# Walking Albert Pujols with the bases loaded

August 14, 2009 1 Comment

*Hello, my name is
Brian Kenney and I’m another writer from Mike’s blog 4parl.wordpress.
I’m a huge Cardinals fan, as you might notice from my first post-which
is about a week and a half old by the way. It took a while for me to
get publishing privileges on my account . In about a week I’m going to
go to The University of Missouri-Columbia for my first year of college
where I’m going to study mechanical engineering (so my posts might be
few and far between). Some of my hobbies include hockey, golf, and
poker. *

Albert Pujols is the undisputed best hitter in the game. His batting

numbers this year are Bonds-esque, and he is receiving what is now

known as the Bonds treatment. He currently has 36 intentional walks,

which is a whopping 20 more than 2nd place Adrian Gonzalez. As most of

you I’m sure know, intentional walks are almost always an incorrect

play. There is one situation in particular, however, where an

intentional walk is plain ridiculous: when the bases are loaded.

However, many talking heads are debating whether it is a smart idea to

intentionally walk Albert Pujols when the bases are loaded. The basis

of their arguments comes from the fact that Pujols has been insane with

the bases loaded this year. 7/9 with 5 home runs. The sample is so

ridiculously small that almost no useful information could be obtained

from it. Anyway, just how bad of a decision would it be to walk Pujols

with the bases loaded? Let’s break it down.

For the year, Pujols’ at-bats results in the following x % of the time (discounting IBB):

Out-60%

1b-13.5%

2b-5.8%

3b-.2%

HR-8.4%

BB-10.7%

SF-1.2%

The mere fact that a Pujols’ AB with the bases loaded will result in an

out (and 0 runs) 60 percent of the time should tell you that walking

him intentionally is borderline insane. Let’s break down the numbers to

see just how insane it is, though.

(.60)(0)+(1)(.107)+[1(.135*.25)+(2(.135*.75)]+[2(.058*.5)+(3(.058*.5)+(.002)(3)+(4)(.084)+(.0117)(1)=

0+ .107+ .2025+ .683+ .058+ 087+ .006+ .336+.0117=.84785 runs.

*I assumed a single would result in 2 runs 75% of the time and 1 run

25% of the time. I also assumed a double would score 2 runs 50% of the

time and 3 runs 50% of the time.

So, an intentional walk will result in 1 run 100% of the time. Pitching

to Pujols will result in .84785 runs on average. The choice is clear,

especially when you consider the caliber of players hitting behind

Pujols. Matt Holliday and Ryan Ludwick are no slouches, and their

positive run expectancies make this decision even easier.

For more complete analysis you need to calculate the probabilities of the Cards scoring various numbers of runs. Your analysis only shows that if the opposing team wanted to minimize the expected number of runs it gives up, they must pitch to Pujols. But it is not clear that this is the best decision in a two run game with two outs in the bottom of the ninth with a speedster on second. Nobody is credibly saying Pujols should be walked every time he’s up with the bases loaded. The interesting research question is: In what bases loaded situation should Pujols be walked, if ever?