the five back rule revisited

this page has taken a fairly firm stance that, at least as far as the playoffs go, this year is already over. falling back so far of the division leader so early in the season, as has been documented here and here, is highly indicative of clubs that are going to fail not only to make the playoffs but to breach .500 at year end. as to the disparity of runs scored to runs allowed, one need only observe the weakness of the correlation between april run differential and final fates to understand that was has thusfar transpired in these terms means little.

the cubs pythagorean projection at this time is .593 -- implying a 96-win pace. that is the third-highest such figure in the lot, and the peer group is a somewhat happier one. of the top 15, fully 8 broke .500 even though only two continued to post run differential at such a high pace as they did in april. six of this sample even managed to break a .525 winning percentage (corresponding to 85 wins). though the mean winning percentage of these fifteen is .491, the standard deviation is .064 -- implying a probable range of .427 to .555.

indeed, as much can be confirmed by a presentation of previous data regarding the five back rule, updated, expanded and newly tabular.

year	5 back game	10 back game	at year end					through 4/30
			playoff	final gb	w	l	win%	w	l	rs	ra	pythag
1984	n	n	y	0	96	65	0.596	12	8	98	70	0.648
1989	n	n	y	0	93	69	0.574	12	11	85	95	0.450
2001	139	n	n	5	88	74	0.543	15	9	107	91	0.573
1977	115	132	n	20	81	81	0.500	7	9	56	77	0.359
1973	111	n	n	5	77	84	0.478	12	8	85	75	0.557
2003	100	n	y	0	88	74	0.543	15	12	150	109	0.641
1985	80	106	n	23.5	77	84	0.478	12	6	60	46	0.619
1998	76	131	wc	12.5	90	73	0.552	14	13	124	112	0.546
2004	75	93	n	16	89	73	0.549	13	9	115	96	0.581
1978	75	156	n	11	79	83	0.488	11	9	70	84	0.418
1987	60	86	n	18.5	76	85	0.472	10	10	90	81	0.548
1975	59	77	n	17.5	75	87	0.463	12	5	93	73	0.608
1996	52	157	n	12	76	86	0.469	13	14	136	128	0.528
1995	42	73	n	12	73	71	0.507	4	1	29	24	0.585
1974	33	101	n	22	66	96	0.407	7	11	72	109	0.320
1991	32	67	n	20	77	83	0.481	10	11	87	82	0.527
1999	31	89	n	30	67	95	0.414	10	10	88	98	0.451
1980	29	80	n	27	64	98	0.395	9	6	77	77	0.500
2006	27	42	n	17.5	66	96	0.407	13	10	109	112	0.488
2005	25	80	n	21	79	83	0.488	12	11	119	107	0.548
1976	25	38	n	26	75	87	0.463	9	10	99	112	0.444
1993	20	50	n	13	84	78	0.519	11	11	88	91	0.485
2007	19							10	14	112	91	0.593
1990	18	52	n	18	77	85	0.475	8	11	62	82	0.375
2000	17	44	n	30	65	97	0.401	10	17	145	175	0.415
1988	16	39	n	24	77	85	0.475	10	12	97	104	0.468
2002	16	39	n	24	67	95	0.414	8	16	86	110	0.390
1982	13	49	n	19	73	89	0.451	7	14	85	92	0.464
1992	12	114	n	18	78	84	0.481	7	13	61	89	0.335
1994	12	24	n	16.5	49	64	0.434	6	15	95	128	0.368
1986	9	26	n	37	70	90	0.438	7	12	75	96	0.390
1979	8	135	n	18	80	82	0.494	8	9	57	69	0.414
1981	8	14	n	21.5	38	65	0.369	2	13	36	73	0.216
1997	6	18	n	16	68	94	0.420	6	19	95	133	0.352
1983	5	116	n	19	71	91	0.438	6	14	65	94	0.338

from this presentation, it doesn't take a mathematician to see that the 2007 cubs are in very deep trouble. if they go on to win their 82nd game later this season, they will be only the second cub club in the last 25 to do so in spite of falling five games back of the division leader before their 70th game was played. (a third, the 1995 club, may have done so had not that season been shortened by a labor dispute.)

looking at the plight of early laggards from the other side, espn's jayson stark offered this analysis.

We looked at every full season since 1982. Here's what we found:

• Of the 144 teams that made it to the postseason in that span, only eight (or 5.6 percent) came out of April more than three games under .500. Clubs that need to worry most about that history lesson: the Yankees (9-14), Astros (10-14), Cardinals (10-14), Cubs (10-14) and Rangers (10-15).

• Just six of those 144 playoff teams (or 4.2 percent) found themselves more than 4½ games out of a playoff spot after April. Clubs that ought to get nervous about that trend: the Cubs, Cardinals and Astros (all five games out).

• And you wouldn't think the standings would mean much this time of year. But more than half of the 120 teams that found themselves in first place after April (66 of 120) wound up finishing first. And 98 of the 120 (81.7 percent) of the teams that finished the season in first place either led their division or were within 2½ games of the lead at the end of April.

going into today's games, the cubs had further fallen six afoul of the milwaukee brewers. again, it must be said -- the greatest of a handful of barriers now is the inertia of the record itself. with the brewers at 17-9, should they play just .500 ball henceforth -- something they're probable to do or better -- they'll finish at 85-77. this cubs team simply aren't going to be that good barring a miracle. matching that record means 75-63 -- 12 over .500, or .543 baseball.

this page would not dispute that there are worse ways to be 10-14 and six back. the cubs are chasing only one good club -- the brewers -- and not three or four, which would all but nail the coffin shut. and having scored more than they've allowed is certainly a more promising indicator than its opposite -- after all, the 1984 and 2003 playoff sides both posted positive run differentials through april that only modestly exceed this one's.

however, so did the 1985 and 1975 clubs -- teams which finished with 77 and 75 wins, respectively. furthermore -- indicative of the tremedous variance of just a month's worth of play -- the 1989 club that finished with 93 wins had allowed ten more (95) than they had scored (85) through the same date. as can be seen in the following chart, the correlation between pythagorean figures and actual ones over large sets of data are good -- the ratio of theoretical to actual records should approach one, as they do here -- but the quality of the correlation in individual data points is poor.