THE BOOK--Playing The Percentages In Baseball

Tuesday, June 01, 2010

Forcing the opposing manager to walk Pujols

Poz asks:

It was a hustle play for Ludwick, exactly the sort of hustle play that we admire in our players. He took advantage of an opponent’s mistake, got himself into scoring position, did exactly what you would want him to do.

Then again — as you have no doubt considered — there is another factor here. Albert Pujols was hitting next. And, of course, the Reds promptly walked Pujols. In other words, by taking second base, Ludwick took the bat out of Albert Pujols’ hands.

Which leads to our question: In the grand scheme of things, was Ludwick’s taking second base a good play or not?

Poz goes through the exercise to show that you’d rather have Orlando Cabrera with the bases loaded, than Pujols with runners on 1B and 3B.  Let me show you a more theoretical answer, and it starts with the average run expectancy chart, which should at this moment be in your back pocket.  For those of you who still have not printed it, or memorized it, go here.  (At one point in the future, I will no longer link to that page.  That chart should be in your wallet, opposite to the picture of your kid.  And if you have two kids, well, shrink their pictures so they fit on one side.  This is baseball dammit, and it should make up half your life.)

Anyway, with the bases loaded and two outs, and an average hitter at bat, that is worth 0.815 runs to the end of the inning. 

With runners on the corners and two outs, that’s 0.538 runs to the end of the inning?  What about with Pujols and runners on the corners and two outs? 

Pujols is a career .435 wOBA hitter, which is about 100 points above the league average.  To convert wOBA to runs, you divide by around 1.15 or 1.20.  So, +.100 / 1.15 = +.087.  So, on average, Pujols is worth about +.087 runs per PA above the average hitter, in an average base/out situation.  You can also look at his WPA/LI career total of 57.5 wins in 6312 PA, or +.009 wins, which is around +.090 runs per PA.  Fangraphs also has his wRAA (runs above average) as +566 runs, which comes out to +.090 runs per PA.  Any way you shake it, on average, Pujols is +.090 runs per PA.

Now, you might be tempted to simply take the 0.538 runs that an average hitter generates with runners on the corner and two outs, and add in Pujols’ +.090, and be done with it.  However, runners on the corner and two outs is not an “average” base/out situation.  In order to figure that part out, you need to know the “leverage” of that base/out situation, or boLI (base/out Leverage Index).  There’s also a simple way to figure out the boLI, and you need to go to this chart.  If you go down to the 1b/3b/2out line, you will see the run value of the out is -.54 runs, which you compare to around -.30 runs for the typical value of the out.  That sets the boLI at around 1.8.  That is, everything that happens in the base/out situation is magnified by 1.8.  You can see the full chart here.

If Pujols really is worth +.090 runs per PA on average, he’s probably worth around .090 x 1.8 = .162 runs per PA with runners on the corners and two outs.  (One could just as well use the LWTS figures for that base/out state and apply Pujols’ specific stats to get a more accurate number.  That would be more correct.  My point here however is to try to find a simpler way so that you can be more comfortable to use this process for other situations.) So, .538 + .162 = .700 runs per PA. 

And that becomes our estimate: Pujols with runners on the corners and two outs plus the average batters coming up generate .700 runs.  An average hitter with bases loaded, 2 outs plus the same average batters coming up generate .815 runs.  And that’s why you don’t see Pujols being IBB with runners on the corners and two outs.  It would have to be a pretty bad hitter for that to happen. 

How bad?  Well, it would have to be -.115 runs per leveraged PA.  And since the boLI was 1.8, that means -.064 runs per average PA.  Which is around -.075 in wOBA.  And if the league average wOBA hitter is .335, that would make our breakeven hitter around .260.  And that’s pretty much the worst true hitter possible in MLB, outside of pitchers-as-batters.  Therefore, in order to walk the best hitter in MLB with runners on the corners and two outs, you have to have the worst hitter in MLB on deck.

(This analysis also ignores the game situation, meaning inning/score.  That requires more leverage index talk.  And if the larger the game LI, the more it makes sense to walk Pujols with runners on the corners and two outs.  That’s the subject of another post.)