The Dollar Value Of A Win

Recently, there’s been some misunderstanding over the application of how to use the dollar valuation we place on players here on the site. I take the confusion as a sign that we haven’t adequately explained what the valuation means, so that’s what I’m going to do this afternoon.

The biggest misconception about the dollar valuation seems to revolve around its purpose. It is not a salary predictor, or in way a projection of what a player is going to get when he becomes a free agent. It is a backward looking value statistic that quantifies the replacement cost of a certain level of production based upon the market price for that value. In terms of function, it is much more of a price than a value. In other words, the best description of the question that the valuation is answering is “how much would you expect to have to pay to replace this performance in free agency if you knew that you were going to get this level of value exactly?”

Once a performance is in the past, there is no uncertainty related to it. We know what happened. When a player signs a contract, of course, that performance is not known. Uncertainty adds risk, and risk drives down price, so we would not expect a team to actually pay a salary equal to the value listed on the players page. This is one of the main reasons why the value is not a predictor of what a player will earn in his next contract.

So, if that’s how you’re using the metric, you will undoubtedly be frustrated by the numbers, and probably conclude that they are worthless. They’re just not attempting to answer the question that you are asking, however.

Here is an example of how you should use the valuation. We have Chone Figgins’ 2009 value at $27.4 million, based on his +6.1 win season. No one is going to pay Figgins that much this winter, of course, nor should they. However, we can say that if the Angels wanted to replace what Figgins gave them last season, they should expect it to cost them about $27 million in free agent spending. Figgins produced at a very high level in 2009, creating a large surplus value for the Angels. The dollar to win valuation quantifies that surplus value, showing how much that performance would have cost if they could have expected to receive it and had to pay the going market rate for that performance.

That’s why we write that he was “worth” $27 million. It does not mean that we think the Angels should have paid him $27 million, or that they should pay him $27 million now, but he produced at a level equal to what you would expect if you had spent $27 million in free agency a year ago.

Obviously, most players are going to earn significantly less than their market value, because only a fraction of the population become free agents in any given season. Players with less than six years of service time have their contracts held down by the nature of the CBA, and none of those players should earn their fair market wage, given the structure of the system. Because the presence of these players who produce at a wage below their market rate, the overal value of a win is less than the market price – in general, it’s about $2.5 million per win, significantly less than the going rate for wins in free agency. However, a large portion of these players are generally not available, so they don’t affect the cost of a win, since they are not in the supply of available talent when teams go shopping. To use an example, the price of John Lackey is not affected by the presence of Zach Greinke, since the teams trying to sign Lackey do not have the option to alternately trade for Greinke, as KC would simply hang up the phone.

Hopefully this is somewhat helpful. There are a lot more issues surrounding the dollar to win conversion that we’ll get into, but the most important point in understanding the metric is to get what it is trying to quantify.



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Dave is the Managing Editor of FanGraphs.


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gnomez
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gnomez
6 years 6 months ago

Great explanation, although I disagree on the Greinke point. Although it would be fan base suicide, I believe the return the Royals could get on a Greinke trade would outweigh his costs.

geo
Guest
geo
6 years 6 months ago

Considering how low his costs are ($7.25 million), that the return would outweigh them is a no-brainer. I don’t think that would justify trading him, however; right now the Royals need him to retain some semblance of believability with their fans.

Joser
Member
Joser
6 years 6 months ago

But to get Greinke, a team would have to offer KC not what he costs, but what he’s worth. Would any team offer the FA equivalent of $30-$40+M in talent?

Logan
Guest
Logan
6 years 6 months ago

*Zack* Greinke. Not “Zach”.

You’ll correct this, and then someone will complain that I’m pointing out a flaw that isn’t there.

Norm
Member
6 years 6 months ago

Is ‘replacement level’ taken into consideration when getting these dollar values?

A question/answer from that last Keith Law chat:

Cesare (Jet City, Washington)
According to Fangraphs, Polanco was worth 50 million over the last three years … does anyone seriously think their valuations have any basis in reality?

Klaw (1:33 PM)
My favorite line on those came from a GM: “Their replacement level is, like, me.”

