Rox Talk - Pitcher Per Runs

This is an update to a post that I did back in July.  The Rox at the time had played 108 games. This post updates through 162 games with both our offensive and pitching...

A couple of weeks ago (June or July 2008) I was listening to the Rockies radio broadcast team, Jeff and Jack, and Jack Corigan made the statement that basically said that as your (i.e. the pitcher) pitch count increases in the inning the more likely a run is going to be scored. From the sound of this it made me go hmmm.  Two questions immediately popped up...1) is this true (logically you would think yes) and 2) what is on average the amount of pitches thrown in an inning that would allow a single run?

Well off to baseball reference where on their box score page they show the amount of pitches thrown in an inning along with the number of runs. By taking this data and plotting the number of pitches per inning, the runs scored for that number of pitches, and annotating in a running log how often this number of pitches occur in an inning, I was able to come up with the number of pitches thrown in 2008 by Rockies pitchers and what is the average number of pitches thrown to allow for one run in an inning (i.e., a 12 pitch inning occurred 127 times and a total of 18 runs were scored for a rate of 0.14 runs).  Conversely the Rox offensive saw 12 pitches only 90 times and scored 10 runs over the season for a rate of 0.11 runs.

Graphically all this data looks like this:

This first plot shows the number of pitches versus the total runs. The size of the circle indicates how often this number of pitches were thrown. The next plot shows the distribution which indicates that 12 and 13 pitches were thrown in an inning approximately 249 times or accounting for about 17.2% of the total innings pitched.  Conversely the Rox offensive saw 12 and 13 pitchers approximately 172 times for only about 11.9% of the total innings pitched to them.  

The final plot shows the rate at which runs are scored. So for instance 26 pitches in an inning occurred 26 times and a total of 45 runs were scored. Thus giving a rate of 1.73 runs scored when 26 pitches are thrown. If you plot this rate you get this...

A relatively nice curve that has a Rsquare of about 0.8189 (versus 0.6766 for our offensive).  If you throw out the outliers you can get a better curve fit.  After about 30 pitches in an inning the number of times a team scores runs tends to mess up the rate  (i.e. 31 pitches in an inning occurred 14 times with 34 runs scored while 32 pitches happened 6 times with only 11 runs scored).  If you take the equation and solve for 1, you get approximately 20.5 pitches for the Rox pitching and 20.6 for the Rox offensive.  Pretty consistent.

So there you have it...it does appear as you throw more pitches in an inning, the likely of runs being scored increases. 

Follow on questions would be could you establish pitcher effectiveness based on this (i.e., Cook threw 3,068 pitches this year, divided by 20.5 would indicate he should have given up 150 runs (but actually only 102)).  Actually a more representative way to look at this would be average pitches per inning that Cook threw (14.5) which would represent approximately 0.53 runs per inning or 113 runs over his 211 innings pitched.  And of course you can turn this around and say that Tulowitzki saw 1,536 pitches and if you divide by 20.6 then he should have scored about 75 runs instead of the 48 that he did.  But if you look how many pitches he saw per plate appearance (3.6) and multiplying the rate (0.10) by plate appearances then he should have scored only 41 runs.  Lowest pitches per inning average was by Buchholz at 13.4 and the most pitches seen was by Podsednik at 4.5 pitches per plate appearance.