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Thursday, January 20, 2005
technical stuff
this is an exchange between me and alec that i thought you would find interesting. it's about the connection between speed and batting average. you see, a long time ago i found a way to relate con and pow to average. for a while actually the pow formula was expressed so that con*pow was a predictor for average. but i junked that in favor of simplicity. anyway my letter is a response to alec's. i have the nagging feeling that i could be clearer about this, but i often have that feeling.

yes, you can. what you wanna do is separate the weak contact, where
speed matters, from the line drives, where it doesn't. a good general
practice is to use pow*2 as the line drive factor; everything else is
weak contact.

the problem is one season is not a good enough sample size to get a
reed on batting average. it takes several seasons. so you have to
calculate speed over several seasons and then average. it's really not
hard to do. i should write about it.

On Wed, 19 Jan 2005 10:24:54 -0600, Alec Wood wrote:
> while i'm on the topic of slow guys, could you use that predictor as a
> method of determining the speed pf a player? EG, calculate the error
> between predicted average and actual? a sort of "speed factor"...
> let's try patterson:
> 632 50 168 24 39 .073 .734 .136 .266
> (0.266 - ((0.734/4)+(0.734*0.136/2)) ) / 0.266 = 0.127
> and, say, ichiro:
> 707 53 63 8 29 .070 .911 .057 .372
> (0.372 - ((0.911/4)+(0.911*0.057/2)) ) / 0.372 = 0.322
> how about sosa in '96:
> 502 39 134 40 23 .072 .733 .171 .273
> (0.273 - ((0.733/4)+(0.733*0.171/2)) ) / 0.273 = 0.102
> Well, just a thought...
> -alec

here's how it works: hard-hit balls tend to be about half hits half outs. we're talking about deep drives and deep flies here. balls that end up being doubles and home runs. and outs. some players hit more line drives, thus more singles, thus their batting averages are higher than predicted. but we're getting ahead of ourselves. or not. the thing is, they sacrifice home runs. they could hit more home runs, but don't. so they get a higher batting average instead.

the cool thing about wal con pow is you can look at it and know the player's value. he may have fewer home runs and more batting average, or he may have more home runs and less batting average, but the walconpow's will be the same. then you can look at home run/double ratios to see if he's a fly ball or a line drive hitter. or a groundball hitter.

anyway, half hits half outs. con/4 + con*pow/2. so all of the doubles and home runs are accounted for. how? con*pow/2 is half of them. what about the other half? they're contained in con/4. because con/4 also contains those contacts that are hit hard. half of those hard hits are doubles and home runs, so that's con*pow/4. the other half are outs. number of hard hit outs = number of doubles and home runs, so that's another con*pow/4. con*pow/4 + con*pow/4 + con*pow/2 = con*pow, so we've accounted for all the doubles and home runs.

maybe this can be expressed better as a mathematical derivation:

avg = con/4 + con*pow/2

avg = (con - con*pow + con*pow)/4 + con*pow/2

avg = (con - con*pow)/4 + con*pow/4 + con*pow/2

con*pow/4 expresses the shit i didn't explain this very well. i have the feeling this is not helping.

let's do it this way. there are as many hard hits as there are hard hit outs. hard hits per contact = pow. so hard hit outs per contact = pow. so hard hits + hard hit outs per contact = 2*pow. so hard hits + hard hit outs per at-bat = con*2*pow. what about weak contact? well, the rest is weak contact. so that's con - con*2*pow. we figure a quarter of weakly struck balls end up as hits, the rest outs, so weak hits is (con - con*2*pow)/4, and weak outs = 3*(con - con*2*pow)/4. anyway lets add up all the hits:

weak hits + hard hits = (con - con*2*pow)/4 + con*pow

weak hits + hard hits = con/4 - con*pow/2 + con*pow

weak hits + hard hits = con/4 + con*pow/2

that was a lot better. i have to go grocery shopping. but the point is you can look at expected batting average and see how much a player exceeded that expectation and you can call that speed. unless it comes from too many line drives. but speed only comes into play on weak contact. so you have to look at weak contact, which is con-con*2*pow, to isolate a speed factor. then you can say

batting avg = speed*(con-con*2*pow)/4 + con*pow

voila! really that's speed + handedness. because lefties are closer to first. you could adjust for that. you can always adjust for things.
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