Position Player WAR

Leaderboard

Position player WAR estimated from a hierarchical Bayesian model fit to per-game wOBA components (HR, 3B, 2B, 1B, BB, HBP). Partial pooling shrinks low-PA players toward the league average. Defense uses a Gaussian shrinkage model on seasonal DRS (framing runs for catchers). Intervals are 80% posterior credible intervals.

2026 Position Player WAR

≥25 PA

Uncertainty

80% credible intervals for the top 40 position players by posterior WAR.

Shrinkage

Each point is a player; the diagonal is y = x (no shrinkage). Low-PA players are pulled toward the league-average wOBA; high-PA players stay close to their observed value.

Component Breakdown

Stacked WAR contributions for the top 20 position players.

Diagnostics

The \(\sigma\) parameters measure batter-to-batter talent spread in each wOBA component. Values well above zero confirm genuine talent variation.

Batting model: 0 divergence(s), 0 max-treedepth hit(s).

Batting model key parameters
variable	mean	sd	q5	q95	rhat	ess_bulk
sigma_hr	0.395	0.029	0.348	0.442	1.0	795.4
sigma_3b	0.348	0.126	0.106	0.538	1.0	366.8
sigma_2b	0.036	0.026	0.003	0.085	1.0	594.4
sigma_1b	0.152	0.016	0.126	0.178	1.0	597.6
sigma_bb	0.316	0.019	0.285	0.348	1.0	586.5
sigma_hbp	0.559	0.047	0.484	0.640	1.0	675.4
phi_hr	43.701	19.173	18.797	79.754	1.0	973.3
phi_3b	30.180	17.806	7.960	63.038	1.0	1,057.9
phi_2b	47.039	18.204	22.436	78.863	1.0	1,120.5
phi_1b	115.042	24.566	78.979	158.586	1.0	1,031.6
phi_bb	79.492	22.917	47.575	121.327	1.0	955.0
phi_hbp	32.829	17.614	10.490	65.360	1.0	965.2

Fielding model: 0 divergence(s), 0 max-treedepth hit(s).

Fielding model key parameters
variable	mean	sd	q5	q95	rhat	ess_bulk
sigma_talent[1]	1.515	0.129	1.326	1.750	1.0	3,808.8
sigma_talent[2]	1.885	0.175	1.622	2.191	1.0	5,126.6
sigma_talent[3]	2.182	0.188	1.902	2.506	1.0	3,539.1
sigma_talent[4]	1.737	0.164	1.490	2.033	1.0	3,916.8
sigma_talent[5]	1.747	0.150	1.524	2.011	1.0	3,466.4
sigma_talent[6]	2.494	0.209	2.169	2.856	1.0	3,748.0
sigma_talent[7]	1.769	0.142	1.555	2.019	1.0	3,498.1
sigma_talent[8]	0.161	0.004	0.155	0.169	1.0	3,295.2
sigma_frame_talent	1.375	0.098	1.224	1.544	1.0	3,530.8

Validation

Total WAR (PA≥25): 268.4 across 502 players
462 players above replacement
Expected: ~250–325 for this season length

League wOBA check: computed = 0.3151, FanGraphs = 0.317 (diff = 0.0019) ✓