fuzzy math

if the cards had gotten competent bullpenning, some of you are saying, they’d be 5-2 on the current road trip and playing for a series win tonight, instead of 3-4 and needing a win to break even on the trip. that’s true as far as it goes --- but it’s also true that the cards very easily might find themselves 1-6 on the current trip, and staring up at the cubs. 2 of their 3 wins came in their last at-bat (monday at colorado and saturday at milwaukee), and in both of those games the opposing team had the go-ahead run on 3d with 1 out in the bottom of the 8th but couldn’t bring him home. st louis got both wins by the skin of their teeth; if they can salvage a win tonight behind wainwright and go home with a pair of splits, i don’t suppose we can really complain. that’d be a good trip.

it doesn’t seem as if they’ve scored a lot of runs on this road trip, only 29 in 7 games. but in truth that’s not drastically below their season average --- 4.1 runs a game on the trip, vs 4.5 runs/game overall. their slash lines on the trip (.282 / .359 / .420) are an almost perfect match for their season-long figures (.278 / .368 / .414). so why does it seem as if they’ve squandered one opportunity after another? well, the truth is they have: they’re 13 for 62 on this trip with RISP, a .210 average, and they’ve lost a passel of runners on the basepaths (including 4 yesterday). those two factors explain why the cards have underperformed by 5 runs on this trip, according to bill james’ runs created formula --- their inputs yield an estimate of 34 runs, vs the 29 actually scored. per dave smyth’s Base Runs formula (which is more accurate in small sample sizes like this one), the cards have underperformed by 8 runs on the road trip --- more than one a game. it turns out that’s a season-long pattern:

runs RC BR
177 197 206

the cardinals are not wringing full value out of their offensive accomplishments; the offense as a whole is less than the sum of its parts, and by a sizeable difference --- at least half a run a game. what gives?

the obvious place to look first is hitting with RISP; on this road trip, anyway, lack of timely hitting helps to explain their low run output. but for the entire season we can’t pin the blame there; the team is hitting .270 with RISP, which ranks 5th in the league. it’s true, as houstoncardinal showed a while ago, that they’re not hitting for much sock with men on base --- slugging only .390 --- but the league slugging average with RISP is .392. so something still doesn’t add up here; the number of baserunners the cards put on base is way above average, and with RISP they have an above-average BA and an average SLG. . . . yet they’re still scoring a slightly below-average number of runs per game. whatever’s going on here, it ain’t a lack of timely hitting.

to double-check that conclusion, i looked at runs scored per RISP plate appearance. in the national league as a whole, the average plate appearance with RISP yields .319 runs --- that’s 2051 runs in 6416 plate appearances, if you’re scoring along at home. the cardinals as a team have scored 143 runs in 452 plate appearances with RISP --- or .316 runs per plate appearance. so they’re plating their fair share of runs in scoring opportunities . . . . . that ain’t the problem.

then what the hell is the problem? i fished around, looking for clues. here’s some of what i found:

  • 21 of the cards’ 30 homers have been solo shots, versus only two 3-run homers. that’s right ---- only two 3-run homers all season, and no grand slams. their 30 homers have been worth just 41 runs, or 1.36 runs per homer; the league average is 1.53 runs per homer. with a normal distribution, the cards would have plated 5 more runs via the longball. i don’t expect this pattern to change, and here’s why: teams won’t pitch to pujols with men on base. 5 of his 7 homers have been solo shots this year; the other two were the team’s lonely pair of 3-run jobs. no other cardinal has hit a 3-run homer this season. (paging mr. glaus; paging mr. duncan . . . . ) by the way, 7 of ryan ludwick’s 8 homers have been solo shots, and 5 have come in low-leverage game situations (a spread of 4 runs or more). without looking at any data, i’d have to guess that he’s just whacking fastballs out of the park --- bases empty; lopsided score; what the hell, here’s your pitch big fellah --- but he’s not seeing those pitches in rbi situations. ankiel, in case you’re wondering, has 4 solo shots and two 2-run shots.
  • the cards are dead last in the league in baserunners reached via error --- they’ve only had 10 gift baserunners, or one per 154 plate appearances. the league average is one per 95 plate appearances. at a normal rate, the cardinals would have 16 reached-on-errors (ROEs), worth about an extra 4 runs.
  • the cards lead the league in grounding into double plays, which isn’t surprising --- they put lots of men on base and hit lots of groundballs. the cards have had 550 plate appearances with a man on first base this year, all-inclusive --- ie, man on first only, first + second, first + third, and bases loaded --- and 40 of them ended in double plays, or one per 13.8 plate appearances. the league as a whole GIDPs only once per 16.5 pa. at a normal GIDP rate, the cardinals would have saved 7 outs / baserunners, or about 5 runs.
  • while the cards are scoring at a normal rate with RISP as a whole, that is not true with respect to scoring men from 3d base with less than 2 outs. the nl as a whole is scoring .61 runs for every plate appearance with a man on 3d and less than two outs, but the cards are scoring only .55 runs per PA, which ranks 14th among the 16 nl teams --- and about 5 runs below average. now this gets a bit fuzzy, because a single PA in this situation can be worth more than one run ---- e.g., you might have guys on 2d and 3d with nobody out, and the batter migh hit a single and drive them both in. it’s possible that the cards, via random chance, have had fewer multi-run scoring opportunities in this situational split; it’s possible this is all noise. but here’s one last consideration for you: the cardinals rank next-to-last in the league in sacrifice flies. only the rockies have hit fewers. the cards have had 85 sac-fly opportunities and only 7 sac flies, or 1 per 12 opportunities. the league average is 1 sac fly per 8 opportunities. the cards ought to have 3 or 4 more sac flies than they do. now, it doesn’t necessarily follow that they stranded all of those un-sac-flied baserunners ---- maybe they simply drove them in via groundball or basehit, rather than via the flyball. there’s so much noise here that i hesitate to jot down a run value, but i do think this is interesting and worth paying attn to.
just looking at homers, ROEs, and GIDPs, i think i can explain about 15 runs’ worth of underperformance. the ROE thing ought to normalize --- there’s no reason the cards should get fewer than their share of ROEs, aside from random chance. the GIDP thing will probably continue; too many groundball hitters on the team, not enough base stealers. and the home-run thing will persist unless and until glaus, duncan, ludwick, and ankiel can make teams pay for pitching around albert.

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