pitching for pay

the rockies are lucky they didn't get blown out again; if a couple of just-foul balls had gone fair instead, the score woulda been 6-1, 7-1, something like that. the long layoff seems to have hurt colorado (although their lack of offense in game 1 is probably josh beckett's fault); their pitchers aren't sharp, and they've made mental errors in the field and on the bases. i haven't counted them out just yet, but in the next two games they will start josh fogg --- a finesse pitcher who the patient red sox hitters ought to slaughter --- and aaron cook, who hasn't pitched in over 2 months. don't like their chances.

today's post is heavily numerical. using a method similar to the one azruavatar employed in estimating eckstein's dollar value, i'm trying to establish rough estimates for what the major f.a. pitchers are worth. i'm particularly curious about lohse and silva, the guys most likely to draw interest by our team. before i lay out the method in detail, let me issue the major caveat: these are very crude estimates. i haven't adjusted for age, playing time, or current health status, all of which can affect what a pitcher gets paid; moreover, i'm using only a couple of broad metrics to assess performance. so i don't consider the dollar figures i'm deriving here to be absolutes; not by any stretch. they're only meant to be rough gauges, give-or-takes. if the exercise says pitcher X is worth $8m a year, it doesn't mean that's his precise market worth; it's just a reasonable starting point. a team that offers said pitcher $9.5m a year isn't necessarily overpaying; a closer look at the guy's overall profile might yield evidence justifying the extra investment.

on with the survey.

i looked at 25 pitchers who signed contracts last year, either new free-agent deals or extensions. the two metrics i used to estimate each player's expected level of performance were pitching runs above replacement (PRAR), a Baseball Prospectus stat devised by chris davenport; and win shares, a bill james stat featured at the Hardball Times. in the latter case, i looked only at pitching win shares (excluding a pitcher's hitting and fielding contributions). while neither of these stats expresses a player's value with unassailable precision, they're both trustworthy and have a long track record. moreover, they're both bottom-line metrics: one expresses performance in terms of runs, the other in terms of wins. the goal here is to calculate how much teams are paying, on average, per run and per win. i only looked at last year because a different collective bargaining agreement was in force prior to that, as well as a different national tv contract; changes to both of those deals significantly altered the economics of the game last off-season, so salaries paid out in 2005-06 and before aren't particularly useful for comparison.

again using azruavatar's method, i took a three-year weighted sample of each metric (.50 for the most recent year, .35 for the year prior, .15 for the year prior to that) to derive an expected performance for each pitcher in year 1 of the contract. just to pull out an example: heading into last off-season, barry zito was coming off a 73-PRAR season, preceded by 67- and 52-PRAR years. so the formula is (.50 x 73) + (67*.35) + (52*15) = 67.75. that's our working estimate of zito's expected performance in year 1 of his contract --- 68 runs above replacement level. the average annual salary of his deal was $18m, so we divide $18m by 68 to yield a bottom line, the dollars per run. in zito's case, the quotient was $265,683.

before we go on, another couple of caveats. one obvious weakness in this method of valuation is that zito's contract runs for 7 years, but we're only working with his expected performance in year 1. if i knew of some quick/dirty method for roughing out long-term projections, i would estimate zito's PRAR over all 7 years of his deal --- but a) i know of no such method, and b) no 7-year projection is gonna be accurate, no matter what method you use. even single-year projections of pitching only correlate to reality at about a 50 percent level; by the time you start projection 2 and 3 years out, the numbers aren't particularly meaningful. a second weakness is that zito's salary isn't structured in equal increments; he'll get paid less than $18m for the first couple years of the deal, more than that in the later years. if i wanted greater precision, i'd adjust these valuations to reflect back-loading of contracts --- and in that case i'd also need to factor in the time-value of money and a bunch of other factors that i don't really understand.

i acknowledge those limitations of the survey, and i ain't doing anything about 'em.

rather than post the full table of all 25 pitchers, i'm just gonna provide a link to the spreadsheet for those who want to look it over. for everyone else, here are the overall averages paid to the 25 pitchers last year:

most of the "major" free agents were very close to these averages: lilly, padilla, schmidt, zito, marquis, pettitte, and suppan all were paid between $204K and $265K per expected run and $1.03m to $1.13m per expected win share. the vazquez and buehrle extensions also fell inside that range on the PRAR side (their contracts were bargains on the win-share scale, paying less than $1m per expected win share). the clustering gives me confidence that these averages actually have some meaning; there was little variation in the rates paid to pitchers who were healthy and still in (or close to) their prime. players who were older, coming off injuries, or coming off a particularly bad season tended to get paid less than average; a few guys were overpaid based on perceived potential (one of them, gil meche, proved worthy of the extra investment for the 1st year of his deal).

if we apply last year's average rates to the free-agent class of 2007-08, we arrive at the following estimated values:

	exp 08 PRAR	exp 08 WS	exp sal PRAR	exp sal WA
schilling	54	11.5	$12.2m	$12.7m
glavine	52	12.6	$11.8m	$13.8m
livan	48	10.7	$10.8m	$11.8m
silva	40	9.2	$9.0m	$10.0m
lohse	38	7.7	$8.6m	$8.5m
jennings	34	6.2	$7.6m	$6.8m
lieber	31	6.4	$7.1m	$7.0m
ro lopez	26	5.2	$5.8m	$5.7m
pineiro	20	3.8	$4.6m	$4.2m
weaver	22	3.5	$5.1m	$3.9m

you'll note the cardinals are paying pineiro about 50 percent more than his expected salary; he's getting $321K per expected RAR and $1.7m per expected win share, well above last year's average rates. he's in the same category that adam eaton, gil meche, randy wolf, and kip wells were in last off-season --- all were priced above the 06-07 market, with the buyer betting that the pitcher could significantly exceed his recent level of performance.

none of the other values particularly surprises; they all pass the smell test, imho. i left guys like bartolo colon and freddy garcia off the list, owing to their injury status; i did include a couple of surgically enhanced arms (jennings and lopez, who are both coming off flexor-tendon fixes) but found the numbers not to be credible. is somebody really going to pay $7m a year to find out if jason jennings can still throw a baseball? lord help us if they do. . . . . of course, if their injuries drive the bidding down far enough, jennings and lopez might represent buying opportunities; should one of them bounce back, he could be a great bargain (much as chris carpenter was a few years ago). lopez in particular strikes me as likely to go cheap; both he and jennings were traded last spring, but lopez was only perceived to be worth a fringe minor-leaguer, while jennings cost an everyday centerfielder and 2 good pitching prospects. it might be worth plunking down a million or two for the privilege of finding out how lopez looks 6 months after that surgery.

another guy who might go below market is kyle lohse, who doesn't have a power arm and sports a string of ugly won-loss records. while most teams don't actually give a lot of weight anymore to w-l, they can still wield it as an argument at the bargaining table. lohse at $8.5m; pass. lohse at $7m? tempting . . . . . . he's prob'y gonna go for at least $8.5m, though.