Can someone with a bigger brain than mine explain how 22 of 24 teams can exceed their Expected Percentages (and of the 2 that didn't, one missed by just .001).  Yes, it was a wacky league -- half the teams had 200K pitching, half had 200K hitting -- but I can't wrap my head around it anyway.

NATIONAL LEAGUE STANDINGS
View Basic StandingsView Your League Only
East	W-L	PCT	GB	Division	1-Run Games	Extra Inning	RS	RA	Exp. Pct.	Owner	LIVE
Philly Schmitters	99-64	0.607	-	27-16	17-13	8-3	2503	2488	0.504	cpdpoet
Cy Young Can Suck It!	98-65	0.601	1	29-14	14-16	4-3	3163	2861	0.570	verbal kint
Soccer Scores II	66-96	0.407	32.5	17-25	30-35	19-10	575	991	0.261	yogsloth
Balsa Bats	56-106	0.346	42.5	12-30	23-29	6-14	496	858	0.268	seamar_116
Central	W-L	PCT	GB	Division	1-Run Games	Extra Inning	RS	RA	Exp. Pct.	Owner	LIVE
Just Score Baby	107-55	0.660	-	30-12	15-14	4-4	3275	2715	0.628	rochayes
Run Run Reindeer	101-61	0.623	6	29-13	16-13	3-3	3047	2838	0.549	sgsmith
Pitching Patriots	62-100	0.383	45	16-26	25-33	12-8	577	831	0.337	helmethead1
Diarrhea	50-112	0.309	57	9-33	21-21	8-14	450	946	0.202	thejuice6
West	W-L	PCT	GB	Division	1-Run Games	Extra Inning	RS	RA	Exp. Pct.	Owner	LIVE
Hit New Show	110-52	0.679	-	25-17	15-18	7-3	3059	2449	0.647	brianjw
do-overs	105-57	0.648	5	31-11	14-15	2-3	3004	2565	0.607	Oli35
Token Hitters	64-98	0.395	46	12-30	31-29	6-13	550	824	0.322	msheaf1
Eierlikor	61-101	0.377	49	16-26	31-20	16-12	365	710	0.242	shawbigred
AMERICAN LEAGUE STANDINGS
View Basic StandingsView Your League Only
East	W-L	PCT	GB	Division	1-Run Games	Extra Inning	RS	RA	Exp. Pct.	Owner	LIVE
Basketball Scores II	100-62	0.617	-	20-22	12-5	2-1	3116	2825	0.568	yogsloth
Trentonjoe's O&P Suck	95-67	0.586	5	21-21	13-12	3-2	2908	2250	0.665	boogerlips
Dream Weaver Pitching	71-91	0.438	29	21-21	29-33	13-10	469	620	0.382	theweave13
Hitting Optional	60-102	0.370	40	22-20	19-43	10-17	540	725	0.371	pinotfan
Central	W-L	PCT	GB	Division	1-Run Games	Extra Inning	RS	RA	Exp. Pct.	Owner	LIVE
Take 2	118-44	0.728	-	36-6	17-10	3-1	2635	1868	0.708	batandball
Josh Towers Eggnog All-Stars	94-68	0.580	24	23-19	18-12	5-6	2221	2227	0.498	crazystengel
I Prefer Borbon in my Eggnog	70-92	0.432	48	11-31	36-30	14-13	706	823	0.428	gardenald
One Offensive Offense II	67-95	0.414	51	14-28	35-27	10-7	520	763	0.334	jfranco77
West	W-L	PCT	GB	Division	1-Run Games	Extra Inning	RS	RA	Exp. Pct.	Owner	LIVE
My Offense and Pitching Suck	94-68	0.580	-	29-13	17-12	8-2	1797	1683	0.539	Trentonjoe
King Kong King Kong King Kong King Kong	91-71	0.562	3	31-11	18-6	5-1	2558	2777	0.445	cuppie1
No Hit KAOS	72-90	0.444	22	19-23	32-39	14-16	439	605	0.367	uncleal
P36.2H3.8	34-128	0.210	60	5-37	17-30	5-21	341	1072	0.107	SophieGiants

I'm probably not smart enough but I will try. The short answer is that the pythagorean win theory breaks down with ridiculous run totals, which this league has. Here's a bit of math:

==========

After further review, I (Clay) have come to the conclusion that the so-called Smyth/Patriot method, aka Pythagenpat, is a better fit. In that, X = ((rs + ra)/g)^0.285, although there is some wiggle room for disagreement in the exponent. Anyway, that equation is simpler, more elegant, and gets the better answer over a wider range of runs scored than Pythagenport, including the mandatory value of 1 at 1 rpg.^[3]

These formulas are only necessary when dealing with extreme situations in which the average number of runs scored per game is either very high or very low. For most situations, simply squaring each variable yields accurate results.

