in case you missed it last week, cardinal stat consultant mitchel lichtman (better known as mgl) took part in a roundtable about sabermetrics at Baseball Analysts. the other two panelists were mgl's collaborator tom tango (aka tangotiger) and eric van, who now works for the boston red sox. among the many things i learned from that discussion about how mlb front offices are integrating stats into their decision-making process, the most interesting was this: the going rate for a run is $200,000; the going rate for a win is $2 million. here's the key exchange:
Tom: Yes, $200,000 per run or $2 million per win should be the going rate. If teams operated on that basis, they wouldn't even need a sabermetrician! . . . .
Mitchel: I do allow some leeway for elite, "top of the pyramid" players, where supply and demand really affects the market (even though it really shouldn't). But anything more than 3 or 4 million per marginal win (per year, of course) is generally a waste of money.
fungoes had a post on this very subject a few days ago, using a baseball prospectus stat called MORP that translates performance into dollar values. fungoes compared each cardinal player's projected 2006 MORP -- ie, the fair price for his expected performance -- with his 2006 salary, to see who looks like a bargain and who doesn't. head on over there to see the results; i will tell you that the team's highest-paid player is also its best bargain. also that all three of this off-season's main free-agent signees (rincon looper and encarnacion) appear to be subpar investments.
fungoes summed it all up in a table; i'm gonna do the same thing here, using mgl's pricing paradigm of $2m per win. before we get going, let's do a quick example from 2005 to make sure we're all down with the concept.
according to baseball prospectus' WARP (Wins Above Replacement Player), albert pujols generated about 10.7 marginal wins in 2005. at $2m per win, albert was worth $21.4 million bucks last season (ie, $2m x 10.7). the cardinals only paid $11m last year, which suggests albert was not only one of the best players in the game but also one of the biggest bargains. the cards paid him just $1m per marginal win -- half the going rate
another "wins" measurement, bill james' Win Shares, places albert's marginal wins total for 2005 at 8.3; at $2m per win, that makes him a $16.6 million player. still a huge bargain. by that measure, the cards got albert's wins at $1.3m per, a 35 percent discount.
got it? not all that complicated -- especially when you're pricing what a player has already produced. the real trick, of course, is to correctly price the production he'll deliver in the future. to do that, being lazy by nature, i'm just gonna use PECOTA --which i know a lot of you hate, and which like any player forecasting system is going to be wildly inaccurate a certain percentage of the time. but its premise is widely accepted; many major-league teams (including the cardinals) incorporate PECOTA or some version thereof into their evaluations. so just go with it for now. when the season's over and the stats are in the books, i'll revisit this post and we can all make fun of assumptions gone awry.
ready? let's begin with this off-season's free agent acquisitions, looking only at 2006. i've listed the players in descending order of price per marginal win (the far right column):
| player | projected marginal wins per PECOTA |
06 salary | price per marginal win |
|---|---|---|---|
| looper | 1.1 | $3.5m | $3.2m |
| rincon | 0.7 | $1.5m | $2.1m |
| encarnacion | 2.4 | $3.5m | $1.5m |
| bennett | 0.7 | $800K | $1.1m |
| ponson | 2.6 | $2.5m | $1m |
| spivey | 1.7 | $1.2m | $700K |
| cruz | 1.3 | $800K | $600K |
| TOTAL | 10.5 | $13.8m | $1.3m |
the cardinals heeded mgl's advice this off-season. they only significantly exceeded the $2m-per-win dictum for one player, braden looper -- and given the inflated market for relievers, it would have been difficult to hold the line there. of course, three of these contracts were multiyear deals and should really be evaluated as such. over the life of those deals, what did the cardinals pay per projected marginal win?
| player | projected marginal wins per PECOTA |
contract value | price per marginal win |
|---|---|---|---|
| looper | 2.8 | $13.5m | $4.8m |
| encarnacion | 5.8 | $15m | $2.6m |
| rincon | 1.4 | $2.9m | $2.1m |
| TOTAL | 10 | $31.4m | $3.1m |
ugh. now the looper signing looks truly disastrous -- and that's not my opinion, i'm simply applying the standards the cards' own consultant uses. they also overpaid for encarnacion, and although the premium is not a crippling one over the life of the deal, years 2 and 3 will be killers -- they'll be paying $3.5m per marginal win those years, nearly twice the going rate.
