Why I Distrust Rate Statistics (Or, Fun With Homers) « Forums

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Why I Distrust Rate Statistics (Or, Fun With Homers)

(5 posts)

Zachary Klaas
Member
Here are some numbers I just crunched for Mark McGwire showing rate statistics for how many home runs he hit in the various years he played.

Most humans who watch this sport prefer to summarize a slugger's prowess via the raw number of home runs hit during a year. But it's also possible to represent things as a "home run average", similar to a batting average except you're dividing homers by At-Bats. (An even more exacting version of the average might divide homers by Plate Appearances, perhaps.)

These wouldn't penalize the player who doesn't play as many games as the person who is leading in raw numbers of homers, so it should be fairer to the player in terms of showing home run hitting ability. The leader in raw homers might be shown to be a "better home run hitter than he really is" because he got to play more games.

Okay, so here are McGwire's numbers for HR, HR/PA and HR/AB over the course of his career, sorted by descending HR/AB.
```
Year	HR	HR/PA   	HR/AB
1998	70	0.102790015	0.137524558
2000	32	0.099688474	0.135593220
1999	65	0.098335855	0.124760077
1995	39	0.092417062	0.123028391
1996	52	0.094890511	0.122931442
1997	58	0.088280061	0.107407407
1993	9	0.084112150	0.107142857
2001	29	0.079670330	0.096989967
1992	42	0.073555166	0.089935760
1987	49	0.076443058	0.087971275
1990	39	0.060000000	0.074569790
1989	33	0.056218058	0.067346939
1994	9	0.052325581	0.066666667
1988	32	0.050393701	0.058181818
1986	3	0.051724138	0.056603774
1991	22	0.037606838	0.045548654
```
Though his 70-HR season still is tops on the list, a 32-HR season is next. Then comes the 65-HR season, but then comes a 39-HR season.

His last creaky season, in which he hit 29 HRs, comes off on this better than his sensational 49-HR rookie year.

Batting averages are, of course, tossed out when the number of At-Bats is so low that the ratio stat could just represent a fluky streak rather than a sustained performance. But what's interesting about this is that McGwire did play enough to have a ratio stat "count" in some seasons when he nevertheless did not play enough to make a serious run at the home run crown for that year...and in some of those years he was hitting homers at a higher clip than he was in years when he did win the home run crown (and by spectacular amounts as well).

What do I conclude from this? Raw numbers of homers _are_ what we want to measure here. What would the Cardinals have preferred to have on their team? The McGwire of 2000 (32 HRs, .135 HR/AB) or the McGwire of 1999 (65 HRs, .124 HR/AB)? _Obviously_ McGwire '99.

McGwire's HR numbers were _only_ higher in 1999 than 2000, however, because McGwire himself played in more games in 1999.

(All of this may be relevant to another thread on this forum site where we were recently arguing about how it might be preferable to have a player who plays more games and gets more Outs than a player with a higher Range Factor, which is a ratio statistic relating Outs to Innings Played, and which can be high even if one plays few games.)
Posted 4 weeks ago #
Padman Jones
Member

This is a good post, and I like the idea. I'd just like to add that it seems like it'd be worthwhile to see what kind of variability the HR rate has - for example, are the highs and lows of McGwire's career a typical range? I'll probably check on that later this afternoon.

Posted 3 weeks ago #
Zachary Klaas
Member

Well, the reason I chose McGwire is that he's had injuries over the years, so I knew from having followed his career that there would be some years when he would have played about half a season or so and thus had diminished HR production for the year, even if he was still hitting them at the same kind of clip in HR/AB as other seasons where he played the full year.

One would generally not expect the HR/AB stat to be that variable under injury free conditions for full-time players, but of course there are examples of people just busting out in a couple years. Take, for example, Davey Johnson in 1974 (his HR/AB was 0.076923077 that year, about 1.5 times his next highest figure of 0.051282051). Or Brady Anderson in 1996 (his HR/AB was 0.086355786 that year, about 2 times his next highest figure of 0.042553191). Compared to those, there's really not much variability even in McGwire's figures...but those were extremely fluky cases of people discovering the HR really in only one year of their entire careers.

Posted 3 weeks ago #
recca
Member

Notice how people don't use home run rate as a predictive statistic. There's a reason for that.

Posted 2 weeks ago #
lee
Member

Another way to look at the guys with the big power HR numbers is to explore their relative rate of batting contact.

The current World Series is a case in point. Ryan Howard is a legitimate 40++ HR guy; but if he fans 160+ times a years, magnifying glass calls our attention to the relative randomness of extreme long ball.

While the whiff exaggeration is more pronounced with howard than McGwire, that is largely a consequence of playing time. McGwire was often out with injuries; but he K'd a great deal relative to AB & PA.

Sure, A-Rod whiffs a good deal; but overall, he is more consistent with batting contact; and the HR is not all that universally the sole catalyst of batting runs.

The Yankees have seven players with 20+ Hr's and nothing near the whiff rates of Werth or Howard.

A guy who fans over 160 times can be expected to whiff once every game. Will that predictable whiff come with the bases loaded? Empty? One on? Then the HR, one in every four games: when will that come: late and close? trailing 10-4, with one man on? A 17-4 romp? A 1-0 shutout?

Predictable K's + random HR's often = disappointment for bigg buck$$$$$ paid out.

Posted 2 weeks ago #