Environmental Modeling for MLB Games: Weather as a Prediction Input
Every baseball game is played inside an atmosphere, and that atmosphere is never neutral. Wind direction, temperature, humidity, and altitude all exert measurable forces on the flight of a baseball, the grip of a pitcher, and the trajectory of outcomes. Sophisticated prediction models treat environmental conditions not as footnotes but as structured input features with nonlinear, park-specific, and interaction-dependent effects on run scoring.
The challenge for modelers is not simply acknowledging that weather matters. It is quantifying exactly how much it matters, under what combinations, and in which ballparks. A 15 mph wind blowing out at Wrigley Field changes the run environment in ways that differ from the same wind at Fenway Park, because the park geometry interacts with the wind vector differently. Environmental modeling is, at its core, the science of encoding those interactions into prediction systems.
Why Weather Effects Are Nonlinear
The most common mistake in environmental modeling is treating weather variables as linear inputs. A naive approach might assume that a 10 mph wind doubles the effect of a 5 mph wind. In reality, aerodynamic drag on a baseball follows a quadratic relationship with velocity, meaning the interaction between bat-exit velocity and wind speed produces effects that scale nonlinearly. A 5 mph tailwind might add 3 feet of carry to a fly ball. A 10 mph tailwind might add 8 feet, not 6. A 20 mph tailwind might add 22 feet. The relationship curves upward because wind assistance compounds with the ball's own velocity through the air.
This nonlinearity extends to every environmental variable. Temperature does not increase home run probability in a straight line. Humidity does not reduce drag by a constant fraction per percentage point. Models that use raw weather values as linear features leave significant predictive information on the table. Polynomial terms, spline functions, or tree-based models that naturally capture nonlinearity all outperform linear weather adjustments in backtesting.
Wind Direction and Speed: The Dominant Variable
Among all environmental factors, wind direction relative to the batter's line of drive has the largest effect on run scoring. The relevant measurement is not simply "wind speed" but the decomposition of the wind vector into components parallel and perpendicular to the most common batted-ball trajectories.
A direct headwind of 15 mph or more can suppress home run rates by 25 to 40 percent relative to calm conditions. Fly balls that would clear the fence on a still day die at the warning track. This compression of the offense shifts the run environment meaningfully, particularly for teams that rely on power-dependent scoring. Tailwinds produce the opposite effect, turning warning-track fly balls into home runs and inflating run totals. But the magnitude is asymmetric: the suppression effect of headwinds tends to be larger than the amplification effect of tailwinds at the same speed, because headwinds also affect the trajectory of balls that were already well-struck.
Crosswinds introduce a subtler effect. A strong left-to-right crosswind at a park with a short right-field porch creates an asymmetric advantage for left-handed pull hitters, whose fly balls curve toward the shorter fence. Models that incorporate batter handedness distributions alongside wind direction can capture this interaction, though the signal is smaller than the headwind/tailwind axis.
Temperature and Ball Flight Physics
The physics of temperature's effect on baseball carry is well-established. Warmer air is less dense, which reduces aerodynamic drag on the baseball. The commonly cited approximation is that every 10 degrees Fahrenheit of temperature increase adds roughly 4 feet of carry to a fly ball hit at typical major-league exit velocity. This translates to measurably higher home run rates and, consequently, higher run totals in warm conditions.
For prediction models, temperature enters as a modifier on batted-ball outcome probabilities. A fly ball with an exit velocity of 100 mph and a launch angle of 28 degrees has a certain probability of clearing a 370-foot fence. That probability shifts as temperature changes the expected carry distance. Models that run batted-ball simulations can apply temperature-adjusted drag coefficients directly. Models that work at a higher level of abstraction typically use temperature as a multiplicative adjustment to park-specific run expectancy baselines.
The effect is not limited to home runs. Line drives carry farther in warm air, potentially turning catchable fly outs into doubles. Ground balls are unaffected by temperature, which means the run-environment shift is concentrated in the fly-ball component of the offense. Teams that generate a high fly-ball rate see larger temperature-driven variance in their run output than ground-ball-heavy teams.
Humidity and Air Density
Humidity is the most counterintuitive environmental variable for many observers. Common intuition suggests that humid air is "heavier" and should suppress ball flight. The physics says the opposite. Water vapor (molecular weight ~18) is lighter than the nitrogen (molecular weight ~28) and oxygen (molecular weight ~32) it displaces. Humid air is less dense than dry air at the same temperature and pressure, which means humid conditions actually reduce drag and increase carry slightly.
The effect is real but small, typically adding 1 to 2 feet of carry at extreme humidity differentials. In practice, humidity's primary modeling value may be less about direct ball-flight effects and more about its interaction with pitcher grip. High humidity causes sweating, which can affect a pitcher's ability to command spin-dependent pitches like sliders and curveballs. Reduced spin efficiency translates to flatter breaking balls and more hittable pitches, an effect that is difficult to isolate statistically but appears in aggregate pitcher-performance data during high-humidity games.
