# Arthur: Forecasting with fastball frequency

From SABR member Robert Arthur at Baseball Prospectus on January 23, 2015:

The fastball is the meat and potatoes of the batter-pitcher contest. Variations in fastball[1] velocity and movement explain a lot of the differences between pitchers, and a good heater can set up a whole arsenal of other pitches to boot. Fastballs are the most commonly thrown pitch by a wide margin, and so they determine to a great extent the results of any given matchup.

It’s no surprise then that pitchers tend to vary how much they use their fastballs on a hitter-by-hitter basis. Some hitters see fastballs rarely, others overwhelmingly, and the difference between hitters tells us something about their power (as well as their proficiency against fastballs). Being that they are the main offering of most pitchers, fastballs are the easiest to tee off against, and so they are thrown more rarely against powerful hitters.

In the past, I’ve advanced the idea that changes in the manner in which pitchers handle each batter can be used as a forecasting tool. Given the noted correlation between fastball percentage and power, it seems plausible that when fastball percentage changes, it reflects an underlying change in the hitter’s ability. This whole line of inquiry depends upon pitchers appraising the opponent’s talent faster than we do, but that seems a reasonable assumption given the greater tools and resources at the disposal of a major-league baseball team.

The problem is that there is always pesky variation in the way, obscuring our ability to notice true changes in fastball percentage. Sometimes a hitter will see a few extra fastballs because they face a series of fastball-happy pitchers all in a row. Sometimes an increase in fastball percentage is just caused by luck. Either way, this kind of random variation has to be handled.

To do so, we can model how many fastballs a hitter should see, given the pitcher they face and the count. Removing the effect of a pitcher is as simple as factoring in their fastball percentage. The count is a little more complicated: As a rule, hitters tend to see more fastballs as the number of balls increases, and fewer as the number of strikes increase.