Fun With Numbers

Back in 2013, I had the pleasure of working as a statistical consultant with my former high school baseball coach as part of an internship for college credit. My coach was a math teacher by day, passionate about the game, and always looking for that next level of analysis that might give him an edge on the competition. Getting to intern with him was a match made in heaven.

Coach had a rather fascinating blend of old-school and new-school philosophies, that successfully came together time and time again during his tenure at my former school. During that season, he enlisted my help to devise statistical models that graded out his players based off of tracking stats most people don’t even think to observe. After putting our heads together, the brainchild that emerged was the Productive At Bat (PAB for short).

The PAB was truly a fascinating stat. The purpose of this stat was to figure out which players made the most use out of their plate appearances, regardless of the outcome, and then build the lineup in a way to maximize productivity. In order to do this, we tried to eliminate as many variables as we reasonably could that fell outside of the players’ control when they were up to bat. Players could be credited with a PAB after all kinds of outcomes, even strikeouts, provided certain conditions were met.

In order to be credited with a PAB, players had to meet at least 1 of the following conditions…

Reach base

Advance a runner

Hit a line drive

See 5+ pitches

Make the defense earn the out/hitter was robbed

Obviously, reaching base and advancing runners are the two main objectives of any offense. This essentially incorporates the concept of On Base Percentage, while including situations where “productive outs” are made.

Including the condition for line drives allows us to remove some of the elements of “bad luck”. The idea behind this was that you wanted players who were hitting the ball well getting more at bats, so we simply disregarded the outcome of the at bat if they struck the ball well (for the purpose of this stat).

After covering the basics, we started to go more in depth and try to think of ways a player could have a positive impact on the game with an at bat that didn't already meet the existing criteria that we had. Pitches seen seemed like the perfect fit. We settled on 5 as the minimum number because, if every player took at least 5 pitches per at bat, a starting pitcher with a perfect game would still hit 85 pitches before they made it through 6 innings. In high school, pitchers are restricted to no more than 85 pitches before they are required to come out. If we could average 5 pitches per at bat, we could grind down even the most elite opponents, and have a chance to win against their bullpen. No matter what happened after 5 pitches, the batter would have at least done their part to tax the opposing pitching staff.

That last condition was a really interesting one. While it would be impossible to use the stat league-wide with that condition (since it would be impossible to know if coaches were all in agreement on when the defense earned the out, or the hitter was robbed), that final condition allowed for Coach to reward his players when he felt they got cheated by the umps, or were the victims of some stellar defense. 

The end result was a very simple metric that told you what percentage of at bats a player made good use of.