Pitcher WAR

Leaderboard

Pitcher WAR estimated from a hierarchical Bayesian model fit to per-start FIP components (K+IFFB, BB+HBP−IBB, HR). Partial pooling shrinks low-inning pitchers toward the league average. Intervals are 80% posterior credible intervals.

2026 Pitcher WAR

Starters, ≥10 IP

Uncertainty

80% credible intervals for the top 30 starters by posterior WAR.

Reliever Leaderboard

Reliever WAR uses the same hierarchical FIP model as starters, fit separately on relief appearances. WAR is scaled by each pitcher’s season-average game-entering leverage index (gmLI): an inning pitched in high-leverage situations counts for more. Replacement level is lgFIP + 1.0 (vs. + 1.5 for starters). Intervals are 80% posterior credible intervals.

2026 Reliever WAR

Relief pitchers, ≥5 IP

Reliever Uncertainty

80% credible intervals for the top relievers by posterior WAR.

Shrinkage

Each point is a pitcher; the diagonal is y = x (no shrinkage). Good pitchers (low raw FIP, left side) are pulled upward toward the league mean; high-FIP pitchers are pulled downward. Low-IP pitchers move the most because the model trusts their small sample least.

Validation

Credible interval width should fall with innings pitched: a 200-IP ace should have a tighter estimate than a 30-IP spot starter. A flat or upward trend would suggest the model is not learning from the data.

Total WAR (IP≥10): 205.9 across 204 pitchers ⚠ outside expected range
292 pitchers above replacement
Expected: ~75–100 for this season length

Diagnostics

The \(\sigma\) parameters measure how much pitcher-to-pitcher spread the model found in each FIP component. Values well above zero confirm genuine talent variation; a spike near zero would mean the model sees pitchers as essentially interchangeable for that component.

Starters

Sampler: 0 divergence(s), 0 max-treedepth hit(s). R-hat < 1.01 and ESS > 400 on all key parameters indicates reliable estimates.

variable	mean	sd	q5	q95	rhat	ess_bulk
sigma_k	0.216	0.019	0.186	0.247	1.0	681.4
sigma_bb	0.220	0.025	0.180	0.263	1.0	857.1
sigma_hr	0.217	0.045	0.143	0.289	1.0	653.7
phi_k	128.635	26.050	90.243	177.988	1.0	832.5
phi_bb	75.288	22.547	43.803	118.704	1.0	810.8
phi_hr	28.504	15.184	10.664	56.890	1.0	810.0

Relievers

Sampler: 0 divergence(s), 0 max-treedepth hit(s). R-hat < 1.01 and ESS > 400 on all key parameters indicates reliable estimates.

variable	mean	sd	q5	q95	rhat	ess_bulk
sigma_k	0.216	0.025	0.176	0.259	1.0	704.8
sigma_bb	0.227	0.034	0.168	0.281	1.0	714.1
sigma_hr	0.120	0.076	0.013	0.252	1.0	485.6
phi_k	109.304	25.255	72.776	154.024	1.0	858.8
phi_bb	61.312	21.104	32.829	101.429	1.0	1,018.8
phi_hr	32.931	17.320	11.926	64.425	1.0	938.5