📂Sabermetrics

Definition of At-Bats in Baseball

Definition¹

The number of times a batter

• gets a hit,
• reaches base on a fielder’s choice,
• reaches base on an error, or
• is put out (excluding sacrifices)

is called the at bat, abbreviated AB.

Theorem

• [1]: For a single batter, the plate appearances PA, at-bats AB, walks BB, hit-by-pitches HBP, sacrifice bunts SH, sacrifice flies SF, and times reaching base on catcher’s/baserunning interference $X$ satisfy the following equation. $$ \begin{align*} PA =& AB + (BB + HBP) + (SH + SF) + X \\ \text{plate appearances} =& \text{at-bats} + \text{walks/HBP} + \text{sacrifices} + X \end{align*} $$
• [2]: For plate appearances PA, at-bats AB, and hits H, the following inequality holds. $$ \begin{align*} H \le AB \le PA \\ \text{hits} \le \text{at-bats} \le \text{plate appearances} \end{align*} $$

Explanation

Fielder’s Choice and Error

A fielder’s choice refers to a case where the batter could have been put out, but the fielder chose to throw to another base, so the batter reached safely. A fielder’s choice is not a hit, yet it increases at-bats, so it is a stat that lowers both batting average and slugging percentage.

An error refers to a case where a fielder should have put the batter out on defense, but the batter reached base due to a mistake.

Sabermetrics

It is an important stat because it affects the calculation of batting average, slugging percentage, on-base percentage, and even OPS. Since it is hard for those unfamiliar with baseball to understand what a fielder’s choice or an error is, it is best to compute it by checking against Theorem [1]; indeed, in the Korean league (KBO) it is defined by subtracting walks/hit-by-pitches, sacrifices, and times reaching base on catcher’s/baserunning interference from the number of completed plate appearances².

The Difference Between Plate Appearances and At-Bats

To someone who doesn’t know baseball well, both look like they begin with the same letters ‘타ㅅ’ (ta-s), so it is one of the especially confusing records. Simply put,

• a plate appearance is the number of times a person stood at the plate regardless of the bat, and
• an at-bat is the number of times the bat physically made contact with the ball.³

In baseball, if you don’t stand at the plate you have no occasion to use the bat, so at-bats cannot exceed plate appearances. If we call the beneficial cases among those where the bat hits the ball a hit, then the inequality in Theorem [2] holds. $$ \text{hits} \le \text{at-bats} \le \text{plate appearances} $$

I know that explaining these records to a layperson who confuses plate appearances and at-bats by using concrete game situations as examples is markedly less effective. Instead, we will try to understand the following records according to the inequality above.

• (1) 4 plate appearances, 3 at-bats, 3 hits: With four chances, the batter seized three of them and contributed to the offense all three times, so it is a good record.
• (2) 5 plate appearances, 1 at-bat, 2 hits: This says that at least two balls flew off a single swing. Such a record cannot exist.
• (3) 5 plate appearances, 2 at-bats, 1 hit: With five chances, the batter seized two of them and got a hit in one of those, making the inequality hold properly.
• (3) 3 plate appearances, 0 at-bats, 0 hits: Despite being given three chances, the batter failed to bat even once and did not contribute to the offense, so it is a bad record.