### Monday, February 07, 2005

**IN WHICH I DEFEND MY MATH**

I don't think I explained something very well.

I said:

So, in looking at Pinto's methods, we can easily see how many outs each shortstop made against expected, which is different from average. What I did here was go through and convert those outs to runs. For all the SS's he lists, the mean Runs Against Expectation was -16.22 per 4000 balls in play ...

Which Richard translates to:

Again going by Pinto's numbers, the average shortstop was 16.22 runs "below average". Chronicles takes this number as 16.22 per 4000 BIP - it isn't.

Actually, it was.

In the data provided by David Pinto, there were 38 shortstops who were in the field for a total of 114,599 balls in play. They made 13,820 successful plays where 14,436.33 were expected, so they were -616.33 plays. That comes out to -464.731 runs, by the method I've been using, which is described and linked to in my original SS post.

So that's -.00406 runs per ball in play ... and when you multiply that by 4000, you get -16.2211 runs against per predicted per 4000 BIP.

David Eckstein, the source of all this, made 356 plays where 400.26 would have been expected, That's -44.26 plays and -33.3734 runs. He had 3562 balls in play, so that's -.00937 runs per play, and over 4000 BIP that's -37.4771. Now, we've established that the average for this group was -16.2211 runs per 4000 BIP, so Eck was -21.256 runs against that.

Now, we've shown that he was -33.3734 runs against predicted in his 3562 BIP. If we apply the average runs per play to that 3562, we find that the average SS was -14.4617 runs over 3562 BIP*. As Eck was actually -33.3734, that means he was -18.9116 against that average, which is how I derive the numbers portrayed here.

Hope that clears it up.

*FYI, there is rounding off here, if you're looking to duplicate all this in a spreadsheet. The runs per BIP for the SS were actually -.004055282, which I rounded off to -.00406 when I was making the calculations. This makes an ever-so-slight difference, but there you go.

**UPDATE:**In re-reading Richard's post, I found the source of the confusion ... remember the sample was -616.33 plays ... and if you divide that by 38 (the number of players), you get 16.22 - the same number of runs below predicted the group was per 4000 BIP! This is what the fates call a coincidence.

This was my fault for being very imprecise in my language and using the word "mean" where I should not have. Hopefully the above makes sense.

Comments:

"So that's -.00406 runs per ball in play ... and when you multiply that by 4000, you get -16.2211 runs against per predicted per 4000 BIP."

Ahhh... I see why I kept coming up with -16.13. I screwed up my spreadsheet so I was coming up with nothing for extra bases. I always make one of those stupid mistakes. My bad.

Ahhh... I see why I kept coming up with -16.13. I screwed up my spreadsheet so I was coming up with nothing for extra bases. I always make one of those stupid mistakes. My bad.

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