Rangers/Mariners Game

April 12, 2005

I chronicle the WPA of last Saturday’s Rangers/Mariners game over at The Hardball Times.  If you have any questions or comments about the article, you can post them here.

A central issue I raise in the article is how to measure the criticality (or importance, or leverage) of a specific situation.  There are three definitions I know of:


These are three very different ways of using Win Probability to define criticality (outs, batter, runs), though all three are based on the same idea: calculating the difference between the current state and some potential future state.

I have another idea.  What if criticality is defined as the difference between two potential future states?  For instance, what if it is defined as the difference between a strikeout in the current situation vs. a home run, given the current situation?

The notion of a “criticality measure” may be the most important thing to come out of Win Probability.  It would be something many fans would find useful, I think.  So it’s worth kicking around.



Why use just two outcomes - there may be situations where certain events are over- or under-rated compared to other events.  Why not take into account all possible outcomes and use the standard deviation of the win probabilities for each situation?

Yes, the next question is how, exactly… but I think that’s the way to go.

Posted by Sky  on  04/12  at  10:41 AM

Well, that’s interesting, Sky.  My approach would basically be to take the “minimum” and “maximum” outcome of the situation and rate the criticality as the difference between the two.  I think you’re suggesting looking at all outcomes of each situation and somehow weighting them to come up with an weighted outcome difference based on standard deviation.

The thing is, how do you weight them?  Is each possible variation of score/out/base situation equal?  That strikes me as even more arbitrary than just the min/max approach.

Of course, I’m sure I’m not totally understanding your suggestion.

Posted by studes  on  04/12  at  10:49 AM

I’m not totally understanding my suggestion, either.  I’ll think about it some more.

Here’s an excellent thread from FanHome discussing leveraged index and Keith Woolner’s version.

http://mb7.scout.com/fbaseballfrm8.showMessageRange?topicID=947.topic&start=1&stop=20

Posted by Sky  on  04/13  at  05:31 AM

Sky, that link is great.  I can’t belive I was in on the beginning of that thread, but didn’t follow through.

Tangotiger and David seem to come together around the idea that measuring criticality by outs isn’t perfect, but better than runs.  I trust their instincts a lot, and this would reinforce the notion that Drinen’s “P” is a good measure for what we want to do.  I’ll try and post more thoughts about this later today or tomorrow.

Posted by studes  on  04/13  at  08:21 AM

The min/max line of thought makes sense to me. Of course it would seem triple play/double play (when possible) rather than strikeout would be min and homerun max.

How in the heck though can you accurately assign values though to all the incremental possible outcomes which lie between these min/max points?

Seems like it all comes down to bases, outs, runs but.......

Suppose man on 2nd no out as present state.

Which is assigned higher value for future state?
a) men on first and second no out or
b) man on third one out

I guess would have to depend on inning(outs) and score but my the possible permutations.......(sigh).......??.....

Posted by Mike  on  04/13  at  11:24 AM
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