21 replies to this topic

[Worst Trade Evah]

Nate Silver had a fun column in BP recently: Lies, Damned Lies: A Mulligan on Guzman

In it, he offers a quick method to evaluate performance value in dollar terms. His idea is that teams spend for performance non-linearly -- the top performers create disproportionately more value and are compensated disproportionately also. He generates a kind of utility function to estimate this, which is

Salary = (WARP^2 * $212,730) + (WARP * $402,530)

The resulting metric he calls MORP, suitably enough. It yields a way to evaluate performance in salary terms. I wouldn't go crazy with this stuff, but it's the off season, and I thought it'd be fun to see how we did.

I got Sox hitters in a table, plugged in their WARP1 values and generated a BP salary figure or MORP with Silver's function. Then I subtracted from that the actual salary paid to the player. The difference yields value derived for money spent: a positive number is a good investment, and a negative number is a poor one.

It's obviously not a total surprise what the results are, but they were a little surprising to me, in terms of magnitude at least.

NAME         WARP         BP SALARY      ACTUAL (EST)        DIFFERENCE
Ortiz, D        8    $16,834,960.00     $6,250,000.00    $10,584,960.00
Mueller, B    5.2     $7,845,375.20     $2,100,000.00     $5,745,375.20
Millar, K     3.9     $4,805,490.30     $3,500,000.00     $1,305,490.30
Varitek, J    6.2    $10,673,027.20    $10,000,000.00       $673,027.20
Youkilis, K   0.9       $534,588.30       $323,125.00       $211,463.30
Damon, J      5.5     $8,648,997.50     $8,500,000.00       $148,997.50
Graffanino, T 1.6     $1,188,636.80     $1,100,000.00        $88,636.80
Kapler, G     0.2        $89,015.20       $150,000.00       -$60,984.80
Stern, A     -0.1       -$38,125.70       $316,000.00      -$354,125.70
Mirabelli, D  1.3       $882,802.70     $1,500,000.00      -$617,197.30
Bellhorn, M   1.7     $1,299,090.70     $2,120,000.00      -$820,909.30
Nixon, T      4.3     $5,664,256.70     $6,500,000.00      -$835,743.30
Vazquez, R   -0.5      -$148,082.50       $700,000.00      -$848,082.50
Cora, A       0.5       $254,447.50     $1,300,000.00    -$1,045,552.50
Payton, J     0.8       $458,171.20     $1,750,000.00    -$1,291,828.80
Ramirez, M    6.6    $11,923,216.80    $20,000,000.00    -$8,076,783.20
Renteria, E   1.8     $1,413,799.20    $10,000,000.00    -$8,586,200.80

Ortiz obviously was a ridiculous value. Maybe Perahlta or someone, but it's hard to see who might have yielded the kind of value Ortiz did. And WARP even under-rates Ortiz, missing his 3-4 extra wins just derived from leverage this year.

Everyone's favorite Billy Mueller was second, which is no surprise. Thanks be to Jesus, for all glory and praise go to him, for giving us such a deal at third base!

Much-maligned Kevin Millar was a net positive value, and ranked 3rd on the team on a value basis. Surprise!

Johnny Jesus did about what he should have. Not looking good for 10,000,000/yr for 5 years though Johnny.

Who were the goats? Edgah, Manny, Payton (why'd he ever sign here anyway?), and Cora aren't looking too good. Trot's on the bubble with Bellhorn and Vazquez, but on a percentage basis he's not so bad.

If I get motivated or there's interest, it might be fun to see how other teams did.

I couldn't find salary data for Olerud or Petagine, so they are omitted, as are some scrubs like Machado, etc.

Just thought it was kind of fun.

Edited by Worst Trade Evah, 13 October 2005 - 10:40 PM.

[epraz]

Trot's on the bubble with Bellhorn, but on a percentage basis he's not so bad.

Wouldn't percentages be more accurate?

Player           Percentage

Ortiz, D	269.4
Mueller, B	373.6
Millar, K	137.3
Varitek, J	106.7
Youkilis, K	165.4
Damon, J	101.8
Graffanino,	108.1
Kapler, G	59.3
Stern, A	-12.1
Mirabelli,	58.9
Bellhorn, M	61.3
Nixon, T	87.1
Vazquez, R	-21.2
Cora, A          19.6
Payton, J	26.2
Ramirez, M	59.6
Renteria, E	14.1

Can't figure out how to line it up well, but here it is.

Edited by epraz, 13 October 2005 - 10:47 PM.

[Worst Trade Evah]

Wouldn't percentages be more accurate?

<{POST_SNAPBACK}>

I guess, but there's a finite budget and being wrong on a guy by a lot is still bad, even if it looks better on a percentage basis. Could do it and see how it looks I suppose.

[PedroKsBambino]

Hmm...Kind of interersting, thanks for collecting the info.

I could see a case for percentages, though that gives you "efficiency" more than total value, I'd think.

