just got done skimming this thread and figured I'd contribute to the confusion (and the poor spalling).
My take on FBB categories is that an optimal set (whether it is 4x4 or 5x5 or anything like that) would only contain categories that are as independent of each other as possible. This is probably next to impossible to do for real baseball, but maybe it can be approximated. Also, an optimal set would emphasize the importance of individual player achievements rather than stats that are greatly dependent on the performance of the team the player is on.
I like to dabble with numbers. I recently made a plot of various stats vs. other stats and found some intersting things.
1) I think someone actually studied this a little more in depth, I saw an article on it, ERA and WHIP are not independent. Larger WHIP usually means larger ERA. There is, of course, scatter but that is to be expected in statistical data.
2) it shouldn't surprise anyone that RBI/PA and SLG% are highly correlated. I don't know how to fix this, but the "best" set of categories would probably feature not use one of the two stats.
3) I don't like OPS as a stat. I do like it much more than AVG though. I think it should be OPS-HITS/PA, the reason for this is that hits get double counted in OPS compared to BB or HBP. (just look up the formulas for OBP and SLG and you'll see that hits figure in both)
4) the original poster is right, IMO, that W are a flawed category. In some sense, maybe, something like QS+CG might work better (or some combination like that). QS are a fickle stat and I don't think they are constrictive enough (I mean, 3ER in 6IP isn't THAT great...)
5) K for pitchers are a good stat, I think. I'd like to maybe see something like 'K with runners at 3rd' as a possible stat. but I see no problems with Ks.
6) I really don't like HRs as a category. My main issue with is is that when someone hits a HR four of the five standard categories are changed (R,RBI,HR and AVG). This is not right. In some sense, maybe the categories should be R-HR, RBI-HR, HR and AVG (I'll live with just the average being affected and getting the RBI for the runners on base already)...
i have some other ideas, but maybe I'll put them in another thread