From this link: http://www.baseballprospectus.com/glossary/index.php?mode=viewstat&stat=136

==========

So I think that "x" they are talking about is the exponent to use. If that's right then the proper exponent would be ~5.82 and not 2. So you can see why things would be off a bit.

using that, only 16 of the 24 teams are above their EXP%.
 

Team	Record	ACT%	RS	RA	EXP%	EXP181	EXP582	582>ACT%
Philly Schmitters	99-64	0.607	2503	2488	0.504	0.503	0.509	yes
Cy Young Can Suck It!	98-65	0.601	3163	2861	0.57	0.545	0.642	no
Soccer Scores II	66-96	0.407	575	991	0.261	0.272	0.040	yes
Balsa Bats	56-106	0.346	496	858	0.268	0.271	0.040	yes
Just Score Baby	107-55	0.66	3275	2715	0.628	0.584	0.749	no
Run Run Reindeer	101-61	0.623	3047	2838	0.549	0.532	0.602	yes
Pitching Patriots	62-100	0.383	577	831	0.337	0.341	0.107	yes
Diarrhea	50-112	0.309	450	946	0.202	0.207	0.013	yes
Hit New Show	110-52	0.679	3059	2449	0.647	0.599	0.785	no
do-overs	105-57	0.648	3004	2565	0.607	0.571	0.715	no
Token Hitters	64-98	0.395	550	824	0.322	0.325	0.087	yes
Eierlikor	61-101	0.377	365	710	0.242	0.231	0.020	yes
Basketball Scores II	100-62	0.617	3116	2825	0.568	0.544	0.639	no
Trentonjoe's O&P Suck	95-67	0.586	2908	2250	0.665	0.614	0.817	no
Dream Weaver Pitching	71-91	0.438	469	620	0.382	0.376	0.165	yes
Hitting Optional	60-102	0.37	540	725	0.371	0.370	0.153	yes
Take 2	118-44	0.728	2635	1868	0.708	0.651	0.881	no
Josh Towers Eggnog All-Stars	94-68	0.58	2221	2227	0.498	0.499	0.496	yes
I Prefer Borbon in my Eggnog	70-92	0.432	706	823	0.428	0.431	0.291	yes
One Offensive Offense II	67-95	0.414	520	763	0.334	0.333	0.097	yes
My Offense and Pitching Suck	94-68	0.58	1797	1683	0.539	0.530	0.594	no
King Kong King Kong King Kong King Kong	91-71	0.562	2558	2777	0.445	0.463	0.383	yes
No Hit KAOS	72-90	0.444	439	605	0.367	0.359	0.134	yes
P36.2H3.8	34-128	0.21	341	1072	0.107	0.112	0.001	yes

  ExP181 is using 1.81 as an exponent. ExP582 is using 5.82 as an exponent.

Thanks, jfranco.  That's a little over my head, but the gist seems to be that the Pythagorean method (used by WIS) is based on the number of runs that should be scored in a typical baseball game, while the other method allows for a greater range of results (which is obviously what this league had).  Is that right?

That's about right. It's a little over my head too. But the pythagorean EXP% that WIS uses was derived for "normal" leagues that are around 4 runs per game. This league was around 10 so it's way outside the intended purpose. The further away from 4 you get, the worse the results will be.

BP has a way of modifying the EXP% for outlier leagues but it's a little over my head so I'm not 100% sure if I have it right.

What the change in exponent does is push the extreme teams more to the extremes. Philly Schmitters only go from .504 EXP% to .509 EXP% with the changed exponent. But Take 2 goes from .708 to .881 and P36.2H3.8 goes from .107 to .001 (which can't be right, but is hysterical)

So, I guess this answered that offence is more important than pitching, no?

No.  Results measured at extremes should not be applied to the rest.

Posted by bottomlee on 2/28/2011 3:54:00 PM (view original):
So, I guess this answered that offence is more important than pitching, no?

Well this league showed that offense + fielding >>> pitching alone. Remember, the hitters were at 0% so they were also fielding at 0%. Which meant each pitching team allowed a few hundred unearned runs.

Or, more accurately, this league showed that a helluva lot of offense is better than a pretty good amount of pitching. Because in general, it is better to have more pitching. If you had a team that scored and allowed 600 runs, and you gave them 100 marginal runs, they'd be better off applying those runs to the pitching side of the equation:

RS	RA	Pyth
600	600	0.500
700	600	0.569
600	500	0.582

However, if you gave them a choice of 300 less runs allowed or 1000 more runs scored, they would much prefer the offense (though it's closer than you might think):

RS	RA	Pyth
600	600	0.500
1600	600	0.855
600	300	0.778

It would actually be interesting to run this league again and take the fatigue out of it.

"Hitting" teams would get ~1600 innings of crappy pitching
"Pitching" teams would get 8 semi-decent fielders with 700 PA who can't hit their way out of a paper bag.