Adam W
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Adam W
6 years 6 months ago

Replacement level is the point where someone would not be able to make the majors based on ability alone (i.e. reputation, service time, and “intangibles” are not considered). If you are playing every day, you are likely well above replacement level.

Adam W
Guest
Adam W
6 years 6 months ago

It’s a little outside the realm of discussion, but I’ve always wondered why Fangraphs uses a linear conversion of WAR to $$$.

If there are significantly more 0 WAR players than there are 4 WAR players, and significantly more 4 WAR players than there are 8 WAR players, shouldn’t the model be exponential? Or did you choose a linear conversion for the sake of simplicity?

tangotiger
Guest
tangotiger
6 years 6 months ago

Linear was chosen because it conforms to reality.

The Real Neal
Guest
6 years 6 months ago

I don’t think that’s the case.

I think in reality, what happens is that teams pay what they think a free agent is going to be worth. This is going to be quite different from what a “one size fits all” projection system says they’re going to be worth.

I can’t remember what the projection system referenced was but let’s say it’s a 3-year 50%30%20% system.

Now you have two free agents.

FA one has a 3 year WAR score of 4/4/4
FA two has a 3 year WAR score of 5/1/1

In both cases, they’re likely to get an offer of 4*$wins
In the later case the system says he should get an offer of 3*$wins

When you talk about 30 companies vying for the services of one employee, that employee is going to tend to take the offer from the company that most highly values his services. The nature of the business means that teams with the most optimistic projections tend to get the players, whereas the valuation system here is based more on a “reasonable’ projection. FA contracts are not based on reasonable projections, they’re based on very optimistic projections.

To get accurate projections for valuation, you would actually need to custom tailor the evaluations. Sometimes a team will base the contract on a 3-year average, but more often the team will base it on the best season a player has had in the last two or three years.

acerimusdux
Guest
acerimusdux
6 years 6 months ago

If people are looking for the best economic explanation for why, I think it is that wins in baseball are largely a fungible commodity.

I’m surprised how many people seem to miss this, but it seems many want to think that a very unique player should have a market of his own. But take a unique player, a 5 win SS for example. If a team needs 90 wins to get to the playoffs, they aren’t going to get any extra credit for doing it with a 5 win SS and a 1 win LF, than if they did it with a 3 win SS and a 3 win LF.

Fans seem to be accustomed to go into the offseason looking at whoever seems to be the best player available, and thinking, “we have to have that player — he’s what this team needs”. But that isn’t the way it normally works.

Most of the time, a team is going to have multiple positions which could be upgraded, and multiple players to choose from. There is really no need to pay more than market rate for wins. Likewise, most players will have multiple teams who can use their services.

In such a competitive market, the overall supply and demand should produce a market price for wins that applies to all players. Neither the unique attributes of an individual player, nor the specific differing needs of individual teams, will change the market rate. A win is a win wherever you get it.

JoeR43
Member
JoeR43
6 years 6 months ago

You should feature this story, Dave. I know a lot of people who probably could use a little explaination of dollar values, who just assume this site advocates $27 mil a year contracts to Chone Figgins.

Scottwood
Member
Scottwood
6 years 6 months ago

With regards to relievers, do we have to manually account for their leverage index or is that already accounted for in their WAR. I was a bit confused with the Rivera post. If it is not, then wouldn’t that change the WAR and salary data for a handful of relievers?

MattC
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MattC
6 years 6 months ago

Honestly I still don’t understand it, well I guess I should say I understand what you are saying and the concept I just don’t really understand the dollar figures. Like you have Zobrist at 39 million dollars. How could it cost a team that much to replace him when the highest paid player in baseball is only like 25 million dollar? And that was signed after he(A-Rod) put up a season with a higher War than Zobrists. It just doesn’t make sense to say “This is what you would expect to pay in Free agency to get that kinda production” when there are no contracts even in the same ball park as that and nobody is gonna pay that even if they were guaranteed that kind of production as evident by the A-Rod contract. So basically I like the concept I just think the numbers are a bit inflated.

