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?
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.
We’ve talked about this a lot. Teams chose the linear model, not us. We just reflect what they’re spending.
The best explanation for the linear nature of spending is that teams are apparently assuming that the risk offsets the scarcity. In other words, while the higher WAR player receives a value boost due to the lack of comparable players, he gets docked because teams would rather diversify, spreading their risk around so that one player can’t sink a season. These effects cancel out, or really close to it.
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.
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?
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.
Was the joke at FG’s expense or the GM’s? It sounded like he agreed that there was a problem with the replacement level, but I don’t know enough about various replacement levels to know the difference.
By the way, how many games would a replacement level team win in your model and does that number flucuate from year to year?
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.
I don’t think he was saying there was a problem with replacement so much as making jest at how funny the concept of 48-49 win team is.
Comment by The A Team — December 4, 2009 @ 2:44 pm
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 $39M, because he’ll probably average a lot less than 8.6 WAR).
Speaking of risk, I’m surprised it didn’t get its own paragraph in the article. Suppose Chone Figgins is truly a 6.9 win player and you know that IF HEALTHY he’ll be worth 6.9 wins next year. You then have to consider the likelihood of him not being healthy to various degrees. He could have a mild ankle sprain and lose half his skill set (hurting his value) while still being able to play or he could completely blow out his knee and miss half the season. So if you have a true talent 6.9 WAR player on the market, you should in theory see him paid at a lesser amount…unless of course we start trying to model in scarcity.
It all gets very complex very quickly…
Comment by The A Team — December 4, 2009 @ 2:50 pm
If ARod signed a one year deal, he’d have signed for 30-35MM$. If ARod would have GUARANTEED an MVP performance, AND also signed for 1 year, he would have signed close to 40MM$
Comment by tangotiger — December 4, 2009 @ 2:51 pm
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.
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.
Comment by tangotiger — December 4, 2009 @ 4:17 pm
Hey Dave, glad to see that you are putting your economic degree to better use then mine
Comment by Trenchtown — December 4, 2009 @ 4:34 pm
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.)
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.
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.
Thanks Dave, that’s very interesting to consider. I wonder if maybe it’s not so much that teams are risk-averse but that there is a quasi-monopsony depressing the market for the free agents that would command the highest salaries.
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.
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 $6 million in 2009 for the opportunity to play, the cost to replace him with free agent talent would be the minimum salary.
I think in reality, what happens is that teams pay what they think a free agent is going to be worth. This is going to be quite different from what a “one size fits all” projection system says they’re going to be worth.
I can’t remember what the projection system referenced was but let’s say it’s a 3-year 50%30%20% system.
Now you have two free agents.
FA one has a 3 year WAR score of 4/4/4
FA two has a 3 year WAR score of 5/1/1
In both cases, they’re likely to get an offer of 4*$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.
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.
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.
Comment by acerimusdux — December 4, 2009 @ 11:24 pm
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.
“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?
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.
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.
Scarcity also only matters when teams start filling every spot on the team with player significantly above replacement level. Why spend more on a 6 WAR player when you can sign two 3 WAR players and stick them both in the lineup without kicking anyone of value out of the lineup? The better/richer teams will encounter this problem occasionally.
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.
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.
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?
Comment by Ivan Grushenko — December 7, 2009 @ 5:35 am
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.
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.
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.