“I identify the constraint that will force the market to move before the market realizes it has to. In baseball, that constraint is variance structure. The market prices the mean. The distribution is where the edge lives.”
The same blind spot across baseball, private credit, and real estate: markets price the mean while constraints reshape the distribution.
The Problem This Solves
Every major evaluation framework in use today — in baseball, in capital markets, in real estate — shares a foundational assumption that is rarely stated explicitly because it has rarely needed to be examined: that the mean of an asset's output distribution is a sufficient proxy for its value.
WAR prices the mean. Yield prices the mean. IRR prices the mean.
That assumption is not wrong. It is incomplete in a specific and measurable way. And the gap between what mean-focused frameworks capture and what the full distribution implies is not random noise — it is systematic, directional, and exploitable by anyone with a framework that prices the distribution rather than the point estimate.
This brief presents the empirical evidence for that claim in baseball, maps the structural parallel to private credit and real estate, and describes the analytical architecture built to price what conventional frameworks miss.
What Conventional Evaluation Frameworks Miss
Standard player evaluation models asset value as a function of mean run production above replacement. That framework is correct for the variables it measures. The variables it does not measure are the structural constraints that determine what a player's production distribution does to a team's aggregate win probability — before the outcomes form around it.
A constraint is not a risk factor. A risk factor is a variable that influences outcomes within a functioning system. A constraint is a variable that determines whether the system produces the expected distribution of outcomes at all — and when it binds, the output changes regime rather than adjusting at the margin.
The blind spot is not in the individual player. It is at the roster level. A single volatile player does not obviously drag a team's performance. Eleven consistent players do not obviously outperform. The effect is only visible in the aggregate — which means it cannot be arbitraged by evaluating players individually. The market evaluates players individually. That is where the edge lives.
The same mechanism operates in private credit. A single callable, illiquid loan does not obviously stress a fund's NAV. A portfolio of them, all callable in the same stress window, produces synthetic liquidity failure that the mean-focused yield metric never flagged. In real estate, two parcels with identical projected IRR can have development margins that differ by 15–20 percentage points based on site geometry alone — the Perimeter Tax. The IRR treats them as equivalent. The constraint map does not.
Three domains. One mechanism. The market prices the mean. The distribution is where the edge lives.
The Constraint Intelligence System
Layer 1 — The WAVE Evidence: Run-Scoring Variance and Pythagorean Outperformance
A team-season-level empirical study of 150 MLB team-seasons from 2021 through 2025, testing the relationship between run-scoring variance and wins above Pythagorean expectation.
The payoff function in baseball is discrete: any positive run margin produces a win. A team scoring four runs every night wins more close games than a team alternating zero and eight. The variance of run distribution interacts with the win threshold in a way that consistently rewards stability — independently of mean production.
Core Findings
Run-scoring standard deviation (RS_std) correlates with wins above Pythagorean expectation at r = −0.330 (p < 0.001, n = 150 team-seasons). The slope estimate of −4.9 implies each one-unit increase in RS_std is associated with approximately five fewer wins above Pythagorean expectation.
Teams in the most stable RS_std quartile outperform Pythagorean expectation by +0.78 wins per season. Teams in the most volatile quartile underperform by −2.07 wins. The passive gap — variance structure alone, no deliberate optimization — is 2.84 wins per season.
Individual run-scoring variance is structurally persistent year over year (r = +0.273, p < 0.001, n = 924 player-seasons). Variance is not random. It is a measurable, repeatable player characteristic. That characteristic is not explicitly priced in WAR — WAR may reflect some consequences of stability after outcomes occur, but it does not price variance contribution as a forward roster constraint.
Correlation
r = −0.330 (p < 0.001, n = 150)
Slope estimate
−4.9 wins per RS_std unit
Stable quartile outperformance
+0.78 wins above Pythagorean
Volatile quartile underperformance
−2.07 wins below Pythagorean
Passive variance gap
2.84 wins per season
Variance persistence
r = +0.273 (p < 0.001, n = 924)
The Portfolio-Theory Analogy
The portfolio-theory analogy is familiar: correlation and variance matter because the payoff function is not linear. The baseball application is the original move. The Pythagorean function is the payoff function. RS_std is portfolio volatility. Pythagorean outperformance is the Sharpe ratio analog. Same mathematics, independently documented in a domain where the data is granular enough to test it cleanly at the team-season level.
