What is Relief Probability of Added Stress? Definition, Formula, and Example
Relief Probability of Added Stress (RPAS) is a Statcast metric that quantifies the likelihood a relief pitcher enters a game and immediately faces a high-leverage, stressful situation.
What is Relief Probability of Added Stress?
Relief Probability of Added Stress (RPAS) is a Statcast metric that quantifies the likelihood a relief pitcher enters a game and immediately faces a high-leverage, stressful situation. Instead of evaluating what a pitcher does after he enters the game, RPAS evaluates the context of the entry itself. It measures the inherited runner situation, the score differential, the inning, and the quality of the opposing batters to determine the exact probability that the pitcher will be forced to pitch under maximum stress before he even throws his first warmup pitch in the game.
How it is Calculated / Measured
RPAS is calculated using historical Run Expectancy tables and Leverage Index data. The formula evaluates four primary variables at the moment the bullpen phone rings:
1. Inning and Outs: Later innings and fewer outs increase the stress probability.
2. Base-Out State: The number of inherited runners and their positions (e.g., bases loaded with one out yields a maximum stress score).
3. Score Differential (Run Differential): A tie game or a one-run lead amplifies the stress probability, while a five-run lead heavily deflates it.
4. Batter Quality: The projected wOBA of the batter due up next adjusts the stress probability based on the specific matchup.
The model outputs a percentage from 0% to 100%. A score of 75% indicates the pitcher entered under severe distress, likely inheriting multiple runners in a late inning with a slim lead.
Worked Example
On July 4, 2023, San Diego Padres reliever Robert Suarez entered a game against the Los Angeles Angels. He inherited a situation in the 8th inning with the Padres leading 3-2. There was one out, and runners were on second and third. Shohei Ohtani was due to hit.
The Run Expectancy for a runner on second and third with one out is approximately 1.20 runs. Because the Padres led by exactly one run, the tying run was already in scoring position. Facing Ohtani, who possessed a .420 wOBA at the time, spiked the context. The RPAS model calculated this entry at an 88% Relief Probability of Added Stress. Suarez was entering a firestorm. He struck out Ohtani and induced a groundout, but the entry itself was quantified as one of the most stressful bullpen entries of the week.
Why it Matters
RPAS matters because traditional bullpen evaluation is heavily skewed by the timing of entries. A pitcher with a 2.00 ERA might look elite, but if his RPAS sits at 25%, he is entering low-leverage blowouts with no runners on base. Conversely, a pitcher with a 3.50 ERA and an 80% RPAS is constantly putting out fires. Front offices use RPAS to identify undervalued middle relievers who handle extreme stress without seeing their ERA explode. Fantasy players and DFS modelers use RPAS to find holds and vulture saves, as managers strictly rely on high-RPAS relievers in tight games.
Limitations / Common Misconceptions
RPAS does not measure the pitcher's actual performance once he enters the game; it strictly measures the entry context. A pitcher can have a 90% RPAS and give up a grand slam, or have a 90% RPAS and strike out the side. It is a usage metric, not a performance metric. It is often confused with Leverage Index, but Leverage Index measures the swing in win probability per plate appearance during the game, while RPAS specifically quantifies the stress of the entry independent of the pitcher's subsequent results. RPAS also does not account for a pitcher's platoon splits; entering to face three right-handed hitters is less stressful for a right-handed specialist than the raw RPAS indicates.
Related Terms
In Legends Deck
In Legends Deck, RPAS heavily influences the Clutch and Relief ratings on pitcher cards. A reliever with a historically high RPAS receives a boost to his Clutch rating, allowing him to perform closer to his baseline stats in high-stress simulation scenarios. When the game engine simulates a late-inning rally, high-RPAS relievers are programmed to maintain their Stuff and Control ratings better than low-RPAS relievers, who suffer simulated penalties when inheriting runners.