This article shows how to estimate the chance that Aaron Judge hits a home run in a specific game using modern, defensible inputs. It focuses on a practical workflow that combines Statcast contact metrics, Baseball Savant expected home runs and park adjustments, pitcher tendencies, and weather modifiers.

Statcast barrels and Baseball Savant xHR by Park are core inputs for defensible per-game HR probabilities.

Pitcher Barrel% allowed and park factors matter more than raw short-term HR counts in matchup adjustments.

Convert per-PA probabilities to a game probability using 1 minus the product of (1 minus pPA) across projected plate appearances.

What does a home-run probability mean for a single game?

aaron judge home run odds

When we talk about a home-run probability for a single game we usually mean two related things: a per-plate-appearance probability and a cumulative per-game probability built from repeated plate appearances. A per-plate-appearance probability is an estimate of the chance that a hitter will hit a home run in a single official plate appearance, given the quality of contact and context. Translating that per-PA estimate into a per-game probability requires combining the chance across the number of expected plate appearances the hitter will have.

Modelers commonly convert a per-PA probability into a game probability using the formula game probability equals 1 minus the product over all projected plate appearances of one minus the per-PA probability. This formulation makes the independence assumption explicit and gives a simple, intuitive result: more opportunities raise the chance of at least one home run in the game. Baseball Savant supplies plate-appearance level expectations designers often use as baselines when building these per-PA estimates, and that baseline is a sensible starting point for Judge in any matchup Baseball Savant expected home runs. For player-specific context see Aaron Judge's Statcast page Aaron Judge Statcast.

It is important to stress that any per-PA or per-game probability is an estimate, not a prediction of what will definitely happen. Year-to-year and game-to-game noise in raw home run rates is substantial, which is why modelers prefer contact-quality inputs to raw HR counts in short windows. Contact-quality measures reduce the influence of luck in recent results and produce more defensible short-term probabilities.

For readers using these estimates in evaluation challenges or skill-based platforms, remember that probabilities are inputs for decision-making, not guarantees. Variance can and will produce outcomes that differ from probability-based expectations, and managing that variance is part of disciplined prediction work. For guidance on challenge formats and evaluation, see the Funded Plays evaluations guide how evaluations work.

Key data sources and metrics: Statcast barrels, xHR, and park factors

At the core of modern home-run probability modeling is Statcast's barrel concept, which isolates batted balls with exit velocity and launch angle combinations that historically produce the highest run value and home-run rates. Modelers treat barrel frequency and the quality of barrels as a primary signal of HR-quality contact because a barrel captures both how hard and how well the ball was struck Statcast barrel definition.

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Baseball Savant's expected home runs, and specifically the xHR by Park product, provide a park-adjusted expectation that serves as a practical baseline. That baseline accounts for differences in fence distance, wall height, and other venue factors so modelers start from a number that reflects the park environment rather than a neutral assumption Baseball Savant expected home runs. Statcast Park Factors are also available for venue-level context Statcast Park Factors.

Separately, published park-factor methodologies explain how to scale batter or league rates for venue effects. Using park factors or the xHR by Park product helps avoid assuming neutral conditions and gives more accurate expectations when a game is played in extreme hitter-friendly or pitcher-friendly venues Park factor methodology.

A step-by-step framework for estimating per-PA home-run probability

Below is a concise, reproducible workflow you can follow to produce a defensible per-plate-appearance home-run probability for Aaron Judge in a specific matchup.

Step 1: pick a recent baseline. Choose either a short-term HR per plate appearance using recent games or use a plate-appearance xHR baseline from Baseball Savant. The xHR baseline is useful because it is already park-aware and summarizes expected home-run outcomes per batted-ball opportunity Baseball Savant expected home runs.

Step 2: translate that baseline to expected batted-ball outcomes. Convert the HR/PA or xHR baseline into a per-PA probability by accounting for the expected share of plate appearances that produce batted balls in play, called the batted-ball rate, and the share of those batted balls that qualify as high-quality contact, notably barrels and near-barrels which are the best predictors of HR outcomes based on Statcast contact metrics Statcast barrel definition.

