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UPDATED: Which Hitters Make Pitchers Work the Most?

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Yesterday, I reported out on the relationship between pitches seen per plate appearance (P/PA) and other hitting metrics.

Today, I want to look at the total impact a hitter has on a pitcher's pitch count by combining their P/PA with the additional pitches generated by the hitter's ability to get on base (OBP). To do that, I came up with a back-of-the-envelope statistic called Cumulative P/PA:

Cumulative P/PA = P/PA + (OBP x lgP/PA)

Cumulative P/PA takes the average number of pitches a hitter sees during a plate appearance and adds in the estimated average pitches they generate by not making an out, which is simply their OBP multiplied by the league average for P/PA. For 2002-2009, lgP/PA was equal to 3.77.

Here's the leader board for all qualified hitters from 2002-2009:

Patient hitters are certainly helpful for making a pitcher work, but you can see that hitters with a higher OBP provide an extra boost to pitch counts through their ability to get on base and bring up another hitter who then has an opportunity to work the pitcher.

The highest Cumulative P/PA? That title goes to Bobby Abreu, who combined a fantastic OBP with the most P/PA. 

The hitter that created the most marginal P/PA during this time period with >= 3,000 PA's was Todd Helton (1.63), followed closely by Albert Pujols (1.62). The worst? Corey Patterson at 1.10. Again, Marginal P/PA is completely driven by OBP, so these results are not that surprising.

For every four plate appearances, Abreu generates almost 23.5 pitches. By contrast, Cristian Guzman--who finished last on this list--generated 17.8 pitches. That's a difference of almost 6 pitches per game. Last year, pitchers averaged 16.3 pitchers per inning, 16.1 for starters. That means on average, starters hit the 100 pitch mark during the 7th inning.

Abreu generated almost 1.5 more pitches per plate appearance than Guzman from 2002-2009. So after just three PA's, Abreu generates 4.5 more pitches than Guzman. If you were able to trade a Guzman for an Abreu you theoretically would get the starter to the 100 pitch mark at the end of the 6th inning rather than in the 7th.

That's just with one hitter, but it's also comparing the best to the worst. So the impact isn't huge, but depending on how you've constructed your roster the effect could potentially be large enough to help you get to the bullpen half an inning or so earlier.

Now, this is not counting actual marginal P/PA. To do that, you would want to look at each hitter and who followed them in the lineup each day and calculate the actual average P/PA based on the specific hitters that followed. I am not a SQL wizard, so I'll leave that work to the experts ("Paging Mr. Tango and Mr. Wyers").

You can play around with the actual dataset here.

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Data courtesy of FanGraphs