Empirical Bayes, reliability
Signal and noise: when a rate starts to mean something
How many plate appearances before a strikeout rate is half talent? The league's own spread answers it, and tells us how hard to shrink every number toward the mean.
Computed on request from the record book (Oct 13, 2026) and 720 finals in the game log.
The finding
Every rate on a stat line is part talent and part luck, and the league's own spread tells us the mix. A hitter's strikeout rate is half signal after about 44 plate appearances, his walk rate after 149. His batting average on balls in play needs about 392 balls in play — more than the 364 a qualified hitter puts in play in a season. So a typical qualified hitter's BABIP this year is only about 48% talent; the rest should be expected to wash out.
For pitchers the gap is starker: BABIP allowed needs about 537 balls in play and home-run rate about 900 batters faced, while strikeout and walk rates settle within a couple of hundred. Last season is the check. Players over the bar in both years repeat their strikeout rate (hitters) at r = 0.81 and their home-run rate (pitchers) at only r = 0.00; across all 10 rates, the order of the year-to-year correlations matches the order the stabilisation points predict with a rank correlation of 0.98.
Hitter K%: half signal at
44
plate appearances
Hitter BABIP: half signal at
392
balls in play
Typical BABIP that is talent
48%
at 364 balls in play
Pitcher BABIP: half signal at
537
balls in play
Trials until a rate is half talent
The stabilisation point M for each rate, on a log scale, with a 95% bootstrap interval. Diamonds mark commonly cited MLB figures for comparison. Further right means noisier.
Does the prediction hold up? Last season to this
Observed year-to-year correlation for players over the bar in both seasons, with a 95% interval, against the correlation the stabilisation point predicts for those same players (diamond).
Shrinking BABIP toward the league
Every qualified hitter's BABIP as recorded (open circle) and after adding 392 balls in play of league-average BABIP (arrow) — the best estimate of the talent underneath.
| Rate | Players | League | Talent SD | M | 95% | MLB | Typical season | Signal share |
|---|---|---|---|---|---|---|---|---|
| Hitter · Strikeout rate | 214 | 19.3% | 5.9% | 44 | 37–54 | 60 | 537 PA | 92% |
| Hitter · Walk rate | 214 | 9.4% | 2.4% | 149 | 117–213 | 120 | 537 PA | 78% |
| Hitter · Home-run rate | 214 | 2.4% | 1.6% | 92 | 71–122 | 170 | 537 PA | 85% |
| Hitter · OBP | 214 | .348 | .032 | 219 | 154–375 | 460 | 530 PA | 71% |
| Hitter · BABIP | 214 | .318 | .024 | 392 | 223–1,152 | 820 | 364 balls in play | 48% |
| Hitter · Batting average | 214 | .270 | .029 | 238 | 164–392 | 910 | 463 AB | 66% |
| Pitcher · Strikeout rate | 243 | 19.6% | 3.7% | 115 | 86–167 | 70 | 663 batters faced | 85% |
| Pitcher · Walk rate | 243 | 9.3% | 3.3% | 76 | 56–104 | 170 | 663 batters faced | 90% |
| Pitcher · Home-run rate | 243 | 2.4% | 0.5% | 900 | 494–3,569 | — | 663 batters faced | 42% |
| Pitcher · BABIP | 243 | .313 | .020 | 537 | 306–1,987 | 2,000 | 460 balls in play | 46% |
Method
Everyone with at least 30 trials this season is included. The observed spread of a rate across players is talent plus binomial sampling noise, and the noise part is known, so the talent variance is what remains (a method-of-moments estimate):
σ²(talent) = [Σ nᵢ(xᵢ − p̄)² − (k − 1)·p̄(1 − p̄)] ÷ [N − Σnᵢ² ÷ N]
M = p̄(1 − p̄) ÷ σ²(talent) · reliability(n) = n ÷ (n + M) · shrunk = (successes + M·p̄) ÷ (n + M)
M is the number of trials at which a player's observed rate is exactly half talent, half noise, and it is also the weight of league average to add when estimating his true rate — the beta-binomial empirical Bayes estimate. Intervals resample players 600 times. The predicted year-to-year correlation is the average of √(reliability₂₀₂₅ × reliability₂₀₂₆) over the players compared.
The method assumes each player's talent is fixed through the season and that outcomes are independent trials; injuries, slumps and role changes break both. Pitcher BABIP and home-run rate carry the defence and the park behind the pitcher, which no KBO data separates. The MLB figures come from a split-half method on far larger samples and are there for orientation, not as a benchmark. With about two hundred players a season, the upper ends of the noisiest intervals are effectively unbounded.