Cricket WAR

WAR stands for Wins Above Replacement. Originally developed in baseball, it quantifies how many more wins a player contributes relative to a "replacement-level" player — a hypothetical freely available, average substitute. In cricket, WAR can be adapted to estimate how many wins a player contributes over replacement based on run-scoring (batting) or run-prevention (bowling).

We construct both batting WAR and bowling WAR, and split all calculations by gender (men's and women's ODIs), acknowledging the substantial differences in scoring patterns and match contexts.

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1. Naive Batting WAR

The naive approach assumes all run-scoring opportunities are equal. It focuses purely on aggregate statistics like total runs, strike rate, and balls faced.

Formula: Let:

• $R_i$: total runs scored by player $i$
• $B_i$: balls faced by player $i$
• $SR_{rep}$: replacement-level strike rate (e.g., 20th percentile of observed strike rates)
• $R_{rep, i} = B_i \times \frac{SR_{rep}}{100}$: expected runs for replacement-level batter

Then:

$$ WAR_i^{naive} = \frac{R_i - R_{rep, i}}{10} $$

Here, we assume 10 runs = 1 win, a simplifying normalization.

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2. Context-Adjusted Batting WAR

Context matters: players bat in different overs, roles, and eras. To estimate performance fairly, we model expected runs per ball as a function of context using a Generalized Additive Model (GAM).

Features used:

• $t$: over number (continuous)
• $p$: inferred batting position (categorical)
• $y$: year (categorical)

Model:

$$ \mathbb{E}[r_{i,j}] = f_1(t_{i,j}) + f_2(p_{i,j}) + f_3(y_{i,j}) $$

Where:

• $r_{i,j}$: runs scored by player $i$ on ball $j$
• $f_1$: smooth spline on over
• $f_2, f_3$: factor effects for position and year

Replacement Adjustment: To define a replacement-level player, we scale down the predicted expected runs:

$$ R^{rep}_{i} = \alpha \cdot \sum_j \hat{r}_{i,j}, \text{ with } \alpha = 0.85 $$

Contextual WAR:

$$ WAR_i^{context} = \frac{\sum_j r_{i,j} - R^{rep}_{i}}{10} $$

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3. Bowling WAR

Bowling WAR focuses on run prevention. For each bowler, we compute their actual runs conceded and compare it to what a replacement-level bowler would have conceded in the same number of balls.

Steps:

1. Aggregate:

   • Balls bowled
   • Runs conceded

2. Compute:

   • Bowler’s runs per ball (RPB)
   • Replacement RPB: 80th percentile of all RPBs
   • Expected replacement runs: $\text{balls} \times \text{replacement RPB}$

Bowling WAR Formula:

$$ WAR_i^{bowling} = \frac{\text{replacement_runs}_i - \text{actual_runs}_i}{10} $$

As with batting, we assume 10 runs = 1 win. This is a simplification that normalizes scale.

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Summary

Metric	Context-Aware	Replacement Defined By	Model Used	Gender Split?
Naive Batting	No	Fixed strike rate percentile	None (formulaic)	Yes
Context Batting	Yes	GAM-predicted runs $\times \alpha$	GAM (spline + factors)	Yes
Bowling WAR	No	Percentile of runs-per-ball	None (formulaic)	Yes

Data

We use data from https://cricsheet.org/downloads/ and parse individual YAMLs to compute WAR metrics separately for men and women, ensuring fair comparisons across formats.