Step 3: apply matchup and park corrections. After the baseline is set, layer in pitcher adjustments, park scaling, and any weather modifiers. Pitcher-level allowed contact-quality metrics such as Barrel percent allowed and cautious use of HR/FB help fine-tune the expected per-PA probability. Park adjustments can be applied either through xHR by Park or using established park-factor scaling so that the baseline reflects the venue where the game will be played Park factor methodology.

How to adjust for pitcher tendencies, park, and weather

Pitcher adjustments should focus on contact-quality metrics because they directly affect the likelihood that batted balls will leave the park. Barrel percent allowed is a practical measure for this purpose, and it provides a clearer signal for HR modeling than raw HR/FB alone. Use HR/FB carefully since it is prone to volatility and benefits from regression toward league norms when samples are small HR/FB rate methodology.

Park adjustments are critical. Rather than assuming neutral conditions, apply park factors or use xHR by Park so the hitter's baseline reflects the venue. This reduces systematic bias when a stadium's dimensions or wall heights materially change the chance that a particular batted ball becomes a home run Baseball Savant expected home runs.

How can I estimate the probability that Aaron Judge hits a home run in a single game?

Build a per-plate-appearance baseline using xHR or recent HR/PA, adjust for pitcher, park, and weather, then convert the pPA into a game-level probability using 1 minus the product of (1 minus pPA) across projected plate appearances.

Weather matters too. Peer-reviewed work shows that higher temperatures increase ball carry and that wind can materially alter home-run outcomes, so incorporate temperature and wind direction when they are available for the game you are modeling temperature influence on home runs.

When combining pitcher, park, and weather effects, be explicit about how each adjustment alters the baseline per-PA probability. For example, translate a pitcher’s higher-than-average Barrel% allowed into a proportional increase in the chance that a batted ball of a given quality becomes a home run. Keep adjustments modest on small samples to avoid overfitting.

From per-PA to per-game: the math and assumptions

Converting a per-PA probability to a per-game probability is straightforward and transparent. The formula is game probability equals 1 minus the product across the projected plate appearances of one minus pPA. In practice, if you estimate pPA for each expected plate appearance you compute the product of the (1 minus pPA) values and subtract from one to get the chance of at least one home run in the game. Baseball Savant’s plate-appearance and xHR outputs are commonly used to set the initial pPA value for this calculation Baseball Savant expected home runs.

Estimating projected plate appearances requires thinking about lineup slot, opposing pitcher substitutions, and platoon usage. A player batting near the top of a lineup will usually see more PAs than someone lower in the order. Use projected lineup data and typical game-length assumptions to set a reasonable projected PA count for the calculation. If you use a constant pPA for each projected PA, the independence assumption simplifies the math, but remember this assumption can fail when plate appearances are not independent due to strategic substitutions or correlated pitcher matchups.

Be explicit about independence assumptions in your documentation. If you expect the pitcher to change and the replacement has markedly different allowed contact tendencies, consider modeling separate pPA values for each expected stint instead of a single pPA across all projected plate appearances.

Common modeling mistakes and how to avoid them

A frequent error is over-relying on small-sample HR/FB rates. Because HR/FB can swing substantially from one short window to the next, it is safer to regress small-sample HR/FB toward a league or career baseline before using it for adjustments. This lowers the risk of overreacting to short-term noise HR/FB rate methodology.

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Another common mistake is ignoring park and weather effects. Failing to account for a hitter-friendly or pitcher-friendly venue, or a warm night with wind blowing out, can bias your per-PA probability substantially. Prefer park-adjusted baselines or explicit park-factor scaling to reduce this risk Park factor methodology.

Finally, using raw home-run counts instead of contact-quality baselines like Barrel% tends to overstate confidence in short-term forecasts. Statcast contact metrics better separate skill from luck in the short run, and FanGraphs discussion of contact-quality makes this distinction clear for modelers who want to understand the underlying mechanics using Statcast contact-quality discussion. FanGraphs also provides player-specific visualizations such as heat maps that can supplement contact-quality analysis FanGraphs heat maps.

