from Amazon
Saturday, September 29, 2007
Why saving a play is worth 0.8 runs
This is the common explanation I give:
Suppose a team with Ozzie at shortstop gives up on average 12 non-home run hits, and 2.6 walks every game (which of course is 27 outs) . Applying .50 runs per non-home run hit (I know it should be closer to .55, but I just want to keep it basic), and .30 runs per walk, and -.10 runs per out, and we get 4.08 runs scored per game. And per game, we see that Ozzie’s team faces 41.6 batters (again, let’s not worry about double plays, etc).
Now, let’s say Ozzie was traded for Spike, and let’s say for every 41.6 batters faced, there is one ball that Ozzie gets to that Spike doesn’t. So, for those 41.6 batters, Spike’s team records 13 non-home run hits (1 more than Oz), 2.6 walks, and 26 outs (1 less than Oz). However, there’s still one more out to go! Since Spike’s team gives up 13 non-home run hits / 26 outs, we can estimate that this team will give up 13.5 non-home run hits, 2.7 walks, and 27 outs per game ( a total of 43.2 batters, a remarkable 1.6 MORE batters than Oz). Anyway, applying our linear weights constants, and we see that Spike’s team gives up 4.86 runs per game.
This number is .78 runs MORE than Ozzie. This is the result of Ozzie getting to one more hit than Spike. .50 runs for the hit, and about .30 runs for the out gives you the .80 runs.
You can also try it with a Markov calculator, like here:
http://www.tangotiger.net/markov.html
Click CALCULATE, and you’ll get 4.905 runs. Click the BACK button, and drop the hits down by 1. You get 4.151 runs. That’s a difference of 0.754 runs. Go BACK, and bring the original value up by 1 instead. Now you get 5.781 runs, or +.876 runs. That’s an average of +.815 runs. Turning a sure hit to a sure out (or a sure out to a sure hit) has an enormous impact. It’s something like +.08 wins each time.
If you still don’t believe me, find all games where one team had exactly one more error than the other team. You will likely find that the team with fewer errors won 58% of the time. Control for team quality if you like.