmetic: scan each league-wide series for the year where the seasons after look least like the seasons before, and rank every break it finds. The sharpest anywhere is strikeouts at 1918: 3.77 per game before, 2.87 after — a discontinuity that towers over a century of ordinary drift.

The rest of the top five: strikeouts in 1918 (t=13); attendance in 1919 (t=12); game length in 1934 (t=11); home runs in 1921 (t=10); errors in 1947 (t=10). Some of these years have famous stories attached; others never get talked about. The algorithm can't tell the difference — it only knows where the sport stopped being one thing and became another.

Raw standings overstate how unequal baseball is — a 154-game season generates a lot of luck-spread even between identical teams. Strip the binomial noise out and what's left is the true spread of team talent. That spread peaked around 1907 and has been shrinking for most of a century, hitting its floor near 1989. Between the early century and the modern game, the talent gap compressed by 34%.

In concrete terms: a two-sigma-good team once separated itself from a two-sigma-bad one by around 60 wins per 162 games; today that same gulf is about 40. This is Stephen Jay Gould's old conjecture about the disappearance of the .400 hitter — that as a sport professionalizes, everyone crowds toward the ceiling and the extremes vanish — showing up in the standings, measured blind by an engine that has never read him.

Every fan base claims to be loyal; the turnstiles keep score. For each franchise the engine regressed year-over-year attendance changes on winning-percentage changes — the slope is what a season of improvement is actually worth at the gate. The steepest in baseball belongs to the Braves: about 4,046 extra fans per game for every ten points of win percentage (r = 0.63 across 51 season-pairs). When the team is good, the park fills; when it slips, the crowd evaporates on cue.

The other end of the ranking is its own compliment. Washington Senators attendance moves just +1,075 fans per ten points — the crowd shows up, or doesn't, almost independent of the standings. Call the steep slopes bandwagons or call them accountability; either way, the elasticity of a city's baseball habit is a stable, measurable trait of the franchise.

The 1998 ad campaign claimed the long ball sells tickets. That's an estimable equation: does a change in the league's home-run rate this year correlate with the change in attendance *next* year, once both series are detrended and the strike and pandemic seasons are excluded? Measured across a century, the answer for home runs is r = -0.04 (p = 0.65), which is to say: no. Runs and strikeouts fare no better.

The offense of one season, it turns out, tells you almost nothing about the turnstiles of the next once the shared eras are removed. What moves attendance is winning — see the panel finding above — not the league-wide flavor of the runs.

Forget the level of a stat for a moment and watch its *jitter*. In the early decades, the strikeout rate lurched an average of 5.8% per year — new parks, new balls, new rules, chaos. In the most recent third of history the same series moves 2.6% a year. That's a 55% collapse in volatility: the loudest series in the sport quietly became one of its steadiest.

Professionalization has a signature, and this is it — standardized equipment, standardized schedules, institutionalized everything. The engine ranks every series by how much it calmed down; the chart shows the biggest tamings. The pitch clock cut game time, but it's the century of creeping standardization that made the sport statistically boring year to year — in the best possible sense.

'He's a different hitter in the big spot' is the most repeated scouting claim in the sport, and it's testable: if clutch hitting is a skill, the hitters who raise their on-base game late-and-close this season should do it again next season. The engine built the test from 11,094 qualifying batter-seasons of play-by-play — every plate appearance from the 7th inning on with the score within a run, since 1914 — and paired 6,361 consecutive seasons. The answer: r = 0.05 (permutation p = 0.000). A real but faint signal — clutch skill exists at roughly a tenth the strength of ordinary hitting skill.

For scale, a hitter's *overall* on-base ability repeats year to year at r = 0.66 in this same panel — ability is stable. The situational premium on top of it is what fails to repeat. Sixty years of sabermetrics said this about modern samples; the archive says it about everyone back to the dead-ball era. The clutch reputation is mostly the memory of a small sample, retold until it sounds like a skill.

Here's a clean way to split skill from luck with nothing but next season: if a slice of a team's record reflects ability, it repeats; if it's noise, it doesn't. Overall winning percentage repeats at r = 0.59 across 2,606 consecutive season-pairs — teams are what they are. Run the same test on seven components of the record, each measured relative to the team's own overall level, and a spectrum appears. The most repeatable component edge is blowout edge (r = 0.27).

At the far end sits the noise. Components that fail to repeat at all: september edge (r=0.02, p=0.40), extra-inning edge (r=0.03, p=0.09). The weakest of everything tested is the september edge — r = 0.02 across 2,518 pairs. A club that thrived in those spots this season is a coin flip in them next season. The gradient runs the way a skill-to-luck spectrum should: the more a component depends on sustained quality, the more it repeats; the more it depends on a single bounce, the more it belongs to chance.

A team's runs scored and allowed pin down what its record *should* be — the engine fit the exponent itself rather than trusting folklore, landing at γ = 1.84. Measured against that, the biggest single-season defiance in history is the 2021 Mariners: a 0.556 winning percentage on run numbers worth 0.468, which is 14 wins conjured from nowhere — sequencing, one-run margins, and timing, compressed into one season.

And here's the verdict the formula implies: beating Pythagoras does repeat a little (r = 0.07) — some clubs really do bank close wins year after year, bullpens and benches being real things. The luckiest-ever list above is exactly that — a list of lightning strikes, not a list of skills.

Momentum is baseball's favorite ghost story: the team that 'can't lose right now.' The clean test takes each season's actual win/loss sequence and asks whether it clusters more than a random shuffle of the same wins and losses — identical record, order randomized. Run on 2,692 team-seasons, the answer aggregates to z = -6.8: streaks genuinely cluster beyond chance.

In tangible terms, the average season's longest winning streak runs 6.94 games, against 6.74 for the shuffled version of the same season. Small per season — a fifth of a game — but across thousands of seasons it is unambiguous: some slice of what looks like a hot team really is a team playing above its own baseline for a stretch. The residual families elsewhere on this page hint at the same thing.

Everyone believes in the schedule: the tired club off a 3 a.m. arrival, the fresh one waiting at home. Measured across every game since 1901 — with team quality, era, and home field already stripped out of the residual — the fresh team's edge is a flat line. A two-day-or-better rest advantage runs -0.2 win points versus baseline; being on the wrong side of it runs +0.5. End to end the curve spans -0.7 points, and a 200,000-shuffle permutation test calls that p = 0.88. Noise.

Nulls like this are why the engine writes up whatever it measures. Fatigue is real in the body; it just doesn't survive into the standings, even at the largest mismatches the schedule ever produces. The tired-legs storyline gets told on broadcasts nightly, and the archive has been voting against it for over a century.

Every manager who has ever reached for a bullpen phone believes in the platoon edge. The play-by-play archive prices it precisely: hitters reach base 26 points of OBP more often against opposite-handed pitching, measured over more than 14 million plate appearances since 1914.

And it has moved: about 31 points in the early decades, 23 in the modern game (trend p = 0.0000). The modern bullpen — one-out lefties, three-batter minimums, matchup chess — has been eroding the very edge it's built to exploit.