In Part 1 we covered how to evaluate challenges in terms of runs using the RE288 matrix. That answered the question "how many runs did this challenge add?" which is great for understanding the immediate offensive impact.
But runs don't tell the whole story. A 0.163 run gain in the 2nd inning of a 10-0 game is the same as a 0.163 run gain in the 9th inning of a tie game. If you're a team in the tie game, that challenge mattered a lot more. To capture that, we need Win Probability Added (WPA).
Win Expectancy
Before we can measure WPA we need to know the probability of winning at any point in the game. That's Win Expectancy.
RE288 gives us run expectancy from 288 states (3 outs x 8 base states x 12 counts). Win Expectancy expands on this by also accounting for:
- Inning (1st through 9th+)
- Half inning (top or bottom)
- Score differential (capped at +/- 10 runs)
So instead of 288 states we're now looking at 288 x 9 innings x 2 halves x 21 score differentials. That's 108,864 distinct game states, each with a win probability for each team.
How it's calculated
Same Markov chain approach from Part 1 (which has a cool interactive simulation you can use to get a better grip on how this works if part of this is going over your head), extended further. Here's the short version:
- Build a transition matrix from 2022-2025 Statcast data
- Simulate 500,000 half innings from each of the 288 starting states, recording the full run distribution (not just the average)
- Use those distributions to compute the probability of the each team winning from every possible game state across remaining innings
The run distribution part is key. RE288 only needs the average. Win Expectancy needs the full picture: what are the chances of scoring 0 runs, 1 run, 2, 3, etc. from this state? That lets you project how likely it is for the leading team's margin to hold up, or for the trailing team to come back.
From there it's a lookup between the two values that the game can end up at after the result of the challenge. The call either stands as is or the challenge brings us to a new state.
Win Probability Added (WPA)
Measuring the win-impact of a challenge
Win expectancy is looked up for both the umpire's call and the hypothetical overturned call. The WPA delta is the difference from the challenging team's perspective.1
Example: Batter challenges a called strike 3
Bottom of the 8th, tied game, runner on 2B, 1 out, 3-2 count, 1 challenge remaining. Called strike 3, and the batter challenges. If overturned, it's a walk instead of a strikeout.
Umpire's call
If overturned
Won
+8.6%
1 Score differences are capped at +/-10 runs.
Why this matters
These two scenarios have the exact same base-out-count state. Identical run expectancy gains from winning but wildly different the win probability impact:
Same Pitch, Different Stakes
Identical base-out-count state, completely different win impact
Both scenarios below have the exact same base-out-count state and therefore the exact same RE delta. But the win probability impact is 5x larger in the close game.
Tie game, Bottom 8th
Runner on 1B, 0 out, 1-1 count. Batter challenges a called strike.
Down 7, Top 3rd
Runner on 1B, 0 out, 1-1 count. Batter challenges a called strike.
Not the flashiest example, but an overturned pitch a tie game in the bottom of the 8th is a game changing event relative to the same overturn in a blowout.
Call Leverage Index
This brings us to Call Leverage Index (callLI), which measures the importance of a specific called pitch.
Traditional Leverage Index measures how much the outcome of a plate appearance matters to the game's result. It considers all possible outcomes: singles, doubles, home runs, strikeouts, groundouts, everything. callLI narrows the focus to just the two outcomes that matter when the batter doesn't swing: ball or strike.
Call Leverage Index (callLI)
Measuring the importance of a challenged pitch
callLI is the ratio of this pitch's win probability gap between a ball and a strike to the league-wide average gap across all game states. A callLI of 1.0 is average leverage. Higher means the umpire's call carries more weight on the outcome of the game.
Example: One call, two outcomes
Bases empty, 1 out, bottom of the 8th, tie game. The count is 2-1 and the batter doesn't swing. The umpire's call sends the game down one of two paths:
Called ball → 3-1
Called strike → 2-2
The higher the gap relative to the league average, the more leverage rides on the umpire's call.
The callLI changes on every pitch within a plate appearance. On a 0-0 count, the gap between a ball and a strike is relatively small. On a 3-2 count in a tie game in the 9th, the gap between a walk and a strikeout is massive. That's a high callLI pitch, and that's exactly when challenges carry the most win value.
A callLI of 1.0 means the pitch has average leverage. Above 1.0 means the call matters more than average. Below 1.0 means less. The highest leverage challenged play during Spring Training as of this post is this spot that got challenged by Austin Wynns that would have been worth over 30% WPA had it been overturned, nearly 20x the leverage of an average call. This challenge by Buddy Kennedy is the current leader, worth just over 20% and almost 15x the leverage of an average call.
Opportunity Cost
In Part 1 we covered how losing a challenge costs you future challenge opportunities. The depletion model calculates how many challenges a team expects to miss based on how many outs are left in the game and whether they went from 2 to 1 or from 1 to 0.
For RE, the cost is straightforward: missed opportunities x win rate x average RE per overturn. That average RE per overturn is a flat number (0.181 runs when I wrote that post), regardless of the game situation.
WPA opportunity cost uses the same depletion model but replaces the flat average with a score differential dependent value.
Average WPA per Overturn by Score Differential
Challenger's perspective · 2026 Spring Training data
Challenges in close games carry far more win probability weight. When the score is within 1-2 runs, a successful overturn is worth ~2% in win probability. In a blowout, it's almost nothing. This is the lookup table used to adjust WPA opportunity cost based on the current score.
Notice the slight asymmetry: trailing by 1 run (2.11%) is worth slightly more than leading by 1 (1.86%). The trailing team has more to gain from any individual pitch going their way.
A successful challenge is worth about 2% in win probability when the game is within a run or two. When a team is up or down by 7+, it's worth basically nothing. This makes intuitive sense: if you're already up 8-1, flipping a called strike to a ball isn't meaningfully changing your odds of winning.
The practical effect of this is that the cost of burning a challenge is much higher in close games and much lower in blowouts:
RE vs WPA Opportunity Cost
Same depletion math, different value per overturn
The number of expected challenges lost (the depletion model) is identical in both cases. The difference is what each lost challenge is worth. RE uses a flat average regardless of score. WPA adjusts for how close the game is, so losing a challenge in a blowout barely registers.
Close game
Bottom 7th, tied, 0 out, 1 challenge remaining
RE Opportunity Cost
WPA Opportunity Cost (score diff: 0)
Blowout
Bottom 7th, up by 7, 0 out, 1 challenge remaining
RE Opportunity Cost
WPA Opportunity Cost (score diff: +7)
The RE opportunity cost is 0.059 runs in both scenarios. The WPA opportunity cost is 7.6x higher in the close game than the blowout. This is why WPA opportunity cost is score differential dependent.
The RE opportunity cost is the same 0.058 runs in both cases because RE doesn't know what the score is. WPA sees the blowout and correctly says losing a future challenge barely matters when you're already cruising.
Both RE and WPA values for every challenge are available in the tables on the site. You'll find pWPA (potential WPA if overturned) and Opp Cost WPA in the Opportunity column group on the Challenges page, with the relevant one brought to the Net WPA field for each challenge.
Thanks for reading.
Nate
Originally posted at 8:56pm ET on 3/21/2026