Winning a batting title in MLB is only allowed to a handful of highly talented players. It is still a very honorable title for a baseball player, despite a controversy regarding the usefulness of batting averages. As such, there have been instances in MLB history where players competing for the batting title have sat out games towards the end of the season to preserve their averages. This is because batting average is inherently based on probability. Even if you hit .333, it is not guaranteed that you can hit 1 out of 3 at-bats in the last game of the season. Therefore, if you play in the last game of the season and do not hit, your batting average will decrease. It increases the denominator with no change in the numerator of the batting average formula. This is not a problem in the middle of the season for top-tier players because they can restore it by hitting more in the next few games. However, at the end of the season, there is no chance to restore it because the season is going to be over after that game. This will have a detrimental effect on the race to the batting title, especially when the second runner is hot on the trail.

One of the most famous examples is Jose Reyes in 2011. On the final day of the 2011 season, Jose Reyes bunted for a single in his first at-bat and was then taken out of the game to protect his average. This move attracted criticism from some quarters, as it was perceived as lacking competitive spirit. Nevertheless, Reyes secured the title with a .337 average, narrowly surpassing Ryan Braun (.332). The story continued in 2016 with DJ LeMahieu of the Colorado Rockies. As the season neared its end, LeMahieu was leading the National League in batting average. To preserve his position, he was benched for several games and had limited at-bats in others, a strategy that sparked debate about the ethics of preserving batting averages. Despite the controversy, LeMahieu clinched the batting title with a .348 average, edging out Daniel Murphy (.347).

How can we fundamentally prevent repeated unsportsmanlike behavior at the end of the season? I have developed an adjusted batting average to address this issue. The core idea is to incentivize players to participate in more games by adjusting the batting average, ensuring that players do not avoid playing more games toward the end of the season. Ultimately, players who consistently contribute to their teams without skipping games will be better recognized in the batting title race.

In baseball, once a player reaches 502 plate appearances with a high batting average, there is a motivation to avoid additional plate appearances. This is because the average probability of hitting in baseball does not exceed about 30%. Even the best hitter in baseball history could only hit 40% of the time. When the probability of success is relatively low, like hitting in baseball, reducing the number of attempts can increase the probability of success by luck. Conversely, increasing the number of attempts will cause the success rate to regress to the average.

Therefore, the key idea of the adjusted batting average is to incentivize players with many at-bats and penalize those with fewer at-bats. The challenge is determining an appropriate level of adjustment.

To determine the optimal adjustment factor, we refer to other players’ performance. We first need to calculate how many plate appearances result in at-bats. This can be simply calculated by the league average of at-bats per plate appearances ratio.

To determine the optimal adjustment factor, we refer to other players’ performance. We first need to calculate how many plate appearances result in at-bats, on average. This can be simply calculated by the league average of at-bats per plate appearances ratio.

Where i represents a player with at least oneplate appearances in MLB in the season and n is the total number of hitters inthe season

The next step is to calculate the average batting average of players who had at-bats more than at-bats threshold. This batting average represents the expected number of hits per at-bat. In statistics, the expected value of an event with multiple outcomes can be calculated as follows:

As we usually use P(X) to abbreviate the probability of event X happening, the probability of event  happening can be denoted as . Also, let’s denote  as the outcome of event . Then, the above formula can be simplified as follows:

Do you remember ∑ (called “sigma”) from high school mathematics class? Using ∑, we can further simplify the formula as follows:

Where  is the outcome of event , and  is the probability of event  happening. For example, when flipping a coin, there are two possible outcomes: head or tail, each with a probability of 1/2. If you receive $1 for heads and $0 for tails, the expected prize money is:

This principle can be applied to baseball. When calculating a batting average, the outcome of an at-bat is simplified into a binary variable: hit or no hit. If a player hits, the outcome is 1 additional hit, and if no hit, the outcome is 0 additional hit. The probability a player hits is his batting average. The probability a player cannot hit is (1-batting average).

Imagine a hitter with 600 at-bats and 200 hits, resulting in a batting average of .300. If he hits in his next at bat, there is 30% chance that he hits the ball, and if it happens, he will have 601 at bats and 201 hits. There is 70% chance that he cannot hit the ball, and if it happens, he will have 601 at bats and 200 hits. Therefore, the expected number of hits per at bat can be calculated as:

Thus, the batting average is always the expected number of hits per at bat. You do not even have to calculate the expected number of hits. In the above example, it is .300, which is his batting average. In reality, a hitter cannot hit 0.300 balls in an at-bat. Theoretically, however, we can use this expected value as an adjustment factor.

In the 2025 season, the average batting average of players with more than at-bats threshold (which was 451.45 in the 2025 season) was .258. Thus, we can adjust the batting average by adding a bonus of .258 hits for each additional at bat beyond 451.45 or penalizing by .258 hits for each at bat below 451.45. These numbers vary across seasons, so it has to be separately calculated for each season. This adjustment can be mathematically represented as:

where AB is a player’s at-bats, AB threshold is the threshold derived from the minimum required plate appearances (89.93% of 502 in the 2025 season), and the adjustment factor is the average batting average of players whose at-bats are greater than the at-bats threshold.

For example, in 2025, Aaron Judge’s batting average was .331 with 179 hits and 541 at-bats. He had 541 – 451.45 = 89.55 more at-bats than the threshold. Therefore, his adjusted batting average (adjBA) for 2025 can be calculated as follows: