Bullpen Usage Prediction: Reliever Sequencing in MLB
Prediction models can project starting pitchers with reasonable confidence. The rotation is published days in advance, and a starter's expected workload follows a roughly predictable distribution around 5 to 6 innings. But once the starter exits, the game enters a domain of compounding uncertainty. Which reliever comes in? For how long? Against which batters? In what leverage context? These questions represent one of the most difficult forecasting challenges in baseball, because the answers depend on a cascade of decisions that are themselves contingent on game events that have not yet occurred.
Bullpen usage prediction is not simply about guessing who pitches the eighth inning. It is about modeling a sequential decision process where each managerial choice constrains the next, where reliever availability shifts daily, and where the game state at the moment of each decision can radically alter the deployment strategy. Getting this right matters enormously for run expectancy, because the difference between a team's best reliever and its worst can easily span a full run of ERA, and in high-leverage situations that gap is amplified further.
Why Bullpen Prediction Is Uniquely Difficult
Starting pitcher prediction is comparatively straightforward because the decision space is narrow. A team announces its starter, the starter pitches until he is removed, and the primary question is simply how deep he goes. Bullpen prediction inverts this structure. The decision space is wide, with six to eight available relievers on any given day, and the selection among them depends on variables that unfold in real time: the score, the inning, the handedness of upcoming batters, the number of baserunners, and the specific leverage index of the moment.
This creates a branching problem. If the starter exits after five innings with a two-run lead, the bullpen deployment will look entirely different than if the same starter exits after four innings trailing by three. Since the model cannot know in advance which scenario will materialize, it must either simulate the game forward through many possible paths or estimate a probability-weighted average over likely bullpen configurations. Both approaches introduce substantial uncertainty, and that uncertainty propagates into the final game prediction.
The second layer of difficulty is availability. Unlike starting pitchers, who operate on regular rest schedules, relievers accumulate fatigue on irregular and often unpredictable timelines. A closer who pitched two consecutive days may be unavailable on the third day, but "unavailable" is not always binary. He might be reserved for save situations only, or limited to one inning instead of two, or available but at diminished effectiveness. Modeling this spectrum of partial availability is a significant challenge that most public prediction systems handle crudely, if at all.
Manager Tendencies and Role Hierarchies
Despite the theoretical flexibility of bullpen deployment, most managers operate within identifiable patterns. The closer pitches the ninth inning of save situations. The primary setup man handles the eighth. A middle-relief bridge connects the starter to the late-inning arms. These role hierarchies are not rigid, they bend under pressure, but they provide a baseline prior that prediction models can exploit.
Manager-specific tendencies are a legitimate modeling feature. Some managers use their closers almost exclusively in save situations, while others deploy them in the highest-leverage moment regardless of inning. Some managers have a short leash with starters, pulling them at the first sign of trouble, while others let starters work through jams. These behavioral signatures are measurable from historical data and can be encoded as parameters in a bullpen deployment model.
The practical approach is to build a decision tree or probabilistic model that, given a game state (inning, score differential, runners on base, outs), predicts the probability that each available reliever enters the game. The inputs include the manager's historical tendencies in similar situations, the reliever's role designation, handedness matchup considerations, and the fatigue state of each available arm. The output is not a single deterministic prediction of "Reliever X pitches the seventh" but a probability distribution over possible reliever-inning assignments.
Leverage-Based Deployment
The concept of leverage index, which measures how much a given plate appearance affects the team's win probability, is central to understanding bullpen sequencing. In a tie game in the eighth inning with runners in scoring position, the leverage index is extremely high. In a blowout in the sixth inning, it is negligible. Managers, whether consciously or intuitively, tend to deploy their best relievers in the highest-leverage situations and their weakest arms in low-leverage mop-up duty.
For prediction models, this means that projecting bullpen effectiveness requires not just knowing which relievers are available but estimating the leverage distribution they will face. If a model projects a close game, it should expect the team's best relievers to see the majority of high-leverage innings. If it projects a blowout, the lower-tier arms will absorb most of the work. This creates a feedback loop between the game projection and the bullpen projection: the expected closeness of the game influences which relievers pitch, which influences the expected run scoring, which feeds back into the expected closeness of the game.
Breaking this circularity typically requires simulation. The model simulates the game inning by inning, making bullpen deployment decisions at each branch point based on the current simulated game state, then aggregating the results across thousands of simulations to produce a final probability distribution. This is computationally expensive but captures the conditional dependency structure that simpler approaches miss.
The Cascade Effect
One of the most important, and most undermodeled, phenomena in bullpen prediction is the cascade effect. When a starting pitcher has a short outing, it does not simply mean that the bullpen absorbs more innings that day. It means the bullpen absorbs more innings with a particular configuration of fatigue states, which then affects availability the next day, and the day after that. A single short start can create ripple effects that persist for three to five days through the bullpen rotation.
