Glossary

The change in expected runs for the challenging team due to the result of the challenge. Gains are calculated using the RE288 matrix, which maps every base/out/count state to the average runs expected to score in the rest of the inning. The delta is the difference between the RE of the umpire's call and the RE of the overturned call. Losses are calculated by determining the opportunity cost of the missed challenge, which takes the expected number of challenges the team will not be able to make through the rest of the game due to the miss, the league average challenge win rate, and the average RE per overturn into account.

The change in the challenging team's win probability due to the challenge. Unlike RE, WPA accounts for the full game context: inning, score, base/out/count state, and which team is batting. The opportunity cost calculation is identical to the RE opp cost, but instead of taking into account the average RE per successful challenge it looks at the average WPA gain per successful challenge at the current score differential.

The leverage index of the current pitch that only considers outcomes where the umpire is making a decision on a ball or strike call. Unlike traditional Leverage Index, which is calculated at the start of a plate appearance and includes all possible outcomes like balls in play, call LI only considers the two outcomes possible on a taken pitch. Call Leverage Index is calculated by finding the WPA distance "swing" between the hypothetical strike call and the hypothetical ball call, then dividing that number by the average swing of all calls. Therefore, a call LI of 2.0 is twice as important, relative to the average call, as a call that has a call LI of 1.0.

The minimum confidence that a call will be overturned needed to justify using a challenge. Calculated as avg_cost / (avg_cost + swing), where swing is the RE difference between a ball and a strike in the current state, and avg_cost is the average run expectancy cost of losing a challenge. Lower values mean the challenge is easier to justify. Originally published by Tom Tango.

The challenge breakeven threshold adjusted for the opportunity cost of losing a challenge. Accounts for how many challenges remain, how much game is left, and the expected value of future challenge opportunities.

The model predicted probability that a given pitch would be challenged, based on pitch proximity to the zone, count, game state, and pitch characteristics. Generated by a logistic regression model trained on historical ABS challenge data.

The sum of xChall% across all of a player's, team's, or umpire's called pitches. Basically answers the question: given the pitches this person saw, how many challenges would you expect them to make (or face, for umpires)? A player with an xChall of 4.2 saw enough borderline pitches that you'd expect about 4.2 challenges from them.

Actual challenges minus expected challenges (xChall). Positive means more challenges than expected, negative means fewer. A batter with a COE of +2.0 challenged two more times than the model predicted.

The model predicted probability that a given pitch would be called a strike by an average umpire. Trained on 358,000+ called pitches from the 2025 regular season using a logistic regression model.

The accuracy an average umpire would have on this umpire's exact pitch mix. An umpire who sees a lot of borderline pitches will have a lower xAcc% than one who gets a bunch of no doubt calls right down the middle.

Actual accuracy minus expected accuracy (xAcc%). This is the difficulty adjusted accuracy metric. An umpire with a raw accuracy of 93% and an xAcc% of 92% has an AOE of +1%, meaning they're performing one percentage point better than an average umpire would on the same set of pitches.