Calculating Relative Stats (July 30, 2003)
I posted this on the Fanhome thread
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Suppose the average hitter hits 10 HR / 500 AB at the Astrodome, and 20 HR / 500 AB at Coors.
You have Mark McGwire who hits 50 HR / 500 AB at the Astrodome. How would he do at Coors?
Now, the traditional example is to say "hmmmm... the average player doubles his output... so let's double McGwire to 100 HR / 500 AB."
This is wrong.
Now, let's try the Odds Ratio method. 20/480 divided by 10/490 = 2.042 factor.
50/450 x 2.042 = .227 HR/ nonHR, or 92 HR / 500 AB.
Hmmm, that looks better no?
How about I tell you the following:
average hitter at Astrodome: 10 HR, (PA = 100 long fly balls, 100 other flyball, 200 GB, 100 K).
average hitter at Coors: 20 HR (and rest the same).
McGwire at Astrodome: 50 HR (PA = 150 long flys, 100 other flys, 150 GB, 100 K).
What do we expect McGwire at Coors?
Well, we see that Coors doesn't give you MORE long flyball (100 in both cases for our average hitter). So, we can expect McGwire to also have 150 long flys.
Now, let's use the Odds Ratio method, but using long flys as the opportunity.
average hitter: 20/80 divided by 10/90 = 2.25 factor
McGwire: 50/100 x 2.25 = 1.125 HR per long non-HR fly, or 79 HR per 150 long flyballs.
Ah, ha!! Quite a large difference wouldn't you say?
It's not like McGwire's HR would split into 2, and you'd go from 50 to 100 right?
So, the #1 thing to get right, is to get the opportunity context of that event. For HR, it's almost certainly the number of long fly balls.
If you want to argue that Coors turns medium flys into long flys, I can accept it. That's another factor you have to figure first.
If that average player had 100 long flys and 200 total flys at Astrodome, and 120 long flys and 200 total flys at Coors, that's your first adjustment to do for McGwire.
THEN, you do as I've mentioned.
For Cobb, his HR are inside-the-park as well, so you have multiple opportunity contexts to understand.
Hope that was clear?
--posted by TangoTiger at 05:42 PM EDT
Posted 6:09 p.m.,
July 30, 2003
(#1) -
tangotiger
In that new McGwire example, with Coors affecting the medium/long flyballs, he gets 173 long flys, and 82 HR.