Barry Zito, Consistency, and the 2009 Giants

In a recent column, Tim Kawakami suggested that Barry Zito was worse than his statistics suggest due to his inconsistency, that his higher percentage of “dud games” hurt the San Francisco Giants win-loss record.

So, is it true?  It’s a quick, simple question, so I went and did a quick look at the distribution of Giant run-scoring and Zito run-scoring to try to ascertain if Zito’s really hurting the Giants above-and-beyond having mediocre statistics.  For the purposes of this exercise, I’m considering Zito’s ERA as being 5.00 instead of 5.01.

The first thing to do is make a quickie model of the Giant offense and Zito’s run allowance.  I don’t want to consider past ability or any concept of “true ability” here, which makes making a model of both these things considerably more problematic.  However, you also run into the problem that we have very small sample sizes that can also cause problems in our models.  For example, the Giants have scored 4 or 6 runs on 10 occasions and 5 runs on 8 occasions, so we can’t simply choose a random Giant run/9 outing and a random Zito run/9 outing match them and call it a day.

To make a long story short, we want to extrapolate the likeliest model of the 2009 Giant offense and 2009 Zito outings.  Using STATISTICA, the math nerd’s version of a sex shop, we can extrapolate a bell curve with the skewness and kurtosis that we see from the data, and sample the data so we can easily see the conclusions.

After doing this, I simulated 50,000 Giant offense outings and 50,000 Zito defense outings.  So, how did theoretical Zito do with the theoretical Giants?

                   WPCT    PYTHAG

Zito Model         .433      .367

As one can see, a pitcher with an ERA of 5 and Zito’s distribution of runs allowed theoretically allows a team that scores like the 2009 Giants to win more often than the generic distribution that the James so-called Pythagorean Theorem predicts.  How about some other distributions (all distributions below had a simulated ERA within 1/50th of a run of the ideal 5.00).

- Mr. Consistent, a pitcher that allows exactly 5 runs every 9 innings.

- The Bell Curve Basher, a pitcher that is equally likely to allow every run total between 0 and 10 per 9 innings.

- Mr. Meth, a pitcher that allowed either 2 or 8 runs every 9 innings.

- The Stochastinator, a pitcher that allows either 0 or 10 runs every 9 innings.

- Schizo Samwell, a pitcher that allows 0 runs in 9 innings 2/3 of the time and 15 runs/9 the other starts.

So, how does this Rogue’s Gallery fare?

                   WPCT

Schizo Samwell     .652 

The Stochastinator .498    

Zito Model         .433

Bell Curve Basher  .383

Mr. Meth           .376

Pythagoras         .367

Mr. Consistent     .317

So, why does this happen?

In essence, we’re looking at a phenomenon caused by the hard floor of zero.  A team cannot score or allow fewer than zero runs, and given the patterns in scoring in baseball, in which teams frequently score and allow 5 more runs a game more than average in a single outing but cannot score or allow more than 5 runs less than their average, you run into the issue in which the depreciating values of high numbers of runs cannot be counterbalanced by the depreciating values of low numbers of runs.

As an extreme example, imagine if Barry Zito threw 2 complete games this season and allowed 30 and 29 runs in those games respectively.  Those games were essentially 100% losses for the Giants and the chances don’t improve all that much for the Giants if he cut those runs by a third.  But outside of those 2 losses, every other game Barry threw 5 innings in would be a win for the Giants and he’d be one of the most valuable pitchers in baseball.

Now, depending on the quality of the team and the quality of the pitcher, the break-even points for value shift considerably.