Question: More fun with BINOMDIST

Okay... this is probably easier than I think and I just suck at math, or I'm so bad at math that it's a lot more complicated than I think it should be... Basically, I'm trying to figure out how using something relatively straightforward in Excel like BINOMDIST, how, given a player's wOBA, we can figure out, over a certain number of PAs (say, 700), what the player's chances of having a better or worse wOBA than his expected. Actually, I'm trying to do this with respect to wRAA, so that I can figure out the odds of a player "hitting well enough" to play position x, say, 1B (+12.5). The problem of negative numbers might come up... I dunno. Lil' help?

9 months ago devil_fingers 11 comments 0 recs |

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I'm interested to know this as well, yet completely clueless.

by R.J. Anderson on Jan 22, 2009 12:53 PM EST reply actions 0 recs

SO SOMEONE HELP US!!!!!111111ONE

How am I supposed to graphically make fun of players and GMs without this important tool?

I guess some of the issues are:

what the number of trials? PAs over one full-time season? sasy, 700 (a “full” season that’s appropriate to pos. adjjustments — I know few get it)

But what is the probability of a true talent .340 hitter being above average? Is there a simply calc? Could we get it from, e.g., CHONE’s percentages? I messed with this a bit in Excel,but couldn’t get it right…

What is the “success” number we’re trying to achieve?

Am I going about this all wrong?

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by devil_fingers on Jan 22, 2009 1:05 PM EST up reply actions 0 recs

I did one

but it has to be wrong, since I know there aren’t any possibilities for a below average score…. maybe I should change the baseline to replacement

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by devil_fingers on Jan 22, 2009 1:44 PM EST reply actions 0 recs

but that still wouldn't be work, now that I think of it

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by devil_fingers on Jan 22, 2009 1:44 PM EST up reply actions 0 recs

wOBA does not fit the binomial distribution, as per The Book.

They do discuss a way to translate it so you can use the binomial assumption. There’s even an Appendix in the the back that’s more geeky than hjmoore’s recent FanPosts here.

Beyond the Boxscore // Calling BJ Upton lazy is lazy.

by Sky Kalkman on Jan 22, 2009 5:18 PM EST reply actions 0 recs

Although, devil_fingers, the general approach goes like this:

When doing the team win distribution, avgWins/162 (which we could also call winning percentage) is your rate . 60 or 90 or whatever is your level of success.

For wOBA, you’ve already got your rate (analogous to winning percentage). If a player’s mean wOBA projection is .340, that’s your rate for each plate appearance. You could interpret it as a .340 chance of success, although that doesn’t mean much because of its construction (and it’s not actually accurate, as per my comment before this one: see The Book). Then, using .340 and the player’s expected PAs, you calculate the probability of getting a certain number of “successes”. Those successes divided by the total PAs is the target wOBA.

For example, given a mean wOBA of .340 and 700 PAs, the probability of posting a .350 wOBA would go like this:

700 * .350 = 245

followed by:

=BINOMDIST(245,700,.340,1)

Except for, you know, the whole point I’ve made twice about wOBA not being binomial.

Beyond the Boxscore // Calling BJ Upton lazy is lazy.

by Sky Kalkman on Jan 22, 2009 5:31 PM EST up reply actions 0 recs

yeah, thanks

I actually did finally get my own copy of the Book (shhh…), but that stuff is a bit beyond me at this point.

It doesn’t have to be wOBA, it could be anything that results in runs above average/# of plate appearances. I guess what you’re saying is that there isn’t an easy and accurate way to do something like that, to see the likely-hood of MIke Jacobs being 12.5 runs above some average over 700 PAs.

It would be fun to do it with defense, at least, using CHONE projections per 150, and I messed with it, but I still don’t think I did it right. Negative numbers cause problems, of course.

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by devil_fingers on Jan 22, 2009 5:42 PM EST up reply actions 0 recs

No, it's pretty easy:

I guess what you’re saying is that there isn’t an easy and accurate way to do something like that, to see the likely-hood of MIke Jacobs being 12.5 runs above some average over 700 PAs.

I’ll look for the wOBA modification tonight. It’s the EXACT SAME binomial equation, you just have to do a bit of arithmetic to figure out the pieces of the calculation. Over 700 PAs, find the wOBA that corresponds to +12.5 runs above average. Multiply that wOBA by 700. That’s your “success” number. Plug the player’s projected wOBA into whatever modification The Book says to do. Then apply the BINOMIAL function.

Beyond the Boxscore // Calling BJ Upton lazy is lazy.

by Sky Kalkman on Jan 22, 2009 6:10 PM EST up reply actions 0 recs