Bill
Member
Bill
6 years 6 months ago

Yeah, has there been so much inflation that Barry Bonds’ 12.3 WAR (!) 2004 season was worth 38.1 million (and his 13.3 WAR season worth 34.5), while Ben Zobrist’s 8.6 WAR was worth $38.5 million? I just find it hard to believe wins were worth 3.1 million in 2004 and 4.5 million or so in 2009.

Sky Kalkman
Member
6 years 6 months ago

It’s not that wins were “worth” but how much they “cost”. Back in 2004, teams just weren’t spending as much on players, meaning it wouldn’t have cost as much to replace Barry Bonds’ (or Ben Zobrist’s) production back then versus now. Those wins helped their teams the same.

B
Guest
B
6 years 6 months ago

Well think of the Arod contract not in terms of 1 year- but in terms of the life of the contract. His production at the beginning is expected to be higher than his production at the end. What that’s telling us is that over the life of the contract, they don’t expect ARod to produce as much as Zobrist did, on average. This makes sense, as ARod was 32/33 in the initial year of his contract, and it’s a 10 year contract. It’s very doubtful he’ll average anywhere near 8.6 WAR per year over that 10 year span (which is why he’s making a lot less than $39M, because he’ll probably average a lot less than 8.6 WAR).

Jack Moore
Guest
6 years 6 months ago

Mainly, it’s because it’s so incredibly rare for one player, even the great ones, to put up seasons like Zobrist’s. You’d have to pay for two or even three players to cover the 8.5 WAR he put up, and that very well could cost 39 million dollars.

Meddler
Guest
Meddler
6 years 6 months ago

This is because there are virtually zero players who PROJECT as 8.6 WAR players. No buyer of talent ever looks at the market and assumes a player is going to be that valuable. It may be possible that they’ll be that valuable, but when talking about past performance like Dave said, we don’t have to apply uncertainty principles, we only have to do that when talking about future expectation. If you want to know what Zobrist should have been paid for his 2009 season, you look at the most accurate projection models just before that period and pay him according to the WAR derivation from those, but you can’t assume the knowledge that he was going to be 8.6 WAR. If someone could be absolutely sure that a player would perform at exactly 8.6 WAR with zero risk or upside, they almost certainly would pay about that much for a season of that kind of certain production. But outside of Pujols, that kind of expectation for production just doesn’t exist, so no one gets paid like that.

So, if you want to buy the amount of talent that would project to be an expected 8.6 WAR level, i.e. comparable to the certain level of production that Zobrist had already put up, you have to pony up that kind of dough, and since there aren’t any single players who figure to be available on the market and project that favorably, that investment is going to have to get spread out to multiple players or the win expectation is going to be reduced from the level that Zobrist actually performed at.

tangotiger
Guest
tangotiger
6 years 6 months ago

If ARod signed a one year deal, he’d have signed for 30-35MM$. If ARod would have GUARANTEED an MVP performance, AND also signed for 1 year, he would have signed close to 40MM$

Joe R
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Joe R
6 years 6 months ago

Hey Tom, is the annual $ per win mark basically just ($ spent in free agency) / (WAR produced)?

tangotiger
Guest
tangotiger
6 years 6 months ago

If by WAR produced you mean WAR in the upcoming year, then, basically, yes.

I encourage you to read this thread for a fuller understanding:
http://www.insidethebook.com/ee/index.php/site/comments/how_much_did_the_2009_free_agents_sign_for_per_win/

Joe R
Guest
Joe R
6 years 6 months ago

Pretty good stuff, now I have more than enough ammo to justify the Marco Scutaro signing for the Red Sox*

*assuming he plays closer to the 2008 Scutaro aka the version I expect and not 2007 version that would crush me or 2009 version that would possibly make me dance

tangotiger
Guest
tangotiger
6 years 6 months ago

The Scutaro signing follows the Polanco signing in terms of setting a depressed market. It can only be viewed as nothing but positive by the teams. If someone is complaining, they are complaining that they spent 15K on a new Accord, instead of 25K on a new Lexus. You’re getting a great deal either way, but I presume the Redsox fan want the 25K spent, rather than basking in the 10K they saved in either case.

