On-base Percentage in Baseball
Definition 1 2
The ratio that indicates how often a batter gets on base is called On-base Percentage, abbreviated as OBP. It is defined in relation to Hits H, Walks BB and Hit By Pitch HBP, At Bats AB, Sacrifice Flies SF as follows: $$ \begin{align*} OBP :=& {{ H + (BB + HBP) } \over { AB + (BB + HBP) + SF }} \\ 출루율 :=& {{ 안타 + 사사구 } \over { 타수 + 사사구 + 희생플라이 }} \end{align*} $$
Explanation
Put simply, if a batter has an on-base percentage of 0.400, it means that approximately four out of every ten at-bats result in the batter reaching base, no matter the method. Whether through getting a hit, being walked, or not making an out while still managing to get on base, the result is the same. Moreover, getting walked indicates that the pitcher has thrown at least four pitches, thus serving as an indicator of the batter’s ability to wear down the opposing pitcher’s stamina.
Why Sacrifice Bunts Are Not Included in the Denominator
While both considered sacrifice hits, sacrifice flies are included in the denominator, but sacrifice bunts are not. The difference between a sacrifice fly and a sacrifice bunt can be seen as a difference in the batter’s mindset. Indeed,
- one might hit a sacrifice fly intending to lift the ball, knowing they could get out, and
- while attempting a bunt with the expectation of getting out, it’s conceivable the bunt turns into a hit with some luck,
however, from a strategic perspective, the two cannot be viewed on the same level. They may result in not getting on base and still driving in a run, but strictly speaking, a sacrifice fly results in not getting on base, while a sacrifice bunt does not count as getting on base.
A manager might instruct a player to “hit a sacrifice fly if possible” but does not demand a “sacrifice fly.” If one is to hit, it’s preferable to hit a base hit, and managers usually do not demand a sacrifice fly explicitly. Conversely, managers can instruct to “lay down a bunt” but cannot command “bunt and stay safe.” This is encouragement, not a strategy.
If both were included in the on-base percentage’s denominator, instructing a “bunt” would translate to an unfair directive of “lower your on-base percentage and contribute to the team.” A sacrifice bunt is about sacrificing an out for the team, not sacrificing an individual’s performance. Of course, if one is unfamiliar with baseball, not understanding this distinction is not a major issue. Let’s proceed to the next explanation.
Sabermetrics
What’s peculiar about the on-base percentage is that, for a metric calculated to determine how often a player gets on base per at-bat, the formula for its calculation is surprisingly complex. The conceptual definition prior to its formulation - that is, a ratio meant to represent how often a player gets on base - should have been sufficient as follows: $$ 출루율 \overset{?}{=} {{ 안타 + 사사구 } \over { 타석 }} $$ However, when defensive interference/runners interference resulting in reaching base is defined as $X$, Plate Appearances PA satisfy the following equation: $$ \begin{align*} 타석 =& 타수 + 사사구 + 희생타 + X \\ =& 타수 + 사사구 + (희생플라이 + 희생번트) + X \end{align*} $$ Yet, for reasons mentioned earlier, sacrifice bunts are omitted, and $X$, being infrequent in records, can pragmatically be considered equivalent to $X \approx 0$. Even if instances were frequent, the rationale for excluding $X$ from on-base percentage calculation stands firm. A larger number of at-bats in a player’s record could indicate durability or diligence, so reducing this due to an opponent’s error is irrational; it should only be adjusted in the at-bat records. When calculating on-base percentage, it still remains a sensibly dismissible figure, leading to a redefined on-base percentage as introduced in the definition, which drops to: $$ 출루율 = {{ 안타 + 사사구 } \over { 타수 + 사사구 + 희생플라이 }} $$ If one can understand the complex formula derivation from this induction process, reading this post has been worth it. Since players do not excessively utilize sacrifice bunts, if the instances aren’t significant, eventually the on-base percentage boils down to its original conceptual approximated form, which is the on-base ratio per at-bat: $$ 출루율 \approx {{ 안타 + 사사구 } \over { 타석 }} $$
Moneyball
Sabermetrics played a crucial part in popularizing the on-base percentage as a baseball statistic, largely through “Moneyball.” Moneyball is a film adaptation of a real scenario where a strong team was formed by applying sabermetrics, summarizing that a financially struggling club sought to enhance its roster by recruiting underrated players with high on-base percentages to solve its dilemma.
Characters in the film frequently emphasize the importance of “on-base percentage.” However, a significant misunderstanding to avoid now is that, at the time of the film’s setting, sabermetrics was not as mainstream, and the on-base percentage was not as highly valued. The protagonist’s team situation was as follows:
- The team is financially constrained.
- Key players are leaving the team.
- On-base percentage is one of the most undervalued statistics in the league.
- There are many players with high on-base percentages but low salaries.
Effectively, the narrative is about pioneering in accurately evaluating players and winning with the least expenses, not a success story of winning a championship by simply gathering players with good on-base percentages. To put it bluntly, a strong team cannot be built on on-base percentage alone. In the years following, all clubs became aware of the importance of sabermetrics, and today, most records receive a relatively fair assessment. Hence, a high on-base percentage alone doesn’t guarantee success, indicating its price has adjusted to a justified level.