How is it that Manny produced $5 mil less than Ortiz?

[Bowlerman9]

I think defense must play a huge huge part of it.

No way Manny is worth 5M less than Ortiz. No way Renteria is worth anything less than 4 or 5M.

[Worst Trade Evah]

It's a pretty non-linear function, so small differences at either end of the scale will have large payout effects. He justifies the shape of the curve in the article, though I'm sure plenty more can be done.

I agree the Manny/Ortiz MORP difference is odd, considering the similarity of their seasons, but that's where the numbers fell. Manny had 6.6 WARP and Ortiz 8. That's a what? 17% edge for Ortiz in WARP, and at the high end of the scale where value really piles up.

Edited by Worst Trade Evah, 13 October 2005 - 11:00 PM.

[Worst Trade Evah]

The %'s are interesting, but I see epraz has them already. Vazquez should have paid the Red Sox this year.

[PedroKsBambino]

A couple other notes from the article which were interesting to me.

1. Using a similar metric pre-season, Silver ascertained that the best free-agent signing was (get this) Cristian Guzman. Oops.

2. To adjust the metric (WTE used his revised one) he dumped PECOTA and used a three-year weighted WARP number. That had to hurt for Silver! Though he did maintain it's a "less accurate" number.

Also, there's an analysis of roster construction which emphasizes the value of being near or above-average at every position. He concluded this about the ideal approach:

I prefer the concept of flexibility: avoiding long-term commitments at enough positions that you can properly take advantage of arbitrage opportunities in the market.

What does that remind you of?

[ShoelessJoe]

God knows I am not Renteria's biggest fan, but doesn't 1.4M seem a little low? Based solely on last years performance, 4 or 5 seems more realistic.

[philly sox fan]

I actually have a half written writeup on why the original method Silver used sucked. Idiot went and partially fixed his mistake.

In the original artilce he derived a 2.14M value per WARP. He then went on to do a few articles mindlessly multiplying every WARP number - even very, very low ones - by 2.14. In effect he was saying the incremental value of going from 0 to 1 WARP was worth the same as going from 8 to 9 which is just stupid.

It leads to the idea that five two WARP players are worth the same as one 10 WARP player. It partially leads to the prediction that Christian Guzman was the bargain of the FA season.

One of the second tier BPers took Silver's original method and applied it to the crappy Diamondbacks and calculated that the team was actually worth something like 120M. He never realized how ridiculous that was.

But this is a big improvement.

[Worst Trade Evah]

God knows I am not Renteria's biggest fan, but doesn't 1.4M seem a little low? Based solely on last years performance, 4 or 5 seems more realistic.

<{POST_SNAPBACK}>

It does seem low, but then so does 1.8 WARP. Renteria had a pretty lousy season, all in all. Poor old Bellhorn, booed out of town, came in at 1.7 WARP.

[philly sox fan]

God knows I am not Renteria's biggest fan, but doesn't 1.4M seem a little low? Based solely on last years performance, 4 or 5 seems more realistic.

<{POST_SNAPBACK}>

Not necessarily. Last year they had him as a 3.8 WARP player with a -8 FRAA.

This year he hit about the same and his defense slipped to -22 FRAA.

The Sox contract breaking even was based on an offensive rebound and the fact that he was ranked pretty highly by UZR (and FWIW he was average by UZR at the All Star break).

If you give him credit for average defense than he would move up to the 5-6M range, maybe higher. If you don't, then it was a pretty lousy worhtless year.

[mr guido]

I was using Studes @ Hardball Times' approach on the problem last year... he has a calculator that takes into account the contract status of the player (arb, FA, pre-arb) as well as win shares & expected win shares.

This one makes a whole lot more intuitive sense when you look at the list...

http://www.hardballt...n-shares-value/

A sampling:

Papi, 31 WS, 14 Exp, $625000 = $+13,580,824
Damon, 25 WS, 17 Exp, $8.5 = $+5,215,058
Manny, 34 WS, 17 Exp, $20m = $+5,627,291
Mueller, 18 WS, 16 Exp = $+3,938,322
Wakefield, 16, 12, $4.65 = $ 3,189,673
Nixon, 16, 12, $6.5 = $+2,034,422
Arroyo, 12, 11, $1.85 (arb) = $ 1,489,002
Tek, 19 WS, 14 Exp, $10m = $+1,114,399
Clement, 12, 10, $6.75 = $ -231,006
Miller, 4, 5, $~2.5 = $ -1,162,881
Wells, 13, 10, $10.5 = $ -1,729,006
Millar, 10, 13, $3.5 = $ -1,787,341
Bellhorn, 5, 9, $2.1 (arb) = $ -3,421,641
Renteria, 14 WS, 18 Exp, $10m = $ -5,635,401
Foulke, 2, 5, $7 = $ -5,660,402
Schilling, 4, 6 $14.5 = $ -9,289,197

[jmcc5400]

This made me laugh:

Even Billy Beane would find it hard to stomach the presence of a truly replacement level player in his lineup. The A’s have had a few Scott Hattebergs--players who perform slightly below average and are paid well below average--and a few mistakes like Terrence Long, but they won’t call up an underqualified rookie from Sacramento, pay him the league minimum, play him every day, and sit around patiently while he posts a .235 EqA. That would turn Beane’s job from being difficult into outright impossible.

