Monday, February 7, 2011

The effect of the rising fastball on home run rates (with more clarification)


Last week, I started a thought suggesting that a rising fastball acts as an "anti-sinker" and that the rising action of a fastball like Matt Cain’s could be the explanation for why he is able to induce a lot of fly balls while keeping them in the park.

(The rising action is without gravity and is a way to measure the effect of the spin that a pitcher places on the ball. When gravity is factored in, a pitch with positive vertical movement is not rising but is falling less than expected due to gravity. The opposite is also true for pitches with negative vertical movement, such as curveballs. The spin causes more downward movement then one would see from gravity alone.)

I got to talk a little with Cain at the Giants media event on Friday and he was surprised to hear that he was better at keeping the ball in the ball park than other pitchers. He didn't do anything special and, in his humble way, thought that he gave up too many home runs. The other thought that comes to mind is what opposing batters think of Cain’s stuff. Jimmy Rollins was asked what he thought of Cain after facing him in the NLCS and said that Cain had late movement that kept batters off balance.

The late movement that Rollins talked about is something that is interesting, as I wonder if it could possibly be a pitch that doesn't drop as much as expected, or, as we are referring to here, the rising fastball.

If a pitch has more sink, then it would have from gravity alone that this would cause batters to hit the top portion of the ball and induce ground balls. Common sense suggests that the opposite would be true as well, if a pitch fails to drop as much as gravity suggests (or has the late movement that Rollins described), batters would hit the bottom portion of the ball and induce more pop ups and fly balls.

The hypothesis that I want to test is if pitchers who throw a hard, rising fastball (like Matt Cain) are able to maintain a lower home run per fly ball rate, which is contrary to the common thought that this was something that tended toward league average.

I set out to test this theory and found evidence that this is a plausible explanation for the lower home run rates.

I pulled data from the 2008 to 2010 seasons for pitchers who had logged at least 400 innings over that span. Then, I used the pitch f/x data for these pitchers vertical movement of fastballs (this was for all types of fastballs: four seam, two seam, cut fastball) from
Texas leaguers for the same period.

My initial sample included 87 pitchers, but this was then limited to pitchers who threw a fastball at least 50% of the time. I was interested in the effect of a rising fastball on a pitcher’s home run rate, so I wanted to focus as much as I could on pitchers who primarily threw a fastball. (In the future, I would like to look at just the home run rate of fastballs, but I was unable to locate that data. If anyone has this information or knows where I can get a hold of it, let me know.) The final sample that I tested contains 54 pitchers.

Below is a scatter plot for the vertical movement of a fastball versus that pitcher’s home run rate. Vertical movement is measured in inches:


There is a fairly strong negative correlation between vertical movement and home run rate. As a pitcher’s vertical movement rises, their home run rate falls. Pitchers in the top left have more vertical movement on their fastballs and a lower home run rate, while pitchers in the lower left have less vertical movement and give up more home runs.

My next level to also attempt to measure the effect of a power pitcher included multiple regressions. Initially I included K/9, BB/9, park effects, fastball velocity, and vertical movement. I ended up removing K/9, BB/9 and park effects because they were not statistically significant and did not help to explain the variance.

The final regression has a p-value of 0.0018 and an r-squared of 0.219, meaning that roughly 22% of the variance in home run rates is accounted for by velocity and vertical movement. Both of the independent variables are significant at the 95% level, with p-values of 0.018 for vertical fastball movement and a p-value of 0.006 for velocity.

The regression equation for home run rate per fly ball is: HR/Fly ball= 0.45 - (vertical movement*0.00354) - (Velocity*0.00353)

For example, a pitcher who throws 95 mph with 10 inches of vertical movement on their fastball would have a predicted fly ball rate of 8.25% compared to the league average home run rate of 10.52% over the last 3 seasons.

Areas for Further Study:

I think this is something that could need further research with more data and perhaps a finer look at the effects of a rising fastball on the home run rate per fly ball for just fastballs instead of including other pitches as well. The other pitches in the sample could be clouding the magnitude or giving a false effect, as pitches other then fastballs make up anywhere from 30% to 50% of each pitcher’s sample (the mean percentage of fastballs for the sample was 59.85%).

I would like to be able to break out and measure the effects of vertical movement and velocity on home runs for each different type of fastball or each different pitch.

In the meantime, it may be time to look more skeptically at the assumption that every pitcher regresses toward the league average home run rate.

If you're on Twitter you should definitely follow the The Crazy Crabbers. If you're not you should really consider joining, lots of good stuff going on there.

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