tag:blogger.com,1999:blog-12133335.post4658856297866717152..comments2014-11-18T17:09:59.410-05:00Comments on Walk Like a Sabermetrician: BA/OBA/SLG Calculus, pt. 2phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-12133335.post-73036300365152702162012-03-22T18:44:14.736-04:002012-03-22T18:44:14.736-04:00The other complicating factor here is what the rat...The other complicating factor here is what the rate output should be. I've assumed that it should be analogous to RAA/PA like wOBA. But if you want something that tracks R/PA, you'll get a different answer. <br /><br />If 2*BA + x*(BB/PA) + .8*ISO is correlated with R/O on the team seasonal level, it is optimized somewhere close to x = 1 like Dave is using.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comtag:blogger.com,1999:blog-12133335.post-40353788882118246752012-03-22T18:23:06.568-04:002012-03-22T18:23:06.568-04:00No, you're not.
The technique I used here &q...No, you're not. <br /><br />The technique I used here "freezes" AB%, and thus is not directly comparable with a normal +1 method. I assume that when you add a single to your +1, the player's ISO and walk rate go down (since there is an additional AB/PA as well).<br /><br />The differentiation I've done here assumes that AB% is fixed, and determines the coefficients at that particular AB%. As soon as the player completes his next PA, his AB% will either go up (if he doesn't draw a walk) or go down (if he draws a walk). <br /><br />For example, Pierzynski had 474 AB and 15 walks, so his AB% is 474/(474+15) = .96932. If he were to draw a walk in his next PA, his AB% would drop to 474/(474+16) = .9673, and the weights for every event would change.<br /><br />In the past when I've differentiated OPS, I've taken a similar approach to the +1 method. By freezing the AB% here, I'm able to give a precise formula for OPS at any particular AB%.<br /><br />To put it another way, the +1 method (and the other way to differentiate) asks "What would happen to the player's OPS if he hit an additional single?" This method asks "Given the fixed, observed AB%, how can we express the player's OPS as a function of his per PA event frequencies?"<br /><br />This explanation leaves a lot to be desired, but it's something I struggled with myself for a long time and I still have trouble articulating the distinction between the two approaches.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comtag:blogger.com,1999:blog-12133335.post-58191944583752974292012-03-22T09:11:36.404-04:002012-03-22T09:11:36.404-04:00Re: walks. When I do the "plus 1 event" ...Re: walks. When I do the "plus 1 event" method (poor man's differentiation?) for an avg batter using my 2/1/.8 weights,, I get that a BB is worth .66 of a 1b, which is what it should be. When I do it using your 2/1.8/.8 proposal, I get a BB value which is 1.02 times a 1b.<br /><br />Am I doing something wrong?dave smythnoreply@blogger.comtag:blogger.com,1999:blog-12133335.post-61798981769509330772012-03-21T19:44:37.317-04:002012-03-21T19:44:37.317-04:00Let’s write David’s formula in the same format I u...Let’s write David’s formula in the same format I used in the post:<br /><br />2*BA + BB/PA + .8*ISO = w + (2*s + 2.8*d + 3.6*t + 4.4*hr)/AB%<br /><br />Differentiating, we get a coefficient of 1 for a walk, 2/AB% for a single, 2.8/AB% for a double, 3.6/AB% for a triple, and 4.4/AB% for a homer. Weights for the three examples:<br /><br />Avg 1,2.26,3.16,4.06,4.97<br />Thome 1,2.43,3.41,4.38,5.36<br />Pierzynski 1,2.06,2.89,3.71,4.54<br /><br />With a single = 1:<br />Avg .442,1,1.4,1.8,2.2<br />Thome .411,1,1.4,1.8,2.2<br />Pierzysnki0.484663 1 1.4 1.8 2.2<br /><br />The hit weights are a very good match for wOBA; the walks less so. Something like 2*BA + 1.8*BB/PA + .8*ISO would yield:<br /><br />Avg .80,1,1.4,1.8,2.2<br />Thome .74,1,1.4,1.8,2.2<br />Pierzynski .87,1,1.4,1.8,2.2<br /><br />The walk is always going to bounce around in value due to the different denominator, but this is pretty close to the wOBA weights. David’s version is more stable than OPS because he only has one variable (walks) over a different denominator than for the rest of the events (at bats), whereas OPS puts all the variables except one (walks) over different denominators (all hit types in OPS are divided by PA in OBA and AB in SLG).phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comtag:blogger.com,1999:blog-12133335.post-45718960411599370842012-03-21T10:17:25.734-04:002012-03-21T10:17:25.734-04:00Interesting stuff, Patriot. Maybe you'll want ...Interesting stuff, Patriot. Maybe you'll want to analyze the following formula:<br /><br />2*BA + (BB/PA) + .8*ISO<br /><br />Just a formula I've played around with.dave smythnoreply@blogger.com