Yesterday I started a thought suggesting that a rising fastball acts as an "anti-sinker" and that the rising action of a pitcher like

's fast ball could be the explanation for why he is able to induce a lot of fly balls while keeping them in the park.

If a pitch has more sink then it would 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, that if a pitch fails to drop as much as gravity suggests that batters would hit the bottom portion of the ball and induce more pop ups and fly balls.

So 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. I then used the pitch f/x data for these pitchers vertical movement of fastballs from

Texas leaguers for the same period.

My initial sample included 87 pitchers but I then limited it to pitchers who threw a fastball at least 50% of the time because I was interested in the effect of a rising fastball on a pitchers 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.) So my actual sample contains 54 pitchers.

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

There is a fairly strong negative correlation between between the two. In the plot you will see some outliers the two pitchers with the lowest vertical movement are

and

. The pitchers with the high rates of home runs and vertical movement in the upper right are

,

and

.

My next level of analysis 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, an r-squared of 0.219 meaning that roughly 22% of the variance 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*0.0035) - (Velocity*0.0035)

So 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 10.52% the last 3 seasons.

I think that 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 just the overall home run rate that includes 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 50% to 30% of each pitchers sample.

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

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