right before i got to point 3: "Here is where it gets tricky."

i think my head's going to start hurting pretty soon...

Interesting stuff! You should send a resume to Billy.

One tweak you might consider is your model assesses the predictive power of different coefficients by referring to a reference model of 9 clones batting.  It seems likely to me that you would get something different if there were different random mixes of players hitting around a player with different profiles... e.g. 8 Ichiros with 1 power hitter would probably score more runs than the weighted average of 8 all-Ichiro teams and 1 all-slugger team.

Of course, I'm not the one who has to mess with Matlab...

Interesting. I like the but here are a few other things you might want to consider.

• There's no good mathematical reason to demand that the two variables you use in the regression be minimally correlated. For example, when you run your regression using AVG and ISO, you could get an identical answer using AVE and SLG instead. If it's not a lot of work, I'd like to see what you get using OBP and SLG on the same data. I suspect it would be as good or slightly better a fit as the one using OBP and ISO.(Geek talk: the reason to avoid variables that are too highly correlated with each other is for reasons of numerical stability. If two variables are close to being linearly dependent, you end up trying to invert a matrix that is close to being singluar, which can end up giving the wrong answer. But I don't think that will happen here, and trying to avoid "double counting" is really an aesthetic issue, not a mathematical one.)
  
• If you're trying to judge a players true value, it's probably better to see how a lineup of that player + 8 average players (or that player + a typical lineup of 8 other players) would perform. That's not really an issue for this study, though, and probably only makes a big difference in extreme cases. For example, as you note, a lineup full of players who got on base with a walk or a single every time would score an infinite number of runs, but if you add such a player to a more typical lineup, his actual value would depend mostly on the ability of others on the team to drive him in, though it would still be very high.
  
• Again, it probably doesn't make much difference in this case, but as we discussed before, if you're looking for smaller effects (on the order of a few runs over the course of a season) 1500 games still turns out to be way too small a sample size. matlab=slow.
  
• Miggy had 150 RBI! You need to add a clutchness variable. ;-)

I've always had problems with OPS as a statistic because the AVG is counted twice.  Therefore, hitters with lower batting averages get punished by the statistic more that higer batting avegage hitters.  I like the idea of modified OPS,  Though I think it's unecessary to go scrounging around for ISO (isolated power), in order to calculate it (OBP+ISO) when all one really has to do is go to web sites that give OPS (I believe everyone provides it as a main statistic now) and just subtract AVG - it's the same thing, right?

I find these statistical analysis a bit over my head, but I really appreciate your interest in this side of baseball and our team specifically.....

I'm glad to have you on my team.

isn't supposed to understand this at all, right?

good. [feels less stupid]

Here are a couple more articles that explain why OPS is a good way of measuring offensive value

http://remarque.org/~grabiner/baseball.html

This one, by David Grabiner gives a good mathematical justification for why taking linear combination of OPS and SLG really is a sensible thing to do.

http://baseballprospectus.com/article.php?articleid=2596

This one, from the BPro Basics series compares the correlation of a number of common stats to team run scoring (similar to what Sal is doing, but using historical data rather than simulations). OPS does much better than AVG, OBP, or SLG by themselves. Stats like EqA and RC/27 are only a little better than OPS, at the expense of much greater complexity. So for most purposes, OPS strikes the right balance between simplicity and accuracy.

Aaron Gleeman on his "Gross Production Average" which is (1.8*OBP + SLG)/4:
http://www.aarongleeman.com/2003_11_23_baseballblog_archive.html#106974007971391611

Tangotiger on optimal weights:
http://www.tangotiger.net/ops.html
http://www.tangotiger.net/ops2.html
His articles on linear weights and "How are runs really created" are also relevant.

But good that some people think about baseball in an intelligent way.... not just "how many beers can I drink before the game is over?"
Not that there's anything wrong with that but I like to watch the game when I pay to watch it :)

BTW, there is an article on Kielty being some kind of math whiz over at the official site. They mentioned him doing calculus etc. but then he said something about not using math much anymore for playing baseball.... this reminded me of that article a little.