Sunday, April 03, 2005
The Markov Value of the Stolen Base: Part II
I need to throw in a big caveat regarding my previous post evaluating the value of the stolen base. Using the Markov process, i calculated that stolen bases have a minimal effect on runs scored over a season. What naturally follows is that the more runs you score versus runs allowed, the more games you would expect to win. (the famous Pythagorean Theorem of Baseball)
BUT BEWARE! Runs do not equal actual wins.
All runs are not equal. A run that ties a game in the ninth is more significant than a run while down by 10.
Boston is down by a run in the bottom of the ninth in Game 4 of the ALCS. Kevin Millar leads off the inning with a walk. Francona ponders how to give his team the best chance to win, and chooses pinch-run Dave Roberts and his 92.7% 04 SB rate for the snail-like Millar. Roberts successfully steals 2nd, and scores on an RBI single. Game is tied, and eventually won in extra innings.
The Markovian value of Roberts’ stolen base is a mere 0.231 expected runs. That contribution, however, was the critical run that saved the game.
The following article is a good read on changes of managerial strategy at various stages of the game.
http://ite.pubs.informs.org/Vol5No1/Bickel/
To quote the article:
The types of strategies that maximize expected runs may not be the same as those that maximize the probability of winning late in the game. It is for this reason that baseball strategy changes as the game progresses ... The objective of baseball is to win, not to score runs.
If the game is close, the managerial decisions in the late innings may not optimize runs scored versus runs allowed. At such times, going for a single run can be the best chance of winning the game, whether by a sacrifice bunt, hit and run, or a stolen base - "expected" runs be damned.
BUT BEWARE! Runs do not equal actual wins.
All runs are not equal. A run that ties a game in the ninth is more significant than a run while down by 10.
Boston is down by a run in the bottom of the ninth in Game 4 of the ALCS. Kevin Millar leads off the inning with a walk. Francona ponders how to give his team the best chance to win, and chooses pinch-run Dave Roberts and his 92.7% 04 SB rate for the snail-like Millar. Roberts successfully steals 2nd, and scores on an RBI single. Game is tied, and eventually won in extra innings.
The Markovian value of Roberts’ stolen base is a mere 0.231 expected runs. That contribution, however, was the critical run that saved the game.
The following article is a good read on changes of managerial strategy at various stages of the game.
http://ite.pubs.informs.org/Vol5No1/Bickel/
To quote the article:
The types of strategies that maximize expected runs may not be the same as those that maximize the probability of winning late in the game. It is for this reason that baseball strategy changes as the game progresses ... The objective of baseball is to win, not to score runs.
If the game is close, the managerial decisions in the late innings may not optimize runs scored versus runs allowed. At such times, going for a single run can be the best chance of winning the game, whether by a sacrifice bunt, hit and run, or a stolen base - "expected" runs be damned.
