the cardinals' run differential

the sabermetric evidence that, generally, run differential is more predictive of a team's performance than its record over a partial season is pretty overwhelming. for instance, even at this late date in the season, the cardinals pythagorean record is more likely predictive of its final record than its current record is; current record doesn't become more predictive of the final record, generally speaking, until game 140.

much has been made of the cardinals' bad record in one-run games, especially since evidence shows almost essentially no year to year correlation in record in one-run games.

that's not to say that all deviations from a predicted pythagorean record are exclusively based on luck or non-predictive factors, but one should not discard the hypothesis that luck is the most likely rationale for serious deviations from an expected pythagorean record, except with strong evidence.

but the st. louis media has done just that. in an article full of more spleen than brains, bernie miklasz upbraided the cardinals offense as "phony," a "con," "fraudulent," and some other words he found in the thesaurus. the sitting world champions, in his words, "lack a sharp competitive edge."

his presentation of statistics without context created false impressions in the reader. for instance, he notes that since may 11 (a date of no particular significance) the cardinals have scored three runs or fewer 41 times in 90 games. FORTY ONE TIMES!!!

wow! 41 sounds like a big number. does anybody know how many games we should have expected them to score 3 runs or fewer? if you do, it's not from reading bernie's article. 41 of 90 games is about 46%. over the whole season, the cincinnati reds have scored 3 runs or fewer 49 times, or about 40% of the games they've played. to reach the benchmark of what i can only assume to be such a great offensive outcome, the cardinals would have had to score 4 runs instead of 3 in 4 or 5 more games. presumably, the cardinals offense would then not be an "absurdity," as bernie describes them. in a less-arbitrary sample, the cardinals have scored 3 runs or fewer in 43% of their games which is more or less on par with other division leading clubs (ranging from 47 games in which 3 runs or fewer were scored by the brewers to 53 games by the pirates).

the table below reflects the run scoring data for five top clubs by two-run blocks: e.g., games in which one run or no runs scored; games in which two or three runs scored, etc.

team	0-1 RS	2-3 RS	4-5 RS	6-7 RS	8-9 RS	10+ RS	RS/G
cardinals	15	37	28	14	16	12	4.9
reds	19	30	36	25	10	4	4.4
braves	20	27	31	25	9	11	4.6
nationals	19	32	36	19	10	7	4.4
pirates	27	26	38	15	10	7	4.2

derrick goold followed with an article that was something of an improvement on bernie's article. he acknowledged the heavy evidence indicating luck plays the most substantial role in deviations from pythagorean records. however, having located decent evidence, he wandered down a rabbit hole of correlations without causation. one meandering observation noted that 4 of the cardinals' first 18 one-run losses "were decided" in the seventh inning. i take the words "were decided" to mean that the winning team took the lead in the seventh inning, which sort of misses the point that the game was also lost by the cardinals failure to score more runs in the 8th and 9th innings. since he later criticizes the cardinals' clutch hitting, one would assume that being down by a run in the 8th or 9th inning might count as a potentially clutch situation.

but, yes, in 4 of 18 of a somewhat arbitrary sample of one-run losses, he notes, the leading run was scored in the seventh. and that fewer-than-one-fourth of those losses took place in between the departure of kyle mcclellan and the arrival of edward mujica. i guess he's trying to point out the need for a steady seventh-inning reliever, but this misses the overwhelming evidence that kyle mcclellan is steadily kind of terrible.

to my mind, the central logical explanation for why luck is probably a primary determinant for deviations between pythagorean record and actual record is this: runs scored and runs allowed in any one game are almost totally unrelated.

adam wainwright has a fair amount of control over whether he allows 2 runs or 4 runs. he doesn't have much control (except when he's batting) over whether he's pitching on a day when the offense produces 1 run or 5 runs. and the weird game-by-game variation of pitching results and offensive results will not line up in any orderly way. a good team might produce 7 runs, 4 runs, and 3 runs in the course of a 3 games series, and might allow 5 runs, 4 runs, and 1 run. but depending on how those offensive outcomes and run prevention outcomes lines up, they might win the series or lose 2 games to one.

this individual game variance could easily have a huge effect on a team's record.

sure, it is a team-wide a skill to have more high-scoring games than low-scoring games. it's also a team-wide skill to have more fewer-runs-allowed games than more-runs-allowed games. but no team has a magical ability to align its high-scoring games with its high-runs-allowed games, and its low-scoring games with its fewer runs allowed games.

i don't want to say that there is NO relationship between how many runs a team scores and how many they prevent in a single game. in blowouts, a manager may choose to let his bench play the field or let his long man and his LOOGy pitch, which might tend to exacerbate blowouts (although, one presumes, both the winning and losing team are just as likely to put the B team on the field, so the effects should more or less offset each other). managers can tweak their rotations to obtain advantageous matchups, but that effect is probably pretty limited, given the limited number of days off and the pretty rigorous observation of the 5-day schedule by managers.

