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This week’s question comes from Tolo de Abril who asks:

I am from Portugal and accordingly new to baseball, so this is undeniably easy question. Does the formula for onbase percent count fielder choices? Sorry for my bad English.

Thanks for the question, and no need to apologize–your English is undoubtedly better than my Spanish.

On-base percentage, or OBP, is defined as the sum of hits, walks, and times hit by pitch, divided by at-bats, walks, hit-by-pitches, and (depending on which source you consult) sacrifice flies:

```
H + BB + HBP
OBP = --------------------
AB + BB + HBP + SF
```

As you can see, a fielder’s choice (FC) is not explicitly included in the formula, although it counts as an at-bat, and as such, is treated simply as an out.

However, a more careful examination of the fielder’s choice reveals that this approach is nonsensical. On-base percentage, by its very name, is intended to measure the frequency with which a batter reaches base. This is quite evident for hits, walks, and hit-by-pitches, each of which result in the batter now standing safely on a base (except with home runs, of course).

Similarly, after a fielder’s choice, the batter is occupying first base perfectly legally. But counter intuitively, he gets no credit in OBP for having reached safely! And even worse, he is effectively charged with being put out, as he is credited an at-bat but not credited with a hit or any other recognition of his accomplishment.

While there was an out on the play, it was not the batter who was put out, but instead a runner who failed to advance successfully. This baserunning blunder carries no penalty for the runner who is actually out, but is instead unfairly charged to the batter’s hitting record.

Ironically, other baseball statistics handle this case correctly. When a batter reaches base via a fielder’s choice, and later comes around to score, it is he who is credited with a run scored, not the runner put out on the FC. Why then, do the record-keepers charge the cost of a fielder’s choice to someone other than the person retired on the play? This discrepancy can lead to the illogical state of a player having scored more runs than the number of times he reached base!

Having a flawed OBP formula that ignores FC would be of minor concern if this were a rare event. However, this is not the case. Looking at players between 1978 and 2000 with at least 300 PA:

• 28.48% have more fielder’s choices than hit-by-pitch (a component of OBP)

• 15.62% have more FCs than sacrifice flies (also a component of OBP)

Assuming those percentages are independent, that means that about 40% of players have more fielder’s choices than one of the two key components of on-base percentage. We’re missing a big piece of the puzzle. There are many players losing 10-30 points of OBP each season because fielder’s choices are not counted as reaching base safely. Many of those players bat in the heart of the order, with runners on base when they bat more often than most players. They are the sluggers the teams rely on to drive in runs, yet they are penalized for having more opportunities to hit into this disregarded play.

The solution to this conundrum is obvious. Fielder’s choices must be added to the definition of on-base percentage, in recognition of the fact that the batter is now “on base.” Having laid out the case for our forgotten friend, the fielder’s choice, it would now be foolish to think otherwise. Thus the new and improved formula for OBP should be:

```
H + BB + HBP + FC
OBP = --------------------
AB + BB + HBP + SF
```

Thanks for writing in, Tolo.

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chabels
6/21
I'm pretty sure in Portugal they speak Portuguese not Spanish.
kwoolner
11/01
Quite true. But when do they celebrate April Fool's Day in Portugal? (Check the date this article was posted).