Layer 2 — The VAW System: Individual Player Variance Contribution
The Variance Added Wins (VAW) system formalizes the WAVE calibration at the individual player level. It prices three components WAR does not explicitly price as forward roster-variance constraints across 251 qualifying players, calibrated to the 2.84-win empirical gap, and deployed as a production Python system with walk-forward backtest infrastructure.
COMPONENT 1: PRODUCTION FLOOR Standard wRAA conversion (wOBAScale = 1.157, runs per win = 10.5) extended with Statcast FRV defensive runs, converted onto a common run-based scale (207/251 players), mechanical floor quality (blasts_swing and squared_up_swing carry r > 0.90 year-over-year persistence), positional scarcity, and age trajectory. Bayesian shrinkage for small samples.
COMPONENT 2: VARIANCE STABILITY PREMIUM Calibrated from the 2.84-win WAVE gap. Individual contribution priced via three independent park-neutral signals — monthly approach consistency from batted-ball data using contact-quality and approach-stability fields rather than outcome-only production (40%), CV-based detrended xwOBA (35%), DAS shadow zone decision consistency (25%). Removes the z-score amplification artifact that caused prior implementations to misclassify elite consistent players as volatile.
COMPONENT 3: CONFIGURATION VALUE Career hi/lo leverage wOBA delta (97 players, 2022-2025 actual splits). DVC residual complementarity — 7,761 player pairs from the full Statcast universe. Defensive bridge bonus for the conditional interaction between offensive volatility and elite defensive coverage.
P-TTL TERRAIN OVERLAY Separates durable annual value from live terrain. Monthly contact trajectory is negatively predictive of next-season outcomes (r = −0.139, p = 0.025, confirmed in walk-forward backtest) — hot recent form mean-reverts. The terrain layer is asymmetric by design: declining contact quality compresses Time-to-Leak and burns into the TTL index. Positive recent form generates a mean-reversion risk flag only. No upside wins boost — the backtest does not support it.
Model Audit
| Item | Status |
|---|---|
| WAVE sample | 150 MLB team-seasons, 2021-2025 |
| Backtest window | 2018-2024 walk-forward; 2020 shown for transparency, excluded from headline primary-sample claims due to shortened season |
| Primary validation seasons | 6 full seasons (2018, 2019, 2021, 2022, 2023, 2024) |
| Year-by-year accuracy | 2018: 54% · 2019: 71% · 2020: 69%* · 2021: 50% · 2022: 79% · 2023: 62% · 2024: 77% |
| *2020 note | 60-game season; shown separately |
| Top outcome bucket accuracy | 63% — 1.88x eligible-sample base rate |
| Player universe | 251 qualifying hitters |
| FRV coverage | 207 / 251 players |
| Career leverage splits | 97 / 251 players (actual); 154 shadow zone proxy |
| DVC pairs | 7,761 player pairs |
| Monthly terrain | 2022-2026 batted-ball, downside asymmetric only |
| Case A lift | 61% top outcome accuracy, 1.82x base rate |
| Case D result | 0.61x base rate — correctly negative |
Layer 5 — The Timestamp Archive
Published, timestamped work across baseball variance, private credit liquidity, real estate geometry, and energy-permission constraints — each made before broad public recognition. The purpose is not to claim perfection. It is to show the same constraint-identification process applied consistently across domains before the consensus formed around the mechanism.
The full archive is at hscai.org. Every call includes its mechanism and invalidation conditions. The misses are visible alongside the hits.
Layer 3 — The Finance Parallels: Same Mechanism, Different Domain
PRIVATE CREDIT: HIDDEN DURATION SHOCK The $3T+ private credit market prices yield. It does not price the distribution of redemption calls under parallel stress. Interval fund and BDC structures create synthetic liquidity — an accessibility assumption that holds in normal conditions and gaps under stress.
