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.

For an in depth explanation of this concept, read here.

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.

For an in depth explanation of this concept, read here.

The expected run expectancy cost of consuming a challenge at this point in the game. Computed via a depletion model that estimates the value of future challenge opportunities the team would forgo, weighted by league average challenge win rate and average RE per overturn.

Win probability version of Opp Cost RE. Same depletion model logic, but the per overturn payoff is the league average WPA gain conditioned on 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 as the average call.

The breakeven run value 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 sum of a player's batter CDQ and catcher CDQ. For players who only hit or only catch, CDQ equals their single role value. Used on the homepage leaderboard as the default sort because it captures judgment across every challengeable pitch, not just attempted challenges.

Measures how well a batter makes challenge decisions on called strikes. Rewards correct decisions and penalizes incorrect ones, weighted by how obvious or difficult each decision was (using oxChall%). Scope: every called strike where the batter's team had >= 1 challenge remaining.

Same framework as bCDQ but for the catcher on called balls. Uses cxChall = dxChall% × 0.96, the catcher's share of defensive challenges (catchers initiate ~96% of pitcher/catcher challenges in practice). Scope: every called ball where the catcher's team had >= 1 challenge remaining, excluding pitches the pitcher challenged.

The denominator of bCDQ. Counts every called strike the batter saw under ABS eligible conditions: the batter's team had at least one challenge available, the pitch had a computable xChall%, and the play wasn't a position player pitching edge case.

The denominator of cCDQ. Counts every called ball the catcher saw under ABS eligible conditions, excluding pitches the pitcher challenged.

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. Separate models exist for offense (oxChall%, called strikes) and defense (dxChall%, called balls).

The sum of xChall% across all of a player's, team's, or umpire's called pitches.

Actual challenges minus expected challenges (xChall). Positive means the player or team challenges more often than the model predicts for their pitch mix, negative means more conservative.

Per pitch accuracy on called strikes and called balls.

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 probability is a function of pitch location, count, and a few pitch characteristics.

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. The difficulty adjusted accuracy metric. An umpire with raw accuracy of 93% and 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.