the fallacy of the weak division

in edified circles, many an optimistic analysis of how the chicago cubs might fare in 2007 in terms of wins and losses has for some months hinged on the argument of the weakness of the division in which the cubs play. it is a point this page has made with reference not only to this year but 2006 as well -- more's the pity.

to the credit of analytical optimists commenting on the 2007 cubs, few have been trying to say the cubs are really any good -- just that they're better than their selected lot. indeed, a recent back-of-the-napkin figuring for the pitching staff runs as follows:

taking an average factor for injury:

zambrano - 220 ip - 3.75 ra ... hill - 200 ip - 4.30 ra ... lilly - 120 ip - 4.60 ra ... marquis - 200 ip - 5.20 ra ... this is what to expect out of the starting five, imo -- 740 innings in which they allow about 365 runs -- ~4.43 runs a game. the team is going to have to pitch about 1460 innings.

that means the rest of the staff -- wade miller, angel guzman, sean marshall and whomever else ends up with a start -- plus the extended bullpen that includes wood, novoa, cherry and whomever else -- pitch about 720.

with wood out, the bullpen is not radically changed this year from last -- nor is the starting staff probably going to eat vastly more innings. last year the cubs pen tossed 562 innings allowing 282 runs. let's say they go 540 allowing 280 (which is better than i think they'll actually do, fwiw). totals so far -- 1280 ip -- 645 runs.

now, the remaining 180 innings are usually a disaster for most clubs which highlights their lack of rotation depth. not unusual for this to be 6+ r/g spread over several spot starters -- in the cubs case, miller, guzman, cotts, marshall, etc.

if we figure (conservatively) 6.00 for these last 180, we get about 120 runs. our new totals -- 1460 ip -- 765 runs.

that's 4.71 runs a game, and a 74-run improvement on 2006's 834. in last year's nl, that would've been good for 6th among all staffs. and this is the conservative estimate, mind you. i'll personally be surprised if the staff ra gets under 4.8 runs/game.

this is only one of a few different casual approximations that puts the cub staff in this area. offensive calculations for run generation have already settled in an area around 4.8 runs per game -- making the cubs then to score about as much as they allow, the very definition of a .500 baseball club.

this all, however, is a framework constructed to establish the cubs in a historical context contrasted to the national league in general. should the proper context in fact allow for the projected division instead?

there's merit to that, but only to a point.

the league weights the schedule to intensify divisional play, and central teams indeed play about half their games in division -- a greater proportion than either east or west thanks to the extra team in the central, but still just half. for half the schedule, the team is playing the divisions on either coast. so while half clearly are played against what is probably the weakest division in baseball, the equal remainder are not. but what is that worth?

first, it must be recognized that if, say, the nl west is the weakest division, the difference between that situation and this is one-quarter of the games played -- where you expect now to play half in the weakest division, you would have played a quarter. this amounts to 40 games or so.

second, how much weaker is weak -- that is, what advantage in winning percentage can be expected? in a sport in which the best clubs beat the worst clubs perhaps seven times in ten while evenly matched clubs play to loggerheads, it should be seen that -- even if the cubs were the metaphorical 1927 yankees and the weak division consisted of 1962 mets all -- the difference over 40 games would amount to about eight contests. that is of course very significant -- but the cubs are not the 1927 yankees. they're an average ballclub. in that context, this page would estimate the advantage to the cubs for playing in the weakest division in baseball as opposed to a historically average one probably amounts to no more than two wins.

that is a fair enough basis in reason. but can more be said empirically?

2006	Intradivisional			Extradivisional
	W	L	Pct	W	L	Pct
NY	45	29	0.608	46	27	0.630
Philadelphia	41	34	0.547	39	30	0.565
Atlanta	35	38	0.479	39	35	0.527
Florida	33	42	0.440	36	33	0.522
Washington	31	42	0.425	33	38	0.465
	185	185	0.500	193	163	0.542
St. Louis	39	42	0.481	39	26	0.600
Houston	45	32	0.584	30	37	0.448
Cincinnati	46	38	0.548	28	35	0.444
Milwaukee	37	45	0.451	32	33	0.492
Pittsburgh	34	44	0.436	30	39	0.435
Chicago	42	42	0.500	20	43	0.317
	243	243	0.500	179	213	0.457
SD	39	36	0.520	42	30	0.583
LA	43	31	0.581	40	33	0.548
SF	37	38	0.493	31	40	0.437
Colorado	31	44	0.413	34	38	0.472
Arizona	37	38	0.493	35	37	0.486
	187	187	0.500	182	178	0.506

in 2006, the central was also the weakest division in the game as measured by extradivisional wins and losses (a record of 179-213, or .457). did the leaders indeed fatten up on the sorry clubs of the bottom rung with the advantage of playing them more often, offsetting their sorry beatings to teams like the mets and dodgers?