in the end though, i suspect that RA and RS should vary pretty freely in individual game situations.

looking back up at the runs scored chart, the cardinals don't look like terrible chokers. they are limited to one run or less fewer than any of the top clubs in the NL Central or NL East. there is something to the hypothesis that they end up with a lot of blowouts. the cardinals have scored 8 or more runs in twice as many games as the reds. but still, the cardinals performance is pretty solid offensively, in terms of its overall distribution.

the pitching doesn't look much different. the cardinals have very good pitching, much like the rest of the leaders in the NL East and Central.

team	0-1 RA	2-3 RA	4-5 RA	6-7 RA	8-9 RA	10+ RA	RA/G
cardinals	26	38	22	24	8	4	3.9
reds	27	41	27	15	10	4	3.8
braves	27	37	26	16	14	3	3.9
nationals	22	44	39	9	5	4	3.5
pirates	20	38	38	14	6	7	4

the chart above illustrates the games by runs allowed, in the flipside of the runs scored chart. the cardinals do very well in inducing few runs. they are rarely blown out. the cardinals actually allow 3 or fewer runs in as many games as the braves, more than the pirates, and slightly fewer than the nats and the reds.

what i think is most compelling, in illustrating the heavily luck dependent nature of run distribution, is the winning percentage associated with the runs scored in a game, in isolation, and the runs allowed in a game, in isolation.

team	0-1 RA	2-3 RA	4-5 RA	6-7 RA	8-9 RA	10+ RA
WP-cardinals	1.000	0.632	0.318	0.333	0.125	0.000
WP-reds	1.000	0.658	0.556	0.267	0.200	0.000
WP-braves	0.926	0.730	0.308	0.313	0.214	0.667
WP-nats	1.000	0.728	0.513	0.222	0.000	0.250
WP-pirates	0.900	0.711	0.447	0.357	0.000	0.000

just to pick a fairly flagrant example of the incredible variation in the relationship in-game RA and RS, take a look at the braves winning percentage when their pitchers give up more than 8 runs. they have won 5 of 17 games where their pitchers give up 8 runs or more. by contrast, the cardinals, who are the best among the five teams at scoring 8+ runs, have only won one of the 12 games in which cardinals pitchers allow 8 or more runs.

i suppose that you could take the view that the atlanta braves somehow have the wherewithal and team chemistry to dig deep and selectively score 15 runs when their pitchers give up 12. i think that barely passes the laugh test, though. far more likely that teams score lots of runs because they have a good offense and the other teams pitchers aren't good. whether the day when you score 12 runs corresponds with the day your pitchers allow 10 or the day they allow 2 seems likely a matter of happenstance.

i think the most interesting issue, though, is right in the middle. when pitchers allow 4 or 5 runs (the second most common RA block, after 2 or 3), shouldn't we expect about a .500 performance? most of these teams average somewhere between 4 and 5 runs a game. the cardinals have scored 6 or more runs in 42 games, more than any of the other teams except atlanta, who has 45, and more than one-third of the total number of games they've played. even leaving aside the games won 5-4, shouldn't we expect at least a .333 win percentage in games where the pitchers give up 4 or 5 runs?

yet not only do we not see that trend, we actually win MORE games when our pitchers give up 6 or 7 runs than when they give up 4 or 5. are better at scoring runs when our pitchers give up more runs? or is this just a product of weird game-by-game variation.

why do the reds win more than half of the games where they score 4 or 5 runs, and we win less than a third? why have the pirates won more games 1-0 than the four other teams, even though the pirates are the worst of the five at limiting opponents to 1 run or less?

team	0-1 RS	2-3 RS	4-5 RS	6-7 RS	8-9 RS	10+ RS
WP-cardinals	0.067	0.300	0.679	0.786	0.875	1.000
WP-reds	0.000	0.433	0.778	0.920	0.900	1.000
WP-braves	0.000	0.296	0.548	1.000	1.000	1.000
WP-nats	0.052	0.469	0.778	0.947	1.000	0.666
WP-pirates	0.037	0.538	0.658	0.733	0.900	1.000

in games where the cardinals scored 2 or 3 runs, they won only 30% of those games, while the reds wone 43% of those games. but the number of games in which the reds and cardinals allowed 1 or fewer runs was almost the same (26 to 27). the reds just happened to score 2 or 3 runs more frequently on days when they allowed fewer runs.

obviously, some clubs are better at scoring runs than others, and some are better at preventing runs. but there's little reason to think anything other than chance is animating the distribution of runs game-to-game. the only alternative is to believe that some clubs have the ability to score just the right number of runs. that's a real absurdity.