THE BOOK--Playing The Percentages In Baseball

Wednesday, October 29, 2008

Marcel Q&A

Someone asked me some Marcel questions, and I gave some answers.  I don’t know that I can quote him, but I will at least quote myself.  Hopefully, you can imagine the questions, or if that reader permits it, I will intersperse his emails as well:

200 PA: It was purely done out of regression.

2 x 600: again, purely regression. In this particular case, I am weighting year T at 5, year T-1 at 4 and T-2 at 3. And I’m adding 1200 PA of league average performance to that. If we divide all these numbers by 5, you get:
1.0 T
0.8 T-1
0.6 T-2
240 average

In effect, I’m saying that we need to add 240 PA of league average production to a player’s recent career to figure out the best forecast.

As for how did I come up with 240 PA, the best way to explain it is that if you take 240 PA for a player for one time period, and 240 PA for the same player in another time period, and you do this for hundreds of players, then your correlation will be r=.50.

r = PA / (240 + PA)

If you took 720 PA for two time periods, then r=.75. (Depends on the era of course. 200 PA might work better at some point, and 260 at some other point. 240 is what I settled on.)

So, if you want to know how many assists or points you need to regress by, you need to figure out how many minutes played do you need such that r=.50. Once you have that, you add that many minutes to a player’s recent career total.

Let me know if all that made sense or not.

***

In my case, it’s the overall player value, say ERA or OPS or wOBA. For hitters, if you figure the OPS for a player for around 200 or 250 PA for one time period (say all odd numbered games 1 through 119) and another time period (say all even numbered games 2 through 120), you will get an r=.50.

If we presume the equation for r is also: r = PA / (PA+x)

Then we can set x=240.

So, for your case, take some overall metric, and then figure out various correlations between two time periods. When you can get the correlation at r=.50 for some time period, simply figure out the number of minutes played you have for each player.

Feel free to continue the discussion if it’s not clear.

***

Nope, I meant in-season.

The correlation coefficient would indeed be r=.50, and yes I mean in the strictly statistical sense. And when I say 240 PA, I mean exactly 240 PA, or thereabouts, not a minimum of 240 PA.

See if you can ask for this:
- each player’s first 480 PA, and whether he got on base (H, BB, HBP) or not
- take a random 240 PA for each player and put that in one group; put the remaining 240 in the other group
- figure the OBP for each player in each group
- run a correlation

You should get r=.50 (more or less). You’ll get that whether it’s OBP or OPS.

If he doesn’t have time, let me know, and I’ll see if I can do it.

***

Sure no prob.

Age adjustment: Yes, later in that thread you are quoting, I corrected myself on that.

Applying age adjustment: I first turn all the numbers as per PA, and then I apply the adjustment for positive categories one way and negative categories (K, CS, DP) the other way.

***

Correct.

***

Sure thing. Feel free to ask any time.