Box Score Stat Relationships — Correlation, Redundancy & a Rebalanced Scoring System
My league is Head-to-Head, 5x5 Categories — five batting categories (R, HR, RBI, SB, OPS) and five pitching (K/9, QS, SVHD, ERA, WHIP), each won or lost independently every week. The premise of any categories league is that the ten categories measure ten different things. They don’t. This analysis quantifies how much the categories overlap, shows the two sides are badly imbalanced in their internal redundancy, and then proposes three ways to fix it — finishing by replaying the actual 2026 season under each proposal to see whose record would change.
Methodology & Data Sources
- Data Sources:
- MLB game logs 2023–2026 (
*_mlb_stats_daily/2026_mlb_stats_boxscore) — the single source for every category value across all four seasons, so the player population stays consistent and isn’t biased toward currently-rostered players. 2026_espn_stats_daily— daily per-player fantasy data (rosters, lineup slots, ownership context) used only to overlay fantasy-team holdings and market valuation onto the archetypes.2026_espn_schedule_matchup&2026_espn_scoreboard_matchup— the authoritative matchup-period day map and actual head-to-head pairings/winners, used to re-score the season.
- MLB game logs 2023–2026 (
- Methodology:
- Season totals are aggregated per player per year; rate stats (OPS, ERA, WHIP, K/9) are recomputed from summed components, never averaged-of-averages. Minimum samples: 50 AB for batters, 20 IP for pitchers.
- Redundancy is measured two ways: pairwise Pearson/Spearman correlation among the categories, and the participation ratio of each side’s category correlation matrix — an eigenvalue-based count of how many effectively independent axes the categories represent.
- Archetypes come from PCA + k-means on rate/shape features (hand-rolled with numpy/scipy; no scikit-learn).
- Re-scoring rebuilds each team’s weekly category totals from active-lineup player-days only (bench and IL excluded), then decides each category head-to-head. The pipeline is validated by checking that recomputed current-scoring matchup winners match ESPN’s actual results.
Finding 1 — The categories are not independent
Batting category correlation (Pearson, pooled 2023–2026):
| R | HR | RBI | SB | OPS | |
|---|---|---|---|---|---|
| R | 1.00 | 0.86 | 0.92 | 0.54 | 0.59 |
| HR | 0.86 | 1.00 | 0.92 | 0.31 | 0.64 |
| RBI | 0.92 | 0.92 | 1.00 | 0.39 | 0.61 |
| SB | 0.54 | 0.31 | 0.39 | 1.00 | 0.22 |
| OPS | 0.59 | 0.64 | 0.61 | 0.22 | 1.00 |
R, HR and RBI are effectively one category (pairwise r of 0.86–0.92, stable year over year). Any high-volume bat in a good lineup wins all three together. SB is the lone batting differentiator — it’s the least correlated with everything else, so it has to be targeted deliberately or it’s simply lost.
Pitching category correlation:
| K/9 | QS | SVHD | ERA | WHIP | |
|---|---|---|---|---|---|
| K/9 | 1.00 | -0.03 | 0.37 | -0.27 | -0.26 |
| QS | -0.03 | 1.00 | -0.39 | -0.11 | -0.19 |
| SVHD | 0.37 | -0.39 | 1.00 | -0.35 | -0.28 |
| ERA | -0.27 | -0.11 | -0.35 | 1.00 | 0.79 |
| WHIP | -0.26 | -0.19 | -0.28 | 0.79 | 1.00 |
Only ERA↔WHIP are redundant (0.79); K/9, QS and SVHD are three genuinely independent levers.
Effective dimensionality: the batting set carries only ~1.9 of 5 independent axes; pitching carries ~3.3. Pitching is the far more multi-dimensional side — the two halves of the scoring system are lopsided.
Finding 2 — Player archetypes & a market inefficiency
Clustering on rate/shape profiles produced clean archetypes:
- Batters: Power · Speed-Contact · Contact · Free-Swinger
- Pitchers: Reliever (SV/HD) · Starter · Swingman (volatile ratios)
Overlaying ownership exposes an edge: Speed-Contact bats are only ~28% owned versus ~52% for Power bats — yet SB is the scarce batting differentiator. The market systematically underprices exactly the category that is hardest to win.