Joe R
Guest
Joe R
6 years 6 months ago

Basically.
I personally approve of the signing, obviously. The only whining I’m hearing that may be legitimate (since I really see nothing that suggests that Scutaro can’t at least provide 2.5 WAR) is that we lose a pick.

Okay, 2010 money, $4.8 mil a win (wild ass guessing), 2.5 WAR / season x 2 seasons x $4.8 mil / WAR = $24 million

$12.5 million salary + $5.5 million opportunity cost (aka lost pick_ = $18 million

Even without the pick, this looks like a good contract. Obviously Scutaro comes with injury risk and more years of badness than goodness, but I think the risk is covered by the ~ 25% discount.

Joe R
Guest
Joe R
6 years 6 months ago

Well, closer to a 22.2% discount after I factor in present values of cash flows and the 6% salary increase I fudged between 2010 and 2011, and 2011 and 2012, and dropping Scutaro from 2.5 WAR in 2010 to 2.2 WAR in 2011.

$22.56 million worth of value is Base Year 2010 money, $17.55 million worth of opportunity cost in BY10.

Still nice to me.

Trenchtown
Guest
Trenchtown
6 years 6 months ago

Hey Dave, glad to see that you are putting your economic degree to better use then mine

Patrick
Guest
Patrick
6 years 6 months ago

With the exception of working in leverage index for relievers (I second the above – the Mo post confused me quite thoroughly), this all seems pretty simple.

WAR is saying that teams pay, on average, this much for this much performance. No one gets paid as though they’re going to have an 8 WAR season (Zorilla, wooh!), because even for, say, Pujols, assuming that he’ll do that is a stretch…
Sure, makes sense.

I knew that the WAR to dollar model was linear because it’s derived directly from what teams actually do, but it’s interesting that team spending is linear. (I know why has been touched on above, but it’s STILL interesting that scarcity and increased risk are treated as essentially equivalent and more or less cancel one another out.)

Greg
Guest
Greg
6 years 6 months ago

FanGraphs value always made perfect sense to me, but we economists are well versed in the concept of “replacement cost” as a valuation of an asset:

http://www.investorwords.com/4181/replacement_cost.html

Darren
Guest
Darren
6 years 6 months ago

Nice post.

Did you guys ever come up with a revised $/WAR based on what’s happened since 08? Seems like last years market would knock that $4.4M down considerably.

sean
Guest
sean
6 years 6 months ago

What about players with negative WAR? Delmon Young (siiiigh) has posted negative WAR for two consecutive seasons now. While it’s funny to think of him paying the Twins $6 million in 2009 for the opportunity to play, the cost to replace him with free agent talent would be the minimum salary.

Adam W
Guest
Adam W
6 years 6 months ago

The negative value means is that the team would have to spend an extra $6 million on the FA market to make up for his lack of production (i.e. get back to 0 WAR).

Travis L
Guest
Travis L
6 years 6 months ago

This is almost a good example to show to people who complain about inflated dollar figures. It doesn’t work b/c Young is a restricted player, but imagine he were a FA: for players like Zobrist who look to be worth $38 million, there are negative WAR players (like our FA Young) who are worth negative dollars. That helps balance out the average a little bit.

I think a couple of examples of this are the Dodgers’ Schmidt contract and the Andruw Jones contract. Both those guys really inflated the overall cost per win numbers because of their expensive contracts and low performance.

soxxgo
Member
soxxgo
6 years 6 months ago

I think 4 million per win is inflated. Do you really think that Albert Pujols at 8 WAR has the same value as a pair of 4 WAR players? In terms of wins, yes they are the same. However, a team may be willing to pay Pujols 6 million per win come free agency because he will bring people to the stadium no matter what. You gotta remember that there is more to making money than just wins in sports ( i.e. Ichiro for the Mariners). A superstar can draw fans and sell jerseys even when they are terrible. A trio of 2-3 WAR players doesn’t do much for revenue when a team is 20 games under .500.

Kevin S.
Member
Kevin S.
6 years 6 months ago

So, you’re arguing that Albert Pujols could get $48 million/year on the free market?