Consider a practical example. If a team's starter exits after three innings, the long reliever pitches innings four and five, the middle-relief arms cover six and seven, and the high-leverage arms close out eight and nine. That is five innings of bullpen work instead of the typical three. The long reliever, who threw 40 pitches, is now unavailable tomorrow. The middle relievers, who each threw 20 to 25 pitches, are available but at reduced capacity. The closer and setup man, having pitched on consecutive days, may need the next day off.
Now the following day's game starts with a depleted bullpen, which means a different set of relievers will be deployed in roles they do not normally fill. The team's fifth-best reliever might be pitching the eighth inning of a close game. This degradation in bullpen quality is a systematic, predictable effect that models can capture by tracking fatigue accumulation across the entire relief corps, not just individual arms.
Fatigue Modeling for Relievers
Reliever fatigue does not operate on the same timescale as starter fatigue. Starters deteriorate within a game as pitch count climbs, showing measurable velocity loss and command degradation after 80 to 90 pitches. Relievers, who rarely exceed 25 to 30 pitches in an outing, show fatigue effects primarily across appearances rather than within them. The key variables are days since last appearance, pitches thrown in recent appearances (typically a rolling three-day and seven-day window), and the number of high-stress outings in the recent past.
Research consistently shows that relievers are measurably less effective on zero days' rest compared to one or more days' rest. ERA, walk rate, and hard-hit rate all increase when a reliever pitches on consecutive days, with the effect growing larger on three or more consecutive days. Pitch velocity tends to drop by 0.5 to 1.0 mph on back-to-back appearances, which may not sound significant but corresponds to a meaningful reduction in swing-and-miss rate and a corresponding increase in contact quality.
For prediction models, fatigue enters as a modifier on each reliever's projected performance. A reliever with a 3.00 ERA baseline might be projected at 3.40 on one day's rest and 3.80 on two consecutive days of work. These adjustments, combined with availability probabilities, feed into the game simulation framework that generates the final run expectancy for each team's bullpen innings.
Handedness Matchups and the Three-Batter Minimum
Before the three-batter minimum rule was implemented, managers could bring in a left-handed specialist to face a single left-handed batter, then immediately replace him with a right-hander. This created a rich tactical layer in bullpen sequencing, where the handedness matchup tree could involve three or four relievers in a single inning. The LOOGY (Left-handed One Out GuY) was a distinct roster construction choice that models needed to account for.
The three-batter minimum fundamentally changed bullpen sequencing by eliminating single-batter matchup relievers. Now, every reliever must face at least three batters or finish the inning, which means that handedness considerations extend across the entire upcoming batting order rather than focusing on a single hitter. A manager deciding whether to bring in a left-handed reliever must now consider not just the current batter but the next two as well, potentially exposing a lefty reliever to right-handed hitters he would never have faced under the old rules.
For prediction models, this rule change simplified the decision tree in one sense (fewer mid-inning pitching changes) but complicated the batter-sequence evaluation. The relevant question shifted from "which reliever is best for this one batter" to "which reliever is best for this sequence of three or more batters," which requires projecting platoon-adjusted performance across multiple matchups simultaneously.
Bullpen Composition and Game Simulation
The composition of a team's bullpen, the mix of roles, handedness, pitch arsenals, and quality tiers, is itself a significant variable in game-level prediction. A team with three elite late-inning arms and four marginal relievers produces a bimodal bullpen performance distribution: outstanding in close games where the top arms pitch, mediocre in games where the lower tier is exposed. A team with seven roughly equivalent middle-tier relievers produces a more stable but less explosive bullpen profile.
Game simulation models that account for bullpen composition can capture this effect by assigning each reliever to simulated innings based on the deployment logic described above. The simulation does not assume a generic "bullpen ERA" for the team but instead selects specific relievers for specific innings based on the simulated game state, applying each reliever's individual projection to the batters he faces. This produces a more realistic variance structure in the simulated outcomes.
The alternative approach, using a team-level "bullpen ERA" or aggregate reliever projection, is computationally simpler but loses important information. It cannot distinguish between a team whose bullpen is elite for three innings and terrible for two versus a team whose bullpen is average for five innings. Both might have the same aggregate ERA, but they produce very different outcome distributions depending on how many bullpen innings are needed.
Estimating Effective Bullpen Quality
The final modeling challenge is projecting the effective quality of the bullpen innings that will actually be pitched, as opposed to the theoretical quality of the full bullpen roster. Effective bullpen quality is a function of which relievers are available, what game states they are deployed in, and how many innings they are asked to cover. It is a conditional quantity that changes daily.
A useful heuristic is to weight each reliever's projected contribution by his expected probability of appearing and his expected leverage exposure. The team's closer might have a 2.50 ERA projection, but if he is only available for one inning in save situations, his contribution is weighted differently than a middle reliever with a 4.00 ERA who might pitch two or three innings in varied leverage contexts. The middle reliever, despite being worse on a rate basis, might have a larger absolute impact on the game's expected run total simply because he absorbs more innings.
This weighted-contribution approach produces a daily "effective bullpen ERA" that fluctuates based on availability, fatigue, and expected game state. It is a more informative input for game-level prediction than a static season-long bullpen ERA, and it is where the real predictive edge lies for models that invest in bullpen modeling infrastructure.