Finding 3 — Three ways to rebalance the scoring
The goal: give batting and pitching an equal amount of internal redundancy (the two sides needn’t relate to each other — only be internally symmetric). Candidate categories were restricted to realistic, trackable stats.
| Structure | Batting cats | Bat axes | Pitching cats | Pit axes | Balance gap |
|---|---|---|---|---|---|
| Current | R, HR, RBI, SB, OPS | 1.88 | K/9, QS, SVHD, ERA, WHIP | 3.30 | 1.41 |
| A — Mirror | R, HR, RBI, SB, OPS (unchanged) | 1.88 | ERA, WHIP, BB/9, K/BB, H/9 | 2.13 | 0.25 |
| B — Max independence | SB, SLG, AVG, BB, SO | 2.70 | K, WHIP, W, K/BB, H/9 | 2.70 | 0.00 |
| C — 6x6 add-one | R, HR, RBI, SB, OPS, AVG | 2.13 | K/9, QS, SVHD, ERA, WHIP, H/9 | 3.07 | 0.95 |
- Scenario A (mirror, most adoptable): leave batting alone and swap the pitching side so it carries its own three-category tied bundle (ERA / WHIP / H/9), mirroring R/HR/RBI. Smallest change, biggest gap reduction.
- Scenario B (from scratch, broadest): the most-independent five categories per side, equalized. Hitting stats are intrinsically more correlated, so batting is the binding constraint (~2.7 axes); pitching is capped to match. Spreads value across many more player types. A more familiar variant that keeps HR — HR, SB, OBP, AVG, SO — is equally independent.
- Scenario C (keep 5x5, add one each → 6x6): add the most independent batting category (AVG) and the most redundant pitching category (H/9, which forms an ERA/WHIP/H/9 tied trio). Nothing is removed, but one addition can only partly close the gap because every hitting stat shares the same offensive halo.
Finding 4 — How the 2026 season would actually change
The 11 completed, fully-covered matchup periods (through mid-June) were replayed under each structure. Pipeline validation: recomputed current-scoring matchup winners match ESPN’s actual result on 52/55 decided matchups (95%) — the small gap is daily-lineup reconstruction noise.
Matchup outcomes that flip vs current scoring: A 14/55 · B 13/55 · C 5/55. Scenario C is the least disruptive (its appeal); A and B reshuffle the standings most.
Matchup record (W-L-T) and delta vs current, by team:
| Team | Current | A — Mirror (Δ) | B — Independent (Δ) | C — 6x6 (Δ) |
|---|---|---|---|---|
| This Schlitt is Bazzanas | 7-4-0 | 6-4-1 (-1/0/+1) | 8-3-0 (+1/-1/0) | 7-3-1 (0/-1/+1) |
| Midnight Muncy’s | 6-5-0 | 6-4-1 (0/-1/+1) | 7-3-1 (+1/-2/+1) | 6-4-1 (0/-1/+1) |
| Skubal Snacks | 6-3-2 | 8-3-0 (+2/0/-2) | 7-4-0 (+1/+1/-2) | 7-3-1 (+1/0/-1) |
| Dingers Only | 6-5-0 | 6-4-1 (0/-1/+1) | 7-4-0 (+1/-1/0) | 6-5-0 (0/0/0) |
| Datalickmyballs | 5-5-1 | 7-3-1 (+2/-2/0) | 5-6-0 (0/+1/-1) | 4-6-1 (-1/+1/0) |
| Rock and Aroldis | 5-6-0 | 4-7-0 (-1/+1/0) | 2-9-0 (-3/+3/0) | 5-5-1 (0/-1/+1) |
| Welcome to the JUNGle | 5-4-2 | 4-5-2 (-1/+1/0) | 5-6-0 (0/+2/-2) | 5-4-2 (0/0/0) |
| Shohei Me the Money | 5-6-0 | 3-8-0 (-2/+2/0) | 5-6-0 (0/0/0) | 5-6-0 (0/0/0) |
| All Rise | 4-6-1 | 1-8-2 (-3/+2/+1) | 4-6-1 (0/0/0) | 4-7-0 (0/+1/-1) |
| Big Dumpers | 2-7-2 | 6-5-0 (+4/-2/-2) | 4-7-0 (+2/0/-2) | 2-8-1 (0/+1/-1) |
The pattern matches the theory: teams leaning on the redundant power bundle (e.g. All Rise, Shohei Me the Money) lose ground when it’s de-emphasized, while teams built on the now-distinct categories — ratios, saves/holds, speed, on-base — gain (e.g. Big Dumpers picks up +4 matchup wins under Scenario A once its pitching ratios count as separate categories).
Note: the league actually counts each category as its own win/loss/tie, so the category-level deltas are larger and Scenario C’s 12-category totals inflate accordingly; the matchup-level view above is the cleanest cross-scenario comparison.
Next Steps / TODO
- Re-run at season’s end to confirm the redundancy structure and the win/loss deltas hold over a full 18-period schedule rather than the first 11.
- Pressure-test Scenario B’s “max breadth” claim by re-clustering archetypes under each proposed category set — does the desirable-player pool actually widen as predicted?
- Draft a one-page league proposal recommending Scenario A or the HR-keeping variant of Scenario B, with the per-team impact table, for an offseason rules vote.
Last Updated: 2026-06-20