Wozzyck wrote: I was curious what your qualms with the 2nd orders were (perhaps on principle), which don't neutralize for parks or opponents.
2nd order pythag are based on EqA which is adjusted for parks and league difficulty.
*edit* I think there might be a couple of 2nd order pythags out there that are based on non-adjusted run estimators, IRRC THT's estimator uses Baseruns, but I haven't looked into the accuracy it generates. Most likely it will be somewhat closer since BsR normally correlates better with actual runs produced than EqA does. The closer you get to actual runs produced/saved the more accurate the Pythag is (from what I've seen and tested). It doesn't surprise me that base pythag is more accurate because you don't get any closer than using the actual R and RA.
Well, I did a little research just now. I was under the impression that BP's 2nd Order Pythagenport used Unadjusted Equivalent Runs (as 3rd Order uses Adjusted Equivalent Runs). It turns out they use Equivalent Runs which are based on EqA (however there are conflicting definitions of EqA on their site; the glossary says its adjusted for home parks as I thought it to be, though this article http://www.baseballprospectus.com/article.php?articleid=2596
doesn't make mention of that.)
Regardless, if they used park-adjusted Equivalent Runs for each team, one would expect that the total that they use for the 2nd Order Pythagenport to be quite lower than actual Runs for those teams in hitter's parks, but this doesn't really bear out. Here's a few from last year:
Red Sox: 900 R, 902 EQR
Rangers: 861 R, 867 EQR
Diamondbacks: 695 R, 753 EQR
Rockies: 740 R, 717 EQR
One possibility is that they do use the park-neutral EqA, but the quantity of runs (EQRs) that they use for computing Pythagenports, given your neutral EqA, does factor back in where you played your games (e.g. 19 times at Boston, 19 times at Baltimore, etc.). It's just clear that the EQRs that they use can't be neutral.
Similarly, the final adjusted EQRs that they use for 3rd Order appear to factor back in who a team faced and where they played. If this were true, then I would probably believe them to be more accurate, on principle, at assessing the number of wins a team "should" have had than the 1st and 2nd Order.
Philosophically, the whole reason for looking at 1st Order Pythagenports is because people realize that there's a lot of luck involved in winning games. In order to remove the influence of some of this luck, we instead look one level down: at the number of runs scored and runs allowed and estimate how many wins and losses a team "should" have had given those numbers.
The whole reason for looking at 2nd/3rd order Pythagenports is that people realized that there's also a lot of luck involved in scoring runs. In order to remove the influence of some of this
luck, we look down another level: at the underlying offensive/defensive stats of the team and calculate the number of runs that a team "should" have scored/allowed given those numbers. Then we use those run calculations to figure out the number of wins a team "should" have had, like above.
It doesn't surprise me that base pythag is more accurate because you don't get any closer than using the actual R and RA.
This comment seems to indicate that you acknowledge the luck involved in winning games, but not in scoring runs.
I guess I'd like to know what it is that you're testing and what it is that you've seen. (And if you'd like to continue this discussion, perhaps it'd be best to start another thread, as this is becoming a hijack.)