Worked example: estimating Judge's HR probability for a typical matchup

This worked example outlines the inputs you should gather and the sequence of adjustments, without inventing numeric outcomes so you can reproduce it with live data. Start by collecting the following: Judge’s recent Statcast barrel rate and batted-ball profile, his plate-appearance xHR or HR/PA baseline from Baseball Savant or equivalent, the opposing pitcher’s Barrel% allowed and HR/FB tendencies, park factors or xHR by Park for the venue, and local weather forecasts for temperature and wind direction Statcast barrel definition.

Stepwise, do the following. First, select your baseline: choose either a recent HR/PA or the player’s xHR per plate appearance from Baseball Savant. Second, convert that baseline into a per-PA probability by adjusting for the expected share of PAs that become batted-ball events and the share of those that are high-quality contact. Third, adjust the per-PA for the pitcher by increasing or decreasing the probability in proportion to how the pitcher’s allowed Barrel% compares to league and to how his HR/FB has trended after appropriate regression. Fourth, apply a park scaling factor or use the xHR by Park value so the baseline reflects stadium effects. Fifth, modify slightly for weather if temperature or wind favors carry Baseball Savant expected home runs.

Split 2D vector infographic comparing a hitter friendly park and a pitcher friendly park with visual wall height and distance annotations for aaron judge home run odds in Funded Plays color palette

As you make each adjustment, write down the assumption and the data source. For example, note the date range used to compute the recent barrel rate and whether the pitcher adjustment used a full season or a reliever sample. When you finish the adjustments you will have a defended per-PA probability that you can feed into the conversion formula described earlier to produce a per-game probability.

For model validation, compare your per-PA and resulting per-game probability to Baseball Savant xHR by Park and to league-context benchmarks. Discrepancies are opportunities to re-check assumptions such as lineup slot, park factor choice, or whether a small pitcher sample forced an overly large adjustment Baseball Savant expected home runs.

Limitations, responsible use, and what estimates cannot tell you

Every model produces probabilistic estimates and cannot guarantee outcomes. Estimates summarize our best judgment given available inputs but they do not eliminate variance from single games, unexpected lineup changes, or sudden weather shifts. Use probabilities as decision inputs and avoid treating them as certainties.

Convert a per-PA HR probability and adjustments into a per-game probability

Use realistic baselines and document assumptions

When using estimates in skill-based challenges or practice environments, document assumptions and the data windows you used. Funded or challenge-style platforms reward consistent, repeatable methods and transparent record-keeping more than one-off, high-variance calls. For community resources and posts see the Funded Plays blog.

Residual uncertainty also comes from roster and in-game events. Late lineup changes, pinch-hitters, or bullpen moves that expose a player to unusual pitching matchups will change the calculation. Update your estimate if meaningful in-game information becomes available.

Conclusion: quick checklist and next steps for refining your estimate

Checklist: 1) pick a defensible baseline (xHR or recent HR/PA), 2) convert to per-PA using batted-ball and contact-quality rates, 3) apply pitcher adjustments focusing on Barrel% allowed and regressed HR/FB, 4) apply park scaling or xHR by Park, 5) check weather for temperature and wind, and 6) convert pPA to game probability with the 1 minus product formula while documenting assumptions Park factor methodology.

For updated inputs use current Statcast outputs and Baseball Savant xHR for the 2024 to 2026 context to keep park and contact-quality baselines up to date. Track model performance across many games rather than judging by single outcomes to evaluate whether adjustments are well calibrated. For general information about the Funded Plays platform visit Funded Plays.

Remember that these estimates are informational and should be used responsibly as part of a disciplined forecasting process rather than as guaranteed outcomes. Clear documentation and modest adjustments for small samples help maintain credibility and long-term skill development.

How do you get a per-PA home-run probability?

Start with a baseline such as recent HR/PA or Baseball Savant xHR, adjust for batted-ball and contact-quality rates, then apply pitcher, park, and weather corrections to reach a per-PA estimate.

Should I trust HR/FB for short-term forecasts?

No, HR/FB is volatile in small samples; regress it toward league norms and rely more on contact-quality metrics like Barrel% for short-term adjustments.

Does weather really change home-run chances?

Yes, higher temperatures and favorable winds increase carry and can raise home-run probabilities, so include weather when available.

Use this workflow as a repeatable framework and document each assumption and data source. Over many games, disciplined application of these methods helps separate signal from noise and improves your forecasting as inputs and contexts change.