No, they'll just pay their catcher 10.6 million, play him every day and sit around patiently while he posts a .240 EqA.

Maybe I'm just laughing at myself because I did the same damn thing with Kendall this year on my rotisserie team.

- jmcc5400

[ragnarok725]

I was using Studes @ Hardball Times' approach on the problem last year... he has a calculator that takes into account the contract status of the player (arb, FA, pre-arb) as well as win shares & expected win shares.

This one makes a whole lot more intuitive sense when you look at the list...

http://www.hardballt...n-shares-value/

A sampling:

Papi, 31 WS, 14 Exp, $625000 = $+13,580,824
Damon, 25 WS, 17 Exp, $8.5 =  $+5,215,058
Manny, 34 WS, 17 Exp, $20m = $+5,627,291
Mueller, 18 WS, 16 Exp = $+3,938,322
Wakefield, 16, 12, $4.65 = $ 3,189,673
Nixon, 16, 12, $6.5 = $+2,034,422
Arroyo, 12, 11, $1.85 (arb) = $ 1,489,002
Tek, 19 WS, 14 Exp, $10m = $+1,114,399
Clement, 12, 10, $6.75 = $ -231,006
Miller, 4, 5, $~2.5 = $ -1,162,881
Wells, 13, 10, $10.5 = $ -1,729,006
Millar, 10, 13, $3.5 = $ -1,787,341
Bellhorn, 5, 9, $2.1 (arb) = $ -3,421,641
Renteria, 14 WS, 18 Exp, $10m = $ -5,635,401
Foulke, 2, 5, $7 = $ -5,660,402
Schilling, 4, 6 $14.5 = $ -9,289,197

<{POST_SNAPBACK}>

Manny at a 5.6M POSITIVE? So he was worth 25M this year? Or am I reading this wrong...

[DSG]

His method seems pretty similar to one I came up with a while ago. My formula was:

xSalary = (W^2)/6.25

Salary is expressed in millions. Wins could be win shares/3 or whatever you choose to use. The problem with using WARP is that is vastly overrates fielding. With my method and WS, Renteria comes out to being worth $3.5 million.

[mr guido]

Manny at a 5.6M POSITIVE? So he was worth 25M this year? Or am I reading this wrong...

<{POST_SNAPBACK}>

Yup, according to that calcualtion. 34 Win Shares is pretty valuable, according to this algorithm it's worth about $25m if you could sign him to a 1 year FA deal.

Of course that is saying it's his value in 2005 alone... any team deciding if they would want to hypothetically claim Manny off of waivers now would need to figure out if he will be worth the $60m in the next 3 years.

[NomarsFool]

I have a tough time with Manny being just about equal to Varitek, and only a little bit better than Nixon. Yes, Varitek brings a lot to the table in terms of intangibles, calling pitches, etc., but that formula obviously doesn't count that. Just looking at the stats, Manny has to be worth a lot more than Varitek or Nixon. Of course, a good hitting catcher isn't always that easy to find, but an OF who hits 40 HR and drives in 140 isn't that easy to find either.

[Rudy Pemberton]

It leads to the idea that five two WARP players are worth the same as one 10 WARP player.

Actually, I think a LOT of people believe this.

[DieHard3]

Actually, I think a LOT of people believe this.

<{POST_SNAPBACK}>

It depends on what you're replacing doesn't it?

If you have the 1962 Mets or 2003 Tigers, with lots of worthless players sucking up at bats, then adding five players at two WARP might be equivilent/superior to 1 player at 10 WARP and keeping four scrubs.

If you have the 2005 Red Sox, it's a different equation entirely.

[PedroKsBambino]

Yeah, I think most everyone understands that there's another piece to that---what the "other" player in the 10 warp scenario does for you. If he does nothing, or is a negative, you are as well off with the 2 five warp players.

Keep in mind as well that this model is really only doing a one-year evaluation. As was noted earlier in the thread about Manny, even a guy who is producing a very high warp for a year might not be a good bet to be worth his contract over three years (or at least you'd have to analyze it that way).

[LahoudOrBillyC]

The comparison of Ortiz and Manny breaks down when you think it through. Ortiz gets "credit" for not fielding his position, as opposed to fielding it poorly, and I think DHs also have a lower (statistical) replacement level than left fielders have. I think teams tend to play their best players in the field if they can, so teams with less good hitters end up with a bunch of dreck playing DH while their left fielder can hit.

Of course, this just gives Ortiz more credit for "being able to DH".