as it turns out, insignificantly. the two leading clubs -- saint louis and houston, the only two winning records in the division -- went an aggregate 84-74 (.531) within the central and 69-63 (.522) outside of it (the remainder of the games having been played against the american league). the difference in winning percentages implies, over a 40-game sample, a net gain to each club of 0.4 wins.

this experiment can of course be repeated for past seasons as well -- so this page did, for 2005 and 2004.

2005	Intradivisional			Extradivisional
	W	L	Pct	W	L	Pct
Atlanta	42	33	0.560	41	31	0.569
Philadelphia	38	37	0.507	43	29	0.597
Florida	34	39	0.466	39	35	0.527
NYMets	38	36	0.514	40	33	0.548
Washington	34	41	0.453	35	34	0.507
	186	186	0.500	198	162	0.550
St.Louis	51	29	0.638	39	28	0.582
Houston	43	36	0.544	39	29	0.574
Milwaukee	38	41	0.481	35	33	0.515
ChicagoCubs	43	36	0.544	30	38	0.441
Cincinnati	33	46	0.418	33	35	0.485
Pittsburgh	30	50	0.375	32	38	0.457
	238	238	0.500	208	201	0.509
SanDiego	39	34	0.534	36	35	0.507
Arizona	41	32	0.562	28	43	0.394
SanFrancisco	38	35	0.521	31	40	0.437
LADodgers	33	41	0.446	33	37	0.471
Colorado	32	41	0.438	29	45	0.392
	183	183	0.500	157	200	0.440

in 2005, the weakest division in the league was the west, with an aggregate extradivisional winning percentage of just .440; its lone winning club, san diego at 82-80, went 39-34 (.534) in division and 36-35 (.507) outside of it. the implied difference in wins over a 40-game lot is 1.1.

2004	Intradivisional			Extradivisional
	W	L	Pct	W	L	Pct
Atlanta	51	25	0.671	37	31	0.544
Philadelphia	39	37	0.513	38	30	0.559
Florida	43	33	0.566	33	35	0.485
NYMets	29	47	0.382	32	36	0.471
Montreal	28	48	0.368	32	36	0.471
	190	190	0.500	172	168	0.506
St.Louis	54	36	0.600	40	20	0.667
Houston	55	35	0.611	30	30	0.500
ChicagoCubs	50	40	0.556	31	29	0.517
Cincinnati	38	52	0.422	33	27	0.550
Pittsburgh	37	52	0.416	33	27	0.550
Milwaukee	35	54	0.393	24	36	0.400
	269	269	0.500	191	169	0.531
LADodgers	47	29	0.618	36	32	0.529
SanFrancisco	41	35	0.539	39	29	0.574
SanDiego	42	34	0.553	37	31	0.544
Colorado	39	37	0.513	21	47	0.309
Arizona	21	55	0.276	24	44	0.353
	190	190	0.500	157	183	0.462

in 2004 the weakling was again the west at .462; weighted down by not only 68-win colorado but an epically bad 51-win arizona club. surely here, the division leaders must have feasted -- but the data shows that the dodgers, giants and padres, all of whom won 87 or more, went an aggregate 130-98 in division (.570) and 112-92 (.549) without. again, the implied difference in wins over a 40-game lot is 0.8.

as should now be clear, playing in the weak sister of divisions is not the panacea that many a cub fan (including yours truly) would like it to be -- and to that we must add the uncertainty about whether or not the central will really be as weak as so many expect. it seems to this page that many have overestimated the likely benefit, and in so doing committed a common-enough error of selection bias without thorough statistical vetting. if playing in the central adds a win to the cub total in the end, so much the better -- but this cub club is going to have to stand on its own merits, and not the weaknesses (real or perceived) of its geographic rivals.