OPS-HFAr and Winning

As promised, today I’m back on the subject of HFAr with some graphs to back up my arguments. The purpose of the math here is to demonstrate that HFAr can be a meaningful predictive tool. Sure, it is fine to describe a situation past, but a statistical model that can tell you something about another trend is more important. Although runs scored and runs against obviously work best for determining winning percentage, and would be a better model for prediction than OPS, I dove headfirst into calculating OPS-HFAr for all 30 teams because I thought the lower correlation between OPS and winning percentage would make it easier to demonstrate the effectiveness of HFAr.

First, let’s take a look at the graph plotting winning percentage as the dependent variable of a team’s overall OPS. (Apologies for the image quality, the host will not allow high quality images or images with text, but it should still be demonstrative.)

This graph is messy, the points are scattered all about, and it doesn’t show a statistically significant correlation. To use yesterday’s example of the White Sox, their point is far above the linear approximation, but not far enough to the right. They’re offense is unspectacular, but they have an extremely high winning percentage. The r-squared value for this graph is only about 0.0547, meaning that team OPS only explains about 5.5% of the variance in winning percentage. The correlation between them is 23.39% (read: weak).

Naturally, HFAr will be a better approximation than OPS by virtue of accounting for run production and prevention. The question is: a better approximation of what? Since teams with a high HFAr should have more success at home, let’s first look at HFAr on the X-axis against home field winning percentage on the Y-axis. Using pure winning percentage would not suffice, since a team with an 0-45 road record would have a terrible W%, and could have a high HFAr.

This graph is a little better. There is still no central cluster, but the r-squared value is up to 18.5% and the correlation to 43.01%, meaning that a team with a HFAr should have a better home record than a team with a bad one.

But that measurement is still insufficient, as HFAr doesn’t predict a good home team, just a better home team than road team. Colorado, for example, is not a very good home team, only one game over .500, but they have a very high OPS-HFAr because they are so brutal on the road. Thus, the appropriate measure would be one that looks at how much better a team is at home than on the road. Here I’ve plotted OPS-HFAr as the independent variable once again, but now the dependent variable is home winning percentage minus road winning percentage (WPh-WPr) to paint a picture of the teams that truly get an advantage from their home field.

It’s still not perfect, or even really all that good, but the r-squared is up above 50% (56.86%) and the correlation is 75.4%, meaning that the two values move together about three quarters of the time. That’s not bad starting out with a stat that shows almost no correlation to winning. At very least, we can draw the conclusion that OPS-HFAr will predict a team’s increased winning percentage at home much better than OPS can predict a winning record.

Finally, here’s a graph of the normal distribution of OPS-HFAr:

The data point far above the rest of them is the insane split of the Houston Astros. I alluded to how much more of an advantage they had yesterday than any other team had an advantage or disadvantage. The standard deviation of OPS-HFAr for this data set is 0.0931, putting them 3.25 standard deviations above the mean. The chances of a team performing at that level are fractions of 1%. To me, it seems that the implication would be regression to the mean, as they find a way to hit on the road and cool off at home.