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— A Timely Look at Transactions as They Happen

Monday, July 13, 2009

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.

Dan Szymborski Posted: July 13, 2009 at 06:24 PM | 16 comment(s) Login to Bookmark
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   1. Zoppity Zoop Posted: July 13, 2009 at 07:00 PM (#3252039)
That was quick.
   2. Mike Emeigh Posted: July 13, 2009 at 07:05 PM (#3252052)
This is a fairly well-known phenomenon, with a fairly simple conclusion: Teams prefer consistency from better-than-average performers and inconsistency from worse-than-average performers.

-- MWE
   3. Walt Davis Posted: July 13, 2009 at 07:21 PM (#3252068)
Seems to me the question is whether Zito is really more inconsistent than the standard pitcher of his skill-level (or even the standard pitcher). I recall a few years ago someone praising some "#5" starter (as we quaintly thought of them in those days) for throwing a quality start something like 40-50% of the time (the exact number escapes me) and I looked at the other similar pitchers that season, and they'd all thrown about the same %age of quality starts.
   4. Walt Davis Posted: July 13, 2009 at 07:25 PM (#3252076)
Schizo Samwell .652

He clearly doesn't know how to win.
   5. Der Komminsk-sar Posted: July 13, 2009 at 07:25 PM (#3252077)
and it's not exactly common knowledge outside of hard-core statheads
It isn't?
   6. GGC don't think it can get longer than a novella Posted: July 13, 2009 at 07:28 PM (#3252080)
I don't consider myself hardcore and I'm aware of Michael Wolverton's old work in this area.
   7. zenbitz Posted: July 13, 2009 at 07:36 PM (#3252089)
After doing this, I simulated 50,000 Giant offense outings and 50,000 Zito defense outings.


I am pretty sure when I die and go to H.E. double hockey sticks, Tommy Lasorda will be there waiting for me in the "Clockwork Orange" screening room with the video.
   8. puck Posted: July 13, 2009 at 07:52 PM (#3252106)
I did not know about this effect. Szym has a pretty good explanation, but are there cites to other studies?

This would seem to bode well for the Rockies, who appear to have two such jekyll/hyde types in Jason Marquis and Jorge de la Rosa. And maybe a 3rd in Jason Hammel, who is Hyde in home games (7.62 ERA) and Jekyll in road games (1.97).

Does this work for hitters, too? I wonder if the feast or famine type player tends to put together more WPA than a more consistent one.
   9. Danlby Posted: July 13, 2009 at 09:25 PM (#3252200)
Certainly "main stream" fans think consistency is more valuable, and there's a list of secondary reasons: preserves the bullpen for the next day; the notion that a consistent starter "pitches to the score" and keeps his team in every game...

Re #2, I could see how above-average hitters are more valuable when they're consistent, but with starting pitchers, is it ever true? I think if you defined "likely" starts more realistically, you'd find that, no matter the true talent level, you'd rather have Jekyll and Hyde. How about an assessment based on the win probabilities of these nine outcomes:

ER = 9 - IP and IP = n, where n = 0 through 9.

A 5.00 ERA Sam Stochastinator would actually be: Nine 9.0 IP, 0 ER starts and Five 0.0 IP, 9 ER starts. Based on your numbers, that'd work out to a .640ish winning percentage. A 4.00 ERA Sam S. would generate a .690ish WP with nine shutouts and four 0.0 IP, 9 ER duds. Does it get much better than that?
   10. Orangepeel Posted: July 13, 2009 at 10:29 PM (#3252256)
I think this happened to Jon Garland a lot, at least in 2007 and (sort of, maybe) in 2006.
   11. Nineto Lezcano needs to get his shit together (CW) Posted: July 14, 2009 at 03:49 PM (#3253135)
A 5 ERA pitcher doesn't allow 5 runs in 9 innings; he typically allows closer to 5.5 runs in 9 innings, due to unearned runs. That's going to matter for Pythag.
   12. Bizarro ARod Posted: July 14, 2009 at 05:16 PM (#3253292)
Using the basic Pythag formula {RS^2/(RS^2+RA^2)}, I get a different number:

SF IP 781, Zito IP 106, Zito RA 59

Extrapolating to SF IP, RA becomes 435

SF RS 368

Basic Pythag I get .417
   13. Ray (RDP) Posted: July 18, 2009 at 12:15 AM (#3258033)
Certainly "main stream" fans think consistency is more valuable,


Yes. Mainstream fans and sportswriters. How many times do we hear sportswriters whining about a pitcher being "inconsistent," without realizing that being inconsistent is preferable to being consistent?
   14. cardsfanboy Posted: July 18, 2009 at 12:26 AM (#3258051)
Yes. Mainstream fans and sportswriters. How many times do we hear sportswriters whining about a pitcher being "inconsistent," without realizing that being inconsistent is preferable to being consistent?

I actually liked the comment in post 2. It's a lot closer to the way that I think it should be portrayed.

2. Mike Emeigh Posted: July 13, 2009 at 03:05 PM (#3252052)

This is a fairly well-known phenomenon, with a fairly simple conclusion: Teams prefer consistency from better-than-average performers and inconsistency from worse-than-average performers.

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