From the Hidden Duration Shock in Private Credit (December 2025): A portfolio with stable NAV and strong yield carries a hidden duration shock when underlying exposures are callable, illiquid, and correlated under stress. The yield metric does not flag it. The stress-scenario duration metric does. Published before several public private-credit stress events made the same structural mechanism broadly visible — the mechanism was in the constraint map before it was in the consensus.
REAL ESTATE: THE PERIMETER TAX From the Perimeter Tax framework and Finley Farms retroactive feasibility study (Zenodo, 2025): Two parcels. Identical projected IRR. One compact, one jagged. Development margins differ by 15-20 percentage points. The constraint is encoded in the perimeter-to-area ratio of the site geometry before a single unit is built. The 1994 Gilbert, Arizona Finley Farms case study documented a stormwater basin placement — a geometry decision — that stranded developable lots and destroyed margin the pro forma never surfaced.
| Domain | Threshold | Distributed signal | What the mean metric misses |
|---|---|---|---|
| Baseball | Win/loss per game | RS_std, OVS, xwOBA CV | 2.84-win passive WAVE gap |
| Private credit | Redemption gate | Duration under parallel stress | Hidden duration shock |
| Real estate | Development margin | Perimeter-to-area ratio | 15-20pt margin destruction |
| Portfolio theory | Sharpe ratio | Return correlation | Correlated vol erodes risk-adj return |
What This Is Not
Not a replacement for scouting
VAW prices what Statcast data can measure. It cannot measure makeup, coachability, injury recovery trajectory, or the hundred contextual variables a scout observes in person. The framework is an additional signal layer, not a replacement for the human evaluation that has always been the core of player acquisition.
Not a return forecast
The framework does not predict WAR, wOBA, or contract value. It identifies structural constraints that determine whether a player's value distribution will behave as WAR-based projections expect — and when it will not.
Not a black box
Every component has a named mechanism, a published calibration source, and an explicit invalidation condition. The system documentation, formula specification, backtest audit, and data coverage flags are all visible. Every output is traceable.
Not position-independent
VAW is designed for hitters. The same structural logic applies to pitchers — RA_std drives Pythagorean outperformance at r = +0.227 in the same dataset. Pitcher VAW is the next extension of the framework.
The Proposition
The framework already exists. The empirical evidence already exists. The walk-forward validation already exists. The cross-domain documentation already exists.
What does not yet exist is the institutional context in which this capability is applied to a specific roster, a specific acquisition decision, or a specific allocator's mandate — and a specific decision-maker's process for turning constraint intelligence into action.
The architecture is the same across all three domains. The domain is different. The edge is the same.
That is what this brief is an invitation to discuss.
Related Research
- [1] Hampson, A.C. II (2026). Run-Scoring Variance and Pythagorean Outperformance: Evidence for the Winning Advantage of Variance Efficiency (WAVE). Zenodo
- [2] Hampson, A.C. II (2026). Variance Added Wins (VAW): A Player Evaluation System Pricing Stability, Leverage Configuration, and Defensive Bridge Value. Zenodo
- [3] Hampson, A.C. II (2025). The Hidden Duration Shock in Private Credit. Hampson Strategies. hscai.org
- [4] Hampson, A.C. II (2025). The Perimeter Tax: Site Geometry as Systematic Development Margin Risk. Zenodo / Hampson Strategies
Hampson Strategies — hscai.org
Andrew C. Hampson II — @drampson11 — Lafayette, Louisiana
May 2026
Not investment advice. All views represent independent analysis. Research prototype — architecture and validation logic available on request.
Layer 4 — Positioning Translation
Three Live Examples
Example 1
Nico Hoerner — 2B
Constraint
Headline WAR/wOBA evaluation prices Hoerner primarily through mean offensive production. VAW identifies him as the most consistent hitter in the 251-player dataset — OVS 97th percentile, highest monthly approach consistency score, career leverage lift positive, elite 2B defensive profile (FRV top-10), 1,271 PA over four seasons at full PA confidence.
Transmission
Approach consistency → reduced run-scoring variance contribution → team RS_std compression → wins above Pythagorean that accumulate in games where the mean hitter either produces or does not. These wins are not explicitly captured by WAR as a forward roster-variance constraint. They are the target of WAVE.