Altitude as a Permanent Environmental Factor
Coors Field in Denver sits at 5,280 feet above sea level, where air density is approximately 17 percent lower than at sea level. This produces the most extreme environmental effect in professional baseball: home runs carry roughly 5 to 9 percent farther, breaking balls break approximately 15 to 25 percent less, and run scoring is historically 30 to 40 percent higher than the league average before park-factor adjustments.
While Coors is the extreme case, altitude is a continuous variable that affects every ballpark. Chase Field in Phoenix sits at 1,100 feet. The Atlanta Braves' ballpark is at roughly 1,050 feet. These parks show subtle but statistically detectable elevation effects on ball flight when controlling for other environmental variables. A comprehensive environmental model does not treat altitude as a binary Coors/non-Coors variable but as a continuous input scaled to its effect on air density.
The humidor, introduced at Coors Field and subsequently adopted at other parks, adds another layer. By storing baseballs at controlled temperature and humidity, the humidor affects the coefficient of restitution (the "bounciness" of the ball), partially offsetting altitude-driven carry increases. Models that incorporate humidor status as a categorical variable alongside altitude capture this interaction.
Indoor and Retractable Roof Parks
Stadiums with fixed or retractable roofs eliminate wind as a variable entirely and hold temperature and humidity relatively constant. This has a meaningful modeling implication: the environmental uncertainty band collapses. A game at Tropicana Field in Tampa has near-zero weather-driven variance, while a game at Wrigley Field in April might have an environmental uncertainty component that spans two or more runs in the expected total.
For retractable roof parks, the roof status itself becomes a categorical feature. A game at Minute Maid Park in Houston with the roof open in summer heat produces a different run environment than the same park with the roof closed and the climate controlled. Models need to account for the roof decision, which is often announced only hours before first pitch. This creates a practical data-pipeline challenge: environmental features may need to be updated in near-real-time as roof decisions are made.
Modeling Environmental Features
The technical challenge of environmental modeling is encoding continuous, nonlinear, interacting variables into a prediction framework. Several approaches are common in practice.
Polynomial and Interaction Terms
The simplest extension beyond linear features is adding squared terms (wind speed squared, temperature squared) and interaction terms (wind speed multiplied by temperature). This captures the basic nonlinearity and allows the model to learn that a 15 mph tailwind at 90 degrees Fahrenheit has a different marginal effect than the same wind at 55 degrees. The downside is that manual feature engineering can miss higher-order interactions or impose incorrect functional forms.
Park-Specific Environmental Adjustments
Because park geometry interacts with wind direction, the most accurate environmental models learn park-specific coefficients. A 10 mph south wind at Wrigley (where south means blowing out to center) has a different effect than a 10 mph south wind at Dodger Stadium, where the park orientation and outfield dimensions create a different interaction. Park-weather interaction terms or separate park-level models address this.
Tree-Based and Neural Approaches
Gradient-boosted tree models and neural networks can learn nonlinear environmental effects without explicit polynomial specification. Given sufficient training data, these models discover wind-temperature interactions, altitude-humidity effects, and park-specific patterns organically. The tradeoff is interpretability: a tree-based model may correctly predict that a game at Wrigley with a 12 mph southwest wind and 82-degree temperature will produce elevated scoring, but extracting the precise causal mechanism requires additional analysis.
The Feedback Loop: Weather, Grip, and Command
Environmental modeling is not limited to ball-flight physics. Weather conditions affect pitcher performance through grip and comfort channels that are distinct from aerodynamic effects. Cold temperatures reduce finger dexterity and blood flow, making it harder for pitchers to generate consistent spin and maintain command of off-speed pitches. This is why early-season games in cold-weather cities often feature more walks and wild pitches, not just more fly-ball carry.
Rain and precipitation create obvious game-state effects (delays, slippery baseballs, poor footing), but the pre-rain humidity and barometric pressure shifts can also affect pitcher feel and ball texture before any actual precipitation arrives. Models that incorporate precipitation probability as a continuous environmental feature rather than a binary rain/no-rain indicator capture some of this nuance.
Environmental Inputs in Run Expectancy and Simulation
The ultimate purpose of environmental modeling is to modify the run-scoring expectations that feed into game-level predictions. In run expectancy models, environmental adjustments shift the probability distribution of runs scored per inning. A game played in conditions favorable to offense does not simply add a fixed number of runs to the expected total. It changes the shape of the distribution, increasing the probability of high-scoring innings while leaving the probability of shutout innings relatively unchanged.
In simulation-based prediction systems, environmental inputs modify the parameters of each simulated plate appearance. Exit velocity distributions shift slightly. Home run probabilities adjust. Strikeout rates may change if cold weather reduces breaking-ball effectiveness. The cumulative effect across thousands of simulated plate appearances produces an environment-adjusted run distribution that reflects the specific atmospheric conditions of that game.
The models that handle this well do not treat weather as an afterthought or a simple multiplier. They weave environmental features into the same framework that processes pitcher matchups, lineup construction, and park factors, because in reality, all of these factors interact simultaneously to produce the final outcome.