THE BOOK--Playing The Percentages In Baseball

Tuesday, July 26, 2011

Tango’s Lab: wOBA by base state

I’ve been meaning to do this for a few years now.

In 2010, with Cliff Lee on the mound, his team allowed 84 runs to 842 batters.  Tommy Hanson’s team gave up 86 runs to 845 batters.  As you can see, a pretty solid match.

(Note by the way that I didn’t say Cliff Lee gave up 84 runs.  The defense has 9 fielders on the field.  While the pitcher may be the pivotal player in allowing runs, he’s not the only one.  This is why we should always say “the team allowed with the pitcher on the mound X number of runs”.  This is not only accurate, it keeps us from giving too much credit to the pitcher.)

Hanson’s slash line (BA / OBP / SLG) was: .239/.301/.347
Cliff Lee on the other hand: .240/.255/.363

That works out to an estimated wOBA of:

Cliff Lee
= .277

Tommy Hanson
= .300

How is it that Cliff Lee ended with much better results than Hanson overall, but gave up a similar number of runs?  While Hanson’s slash line with runners on base and bases empty was consistent with the league, Cliff Lee was on the mound when bad things happened with men on base:

Cliff Lee
.214/.230/.333 Bases Empty
.288/.302/.420 Runners on Base

The entire difference is basically BABIP driven, but we’re not concerned about this for now.

So, the question is: can we come up with a BaseRuns equation that is dependent on the base-out situation, such that the total runs estimated will be the same for Hanson and Lee? I don’t know the answer to that question yet.

I do want to present a general wOBA equation for bases empty and runners on base.  For bases empty, we have:

0.85: 1B, BB
1.10: 2B
1.50: 3B
2.25: HR

Obviously, a single and walk are identical with bases empty.  A shortcut to get the above, using only the slash line would be:
wOBAe = (2 * OBPe + SLGe - BAe ) * .42

The little e denotes performance with bases empty.

A general equation for runners on base would be:

0.50: BB
0.95: 1B
1.40: 2B
1.60: 3B
1.75: HR

With runners on base, there’s simply little to distinguish the various extra base hits.  So, a shortcut equation would be:

wOBAr = (3 * OBPr + 2 * SLGr + BAr) * .16

The little r denotes performance with runners on base.

Also note that the Leverage Index with runners on base is 1.4, while it’s 0.7 with bases empty.  And that the bases empty occurs 55% of the time.  (Yes, I know that the better you are, the more often the bases are empty.  This is quick shortcuts here.)

So, to combine the above two equations into an overall wOBA, we get:
wOBA
= wOBAe * 0.7 * .55
+ wOBAr * 1.4 * .45

So, if we take Cliff Lee:
.214/.230/.333 Bases Empty
.288/.302/.420 Runners on Base

We can convert that as:
wOBA
= (2 * .230 + .333 - .214 ) * .42 * 0.7 * .55
+ (3 * .302 + 2 * .420 + .288) * .16 * 1.4 * .45

= .299

Tommy Hanson:
.233/.289/.349 Bases Empty
.249/.319/.343 Runners on Base

We can convert that similarly to:
wOBA
= .303

As you can see, a wOBA based on looking at performance by men on base and bases empty makes Cliff Lee and Tommy Hanson equivalent.