what about some of the deals the cardinals didn't make?
| player | projected marginal wins per PECOTA |
contract value | price per marginal win |
|---|---|---|---|
| burnett | 22 | $55m | $2.5m |
| grud'k | 3.3 | $6m | $1.8m |
| sanders | 2.7 | $10m | $3.7m |
| tavarez | 3.0 | $6.7m | $2.2m |
| nunez | 2.8 | $3.4m | $1.2m |
| mabry | 0.9 | $1m | $1.1m |
comments: first, PECOTA projects reggie sanders as a terrible buy; the cards probably had similar projections of his performance and stayed away for that reason. grudzielanek wasn't a bad buy at all, hence jocketty's reported willingness to meet his price (ownership allegedly vetoed that deal). no loss, though, as spivey -- at least per PECOTA, pre-alarmingly-bad-spring-training -- projects to be a better bargain. the cards could never have signed tavarez at the price he eventually settled for; you'll recall he was seeking a four-year deal until well into january, when he finally realized the market wasn't there -- and by then the cards' deadline for re-signing him had passed.
finally we come to burnett. they could have gotten him for $2.5m per marginal win -- a slight premium, but no worse than what they paid for encarnacion. as i've repeated way too many times, it might have made more sense to pay the premium for a potential difference maker like burnett, as opposed to paying the same premium for a spaceholder like encarnacion.
in case you didn't know i felt that way.
here's a table with info for the whole team -- well, most of it anyway. remember, mgl's $2m-per-marginal-win thing applies only to the free-agent market; the younger players who haven't yet become free-agent eligible shouldn't really be judged by that standard. but what the hell, it's my blog. i've thrown in a few extra columns of data just for fun. the players are listed in descending order of projected marginal wins:
| player | projected marginal wins per PECOTA |
projected value at $2m per win |
06 salary | projected profit/loss |
price per marginal win |
|---|---|---|---|---|---|
| pujols | 9.3 | $18.6m | $14m | $4.6m | $1.5m |
| edmonds | 6.9 | $13.8m | $12m | $1.8m | $1.7m |
| carpenter | 6.8 | $13.6m | $5m | $8.6m | $750K |
| suppan | 4.1 | $8.2m | $4m | $4.2m | $1m |
| mulder | 4.1 | $8.2m | $7.5m | $700K | $1.8m |
| rolen | 4.1 | $8.2m | $11m | -$2.8m | $2.7m |
| eckstein | 3.4 | $6.8m | $3.5m | $3.3m | $1m |
| marquis | 3.2 | $6.4m | $5.1m | $1.3m | $1.6m |
| yadi | 2.8 | $5.6m | $350K | $5.3m | $125K |
| j-rod | 2.8 | $5.6m | $350K | $5.3m | $125K |
| ponson | 2.6 | $5.2m | $2.5m | $2.7m | $1m |
| isringhausen | 2.6 | $5.2m | $8m | -$2.8m | $3m |
| encarnacion | 2.4 | $4.8m | $3.5m | $1.3m | $1.5m |
| bigbie | 1.9 | $3.8m | $900K | $2.9m | $500K |
| luna | 1.8 | $3.6m | $320K | $3.3m | $170K |
| spivey | 1.7 | $3.4m | $1.2m | $2.2m | $700K |
| thompson | 1.4 | $2.8m | $350K | $2.5m | $250K |
| cruz | 1.3 | $2.6m | $800K | $1.8m | $600K |
| looper | 1.1 | $2.2m | $3.5m | -$1.3m | $3.2m |
| flores | 0.9 | $1.8m | $350K | $1.45m | $380K |
| taguchi | 0.9 | $1.8m | ~$800K | $1m | $900K |
| rincon | 0.7 | $1.4m | $1.5m | -$100K | $2.1m |
| bennett | 0.7 | $1.4m | $800K | $600K | $1.1m |