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# What Power Means -- Visualizing the intricacies of power hitters.

### Graph of the Day

This GOTD began as a thought--do player that hit a lot of home runs per fly ball hit more doubles and triples? I looked at all players in 2009 that recorded at least three hundred and eighty four PA's and hit at least one home run (sorry Juan Pierre)--two hundred and eighty three in all--and divided them into three groups: those whose HR/FB was at least one standard deviation lower than the mean, those whose HR/FB was at least one standard deviation higher than the mean, and those within one standard deviation of the mean. Forty six hitters fell into group one, fifty two fell into group two, and one hundred and eighty five fell into group three.

If HR/FB followed a normal distribution, we would expect about sixty eight per cent of the hitters to fall within one standard deviation, and one hundred and eighty five of two hundred and eighty three is nearly that--about sixty five per cent. Here is a visualization of the HR/FB distribution, with the purple line roughly representing the mean and the other colored, straight lines being roughly one standard deviation away from the mean.

So, everything to the left of the red line represents group one (HR/FB < μ-σ), everything to the right of the yellow line represents group two (HR/FB > μ+σ), and everything in between represents group three (μ-σ < HR/FB < μ+σ). Below is what a perfectly normal distribution would look like:

My thinking is a Chi-square distribution might be a better fit, but this one works well enough for our purposes.

Continued below.

Now that we've defined our sample, we can get to the bottom of this. The original question was, "do players that hit a lot of home runs per fly ball hit more doubles and triples?". Surprising to me, the answer is no. All three groups averaged hitting a double or triple in about 5.3 per cent of their plate appearances with similar standard deviations. Almost none of the change in non-HR XBH rate could be explained by the change in HR/FB:

The only result-based differences I noticed among the three groups were walks and strikeouts. The guys that hit more home runs per fly ball walk more and strike out more. Though the correlation between the two statistics is weak, the difference between the two extreme groups is rather vast.

Here are the frequency histograms of the distributions by power group:

If the distributions were perfectly normal, we'd expect them to look something like this:

And, for good measure, a pair of simulated distributions using 9,000 random normal variables:

You probably didn't need me or 12 graphs to tell you that guys who hit for a lot of power strike out and walk more. Hopefully the visualizations and simulations help put it in perspective, though.