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.
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...
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.