I’m not sure if this is a mathfail or a logicfail. Maybe both.

JoeR43
Member
JoeR43
6 years 6 months ago

No, the logic of it is that if Albert Pujols knew that he would produce the season he did and locked in a one year contract, he would be worth that amount of $.

And like Tom Tango said earlier, if you take the $ spent in FA, divide it by the expected WAR of the players, you get about the baseline fangraphs has. Hence ideally, you farm as much of your talent as you can.

Joser
Member
Joser
6 years 6 months ago

And your evidence that teams will overpay superstars for this reason is what, exactly? If anything, it appears teams only use this logic to overpay lesser players who are fan favorites, eg Griffey. The superstars just get longer contracts.

Eddie
Guest
Eddie
6 years 6 months ago

Still new to the concept of WAR and most of the advanced metrics. How much does a season like Soriano’s 2009 skew the cost of a win on the open market?

soxxgo
Member
soxxgo
6 years 6 months ago

I wrote the wrong amount above. I meant 4 million per win for Pujols. just because Pujols will get 4 million per win it doesn’t mean that all of baseball values a win at 4 million.

Kevin S.
Member
Kevin S.
6 years 6 months ago

Except evidence has been provided that players get same amount per win per year on multi-year deals, upthread.

Zooby
Guest
Zooby
6 years 6 months ago

“However, we can say that if the Angels wanted to replace what Figgins gave them last season, they should expect it to cost them about $27 million in free agent spending.”

Really? I’m pretty naive when it comes to this subject, but the numbers don’t seem to add up. Matt Holliday will be the priciest FA on the market and has been a 6 win player for the last two season and…he will cost the Angels about half of that, no?

Kevin S.
Member
Kevin S.
6 years 6 months ago

In a GM’s wetdream, perhaps. Holliday won’t get $27/year, but then again, no reasonable person would expect him to average 6 WAR/season over the course of a five-year deal, especially in the AL. If he gets $18MM/year, a much more reasonable number, that would be figuring an EV of 4 WAR/year, which seems reasonable, given risk factors, league difference, and expected decline.

oldjacket
Member
oldjacket
6 years 6 months ago

values, not prices!

JoeR43
Member
JoeR43
6 years 6 months ago

This

Ivan Grushenko
Guest
Ivan Grushenko
6 years 6 months ago

I still don’t think I understand. Are you saying that if you expect a player, e.g. Marco Scutaro, to be a 2.5 WAR player and you expect that 1 WAR should cost $4.8M in 2010 dollars, you should be willing to pay up to $4.8M X 2.5 = $12M on a one year deal for Scutaro?

Or are you saying that because Expected WAR has more uncertainty than Historical WAR that this formula is invalid in projections, and at the very least, there should be some discount for what a team would pay for Marco?

Adam W.
Guest
Adam W.
6 years 6 months ago

No GM has a crystal ball. The $ value of a win is inflated by guys like, say, Kevin Millar, who got paid ~$4 million in 2008 to be replacement level. Now, obviously, if the Orioles knew he would be replacement level, they wouldn’t have paid him that much – but they didn’t know that, and they did pay him that much.

Cases like 2008 Millar why Dave says that you would reasonably expect to spend $27 million to replace Figgins’ production on the FA market: there are sure to be some 0 WAR clunkers in there, and these guys inflate the average cost per WAR.

Also, as has been pointed out numerous times by others, GMs have biases – they tend to, among other things, overvalue RBIs and undervalue defense. This has a huge impact on the $ per WAR valuation.

So, to simplify, GMs set salaries in advance and pay for things that aren’t WAR. This inflates the average cost of a win on the FA market.

KJOK
Guest
6 years 6 months ago

I understand what Fangraphs is doing, but I’d rather see a different number used. Teams don’t replace players solely thru free agency. They might replace a player by promoting a rookie, for example. The average salary is $3 million. Subtracting out the league minimum $300k would give you $2.7 million ‘over replacement’ average for MLB. i think this would be a better number to use, or at least show in conjunction with the ‘free agent WAR value’ number.

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