Acquisition Window
CV already low and persistent across four seasons. Stability demonstrated, not forming. WAR rank unchanged. The window is when stability is persistent and demonstrated but not yet surfaced by the headline metrics that typically drive valuation — not when stability is forming. Hoerner's consistency has been measurable for three seasons. The headline metrics that typically drive valuation have not repriced it. That lag is structural.
Confirmation Signals
- xwOBA CV below 0.040 across three consecutive seasons
- Monthly approach consistency below 0.050
- Shadow zone DAS percentile above 80th
- OVS above 90th percentile
Invalidation
- xwOBA CV rising above 0.060
- Approach consistency degrading in monthly batted-ball data
- Shadow zone discipline deteriorating under pressure splits
VAW Implication
Hoerner-type players — mid-WAR, top-quartile VAW, Long TTL, elite defensive position — are systematically underpriced relative to their distribution contribution. The acquisition signal is demonstrated multi-season stability with a WAR rank that has not moved. That lag is the window.
Example 2
Rafael Devers — 3B
Constraint
Devers carries 4.17 VAW — real, production-based value. The P-TTL overlay flags Short TTL (0.53 index), Case E (Patch Failure Watch). The constraint is not production — it is the rate at which that production leaks under structural pressure: elevated K/whiff exposure, high recent variance in contact quality, platoon risk emerging in monthly batted-ball data.
Transmission
High burn rate → TTL compression → value leaks faster without structural support (consistent lineup protection, favorable platoon deployment, stable role definition). The production is real. The durability of that production at current value is not guaranteed without configuration architecture around it.
Acquisition Window
This is not an avoid signal. It is a configuration signal. The question changes: not "is Devers worth acquiring?" but "what roster structure is required to sustain his VAW at its current level?" Without that structure the Short TTL implies accelerated value degradation. With it, the production floor holds. WAR does not surface this distinction. The P-TTL overlay exists specifically to surface it.
Confirmation Signals
- Monthly contact CV rising
- Pull rate std increasing across consecutive months
- K% rising under high-leverage splits
- BIP hard-hit rate declining in batted-ball data
Invalidation
- Monthly contact stabilizing across two consecutive months
- K% returning to career baseline under pressure splits
- xwOBA CV declining toward historical floor
VAW Implication
The Short TTL flag surfaces a risk already in the data — identifiable before it shows up in outcomes. This is the direct baseball analog of the private credit hidden duration shock: visible in the constraint map before it appears in the headline metric.
Example 3
Freddie Freeman — 1B
Constraint
Freeman's VAW is 4.36 — correctly pricing his production floor and four seasons of demonstrated stability. His R-VAW is 4.91. The +0.55 divergence is the largest positive context gap in the top-15. The backtest confirmed that positive monthly contact pulse does not add durable annual value — hot form mean-reverts. Freeman's R-VAW divergence is not a monthly form story. It is a configuration and connectivity story.
Transmission
Long TTL (1.70) + strong DVC residual connectivity + zero downside terrain compression → more of Freeman's durable career VAW is transmitting into team-level stability than his baseline alone predicts. The roster context is allowing the existing value to express fully. The monthly terrain is not compressing it. That is the precise read the backtest supports: no deterioration, strong configuration amplification, Long TTL. The monthly layer confirms the absence of drag — it does not add upside.
Acquisition Window
Freeman himself is not the acquisition target — he is correctly valued. The implication is roster construction. Players who share Freeman's DVC residual complementarity profile amplify the value of the configuration he already anchors. The acquisition target is the player whose variance offsets his, not Freeman himself. The divergence tells you the configuration is working. The DVC map tells you what extends it.
Confirmation Signals
- R-VAW divergence sustained across two consecutive monthly updates
- Monthly contact CV stable below 0.045
- TTL index remaining Long
- DVC connectivity scores stable or rising
Invalidation
- R-VAW divergence collapsing toward zero
- Monthly contact CV rising above 0.065
- TTL index declining toward Medium
- DVC pair scores degrading
VAW Implication
The configuration amplifier case is the most actionable for a front office already holding a high-VAW anchor player. The question is not whether to acquire Freeman — it is which players on the available market extend the variance-offset structure he already creates. The DVC universe of 7,761 pairs answers that directly.
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