2010 Season Presents Puzzling Mathematical Results

If you can understand correlations, you can begin to understand something essential to success in baseball. Why? Because correlations show how one variable affects another variable. For example, we can see how strikeouts influence runs scored, and we would find that there is no notable correlation (actually true).

The dictionary describes a correlation as a “mutual relationship.” This relationship can prove that two things affect or do not affect each other.

In this case, we are going to look at how home runs affect runs scored per game. You would assume that there would be a direct correlation, meaning the more home runs you hit, the more runs you score.

Looking at data from 2010, just a week away from the end of the season, we find something very interesting.

Consider the following graph that shows each Major League Baseball team plotted on a graph, with the amount of home runs they hit on the y-axis, and the number of runs they score per game on the x-axis.

What we see is that home runs do, in fact, affect runs scored. The graph shows a general trend of “up and to the right,” suggesting a positive correlation.

However, there is one point that does not fit that trend. For some reason, the team that hit the most home runs did not score the most runs per game. According to our established positive correlation, that point should be considered an outlier. And what do you do when you have an outlier? You investigate it.

As it turns out, the team that is the outlier is the Toronto Blue Jays.

At first you would assume that the league leader in home runs, Jose Bautista, has something to do with it. After all, if it weren’t for him, the Blue Jays would not have the league lead in home runs, and would fit in on the graph above.

But the only way that he could hit that many home runs and not equally affect runs scored would be if he hit a disproportionate amount of home runs without runners on base. However, he hits 46% of his home runs when runners are not on base, much better than the league average of over 57%.

If that is the case, then we need to disregard our initial assumption, and instead go with a more logical approach. Instead of it being player-related, it must be team-related.

As it turns out, the Blue Jays are stacked with hitters that hit a bunch of home runs, while not doing much else.

In all of Major League Baseball in 2010, 22 players have at least 20 home runs, a batting average of at most .270, and a on-base-percentage of no greater than .333. Of those 22 players, four of them are on the Blue Jays, the most for any team in all of baseball.

Our final conclusion is that hitting a lot of home runs does not mean you will help your team. In order to produce an above average amount of runs, a player must be valuable in all areas: home runs, batting average, and on-base-percentage.

For the Blue Jays, it has not helped to have a bunch of home run friendly players, but it has helped us to identify something very important. It is now up to teams to apply this knowledge to off-season signings.

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