Is it worthwhile to sac bunt?

Howdy fellow Braves Fans!

As some of you will remember, a few months ago I asked for baseball-themed ideas for a final project in my Statistics class. I promised to share the results with you when I finished, and so, without further ado...

A friend of mine (who is a member at Bucs Dugout) and I decided to determine if laying down a sacrifice bunt really increased your chances of scoring a run. (I remember many of us asking the same question in Open Threads throughout the season) Because there are so many different variables to control for, we looked at one specific condition: when there is a man on first with no outs. (This prevents confounding variables, such as having to compare the efficacy of sac bunting with, for example, men on 1st and 2nd with one out and a man on first with no outs). We looked solely at the American League, so as not to have to deal with the pitcher.

We began by going through every game played in the AL last year, and notating every instance where a man reached first with no outs. We then recorded whether or not that man scored, if he was sac'd over to second, and how many total runs were scored in that inning. 4,728 data points (and a big headache) later, we had all of our data. For the record, of the 4,728 times a man reached first with no outs in the AL last year, he was sac'd over to 2nd 193 times.

Chance of the man on first scoring... 

Of the 4,728 times that a man reached first with no outs, he scored 39.36% of the time. We then looked at the effect of the bunt and found out that when the man wasn't sac'd over, he only scored 39.25% of the time. When he was sac'd to 2nd however, he scored 41.97% of the time. In testing for statistical significance we found the p-value of this test to be .0001. This means that there is a 99.99% chance that the 41.97% is not due to random chance, and is thus statistically significant.

In conclusion, a sacrifice bunt DOES increase the man on first's chance of scoring.

Chance of the team scoring...

Although we looked at the chances of the man on first scoring, the team sac'ing is not concerned as much with the man on first scoring, but with anyone scoring. So we next examined the chance that the team scores at all given that they have a man on first with no outs. The chance of scoring at all across the the 4,728 times a man reached first last year was 43.23%. When there was no sac bunt, the chance was 43.24%, and when there was a sac bunt, the chance of a team scoring was 43.01% The p-value of this test was .749, meaning that there is no statistical significance.

In conclusion, a sacrifice bunt DOES NOT increase a team's chance of scoring a run. The probabilities are virtually identical.

Average runs scored...

Finally, we looked at the average number of runs scored per inning when a man reached first with no outs. Across those 4,728 instances, those teams averaged .9314 runs per inning. When a team sac'd the man over to second, their average runs per inning were .7098.  When a team did NOT sac the man over however, they scored an average of .9409 runs per inning. The p-value for this test was .0025, indicating a big statistical difference.

In conclusion, sacrifice bunting DECREASES the average number of runs scored per inning.

Putting it all together...

So there you have it. Basically, you should not sac bunt. Not only do you have the same chance of scoring in an inning whether or not you sacrifice bunt, giving up one of your outs means that you will average less runs. 

A few limitations...

Like I said, we had to control across all situations, so we only looked at the AL, and what happens with a man on first and no out. But, since this is the most common bunting situation, it gives us a better, more statistically accurate glimpse into sac bunting. If you examined all situations, you would probably find that these probabilities hold, more or less, but we cannot be sure. Also, how these numbers would translate to the NL is noteworthy. This study shows that you should never have position players bunt, but as for the pitcher, it is probably still prudent to have him sacrifice, as most pitchers have such a low batting average. We avoided the NL for precisely this reason - the pitcher and his abnormally low BA would confound the study. But as I said, this should hold for all position players.

So, dear Bobby: Next time you decide to have Martin Prado and his .310 BA square to bunt, please think again! Sac bunting is a big heap of...