Particle Physics // Machine Learning // Music // Baseball

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# Run Expectation from Hits

Recently with the Cardinal’s struggles in offensive production, I’ve been thinking a bit about run expectancy based on the number of hits in a game. Obviously these are going to be correlated, but I was curious, how strongly, and how well you could predict runs given number of hits.

I went and looked at 2018 data for runs scored based on number of hits and did a linear regression:

As expected, the Pearson Correlation is 0.779, which falls under “strongly correlated.” In an attempt to try to get to some prediction method, I calculated the mean at every hit value, and plotted those values, then tried to fit that data.

Looking at just the means, a linear fit does not match the data well, so a polynomial fit of order 2 was used, which does. The coefficient on the x^{2} term appears small, but once you get to 6 hits, it raises the expectation by an additional run. Once you add standard deviation uncertainty lines to this plot though, you could see that within the 68% confidence interval of 1 sigma, a linear fit could probably work just as well to this data.