Why is WAR valued linearly?

[Dam8610]

Thus far in the White Sox pursuit of building a championship caliber team starting at the prospect/farm system level, we've heard a lot about the concept of surplus value to a contract. The reason the White Sox have prospects and young players like Yoan Moncada, Michael Kopech, Lucas Giolito, Reynaldo Lopez, Dane Dunning, Eloy Jimenez, and Dylan Cease are because of the perceived surplus value in the contracts of Chris Sale, Adam Eaton, and Jose Quintana. Surplus value appears to be calculated by taking the player's WAR, multiplying by a "$/WAR" constant, then subtracting the actual value of the contract. All of this except the $/WAR constant makes sense to me. If we're measuring surplus value, why would the first WAR and the sixth WAR be valued the same? If a team was attempting to replace a 6 WAR player, they're unlikely to try to find another 6 WAR player to replace him with, because those players are rare, expensive, and difficult to acquire. Instead, a team attempting to replace a 6 WAR player would likely try to find two 3 WAR players, three 2 WAR players, or something of the like to replace the 6 WAR player, because those players are more common, cheaper, and easier to acquire. Thus, it seems to me that by valuing WAR linearly, the analytics community is missing capturing some of the value of the most elite players. In the example I gave above (which is intentionally oversimplified), the 6 WAR player's value to the team is not only the WAR he provides, but the additional 1-2 roster spots he frees up while giving the team the same WAR total. Roster spots are finite, and they hold value to teams as a commodity. I feel valuing WAR linearly fails to capture this value.

 

Since I'm not one to present a problem without at least attempting to find a solution, my initial proposed solution to this, which likely can be refined and improved upon greatly, is that rather than using a linear function such as Value(WAR) = 8(WAR) (in millions, I believe this is the current function), for all positive values of WAR, a stepwise sum function of Value(WAR) = Sum[4(WAR)-2] (in millions), with partial WAR values rounded up to the next whole value, then multiplied by the partial value to get the final value. With the new formula, 1 WAR would be worth $2 million instead of $8 million, 1.5 WAR would be worth $5 million instead of $12 million, 2 WAR would be worth $8 million instead of $16 million, 2.5 WAR would be worth $13 million instead of $20 million, 3 WAR would be worth $18 million instead of $24 million, 3.5 WAR would be worth $25 million instead of $28 million, 4 WAR would be worth $32 million as it is under the linear model (this was a goal when I made the formula), 4.5 WAR would be worth $41 million instead of $36 million, 5 WAR would be worth $50 million instead of $40 million, 5.5 WAR would be worth $61 million instead of $44 million, and 6 WAR would be worth $72 million instead of $48 million. I don't think this method is perfect, either, but I think it more effectively captures the market value of WAR and why teams are willing to do so much to get elite players. I also feel because of the flaws of the linear model, it doesn't truly captures the value of WAR until about the 4 WAR point. Prior to that, I feel the linear model inflates its value, and deflates the value after that. I also feel that this can be refined and improved to produce something that even better reflects reality. For example, a piecewise function which slows the acceleration of WAR value at a certain point might be useful. Obviously I've given this some thought, but I'm interested to hear other thoughts and opinions on this.

[Chicago White Sox]

100% agree and have been arguing this for a while. Each incremental WAR should be worth more given there are a finite amount of spots on the field and the scarcity of stars in the game.

[wrathofhahn]

They already take most of this into account via the position adjustment. So for example if a player plays a position where there is scarcity of good players like SS or CF for example they get a positive adjustment if they play one where there are more options like say DH or 1B they are adjusted as such.

 

Which is the right way to account for what you are talking about. I also disagree with the premise you made there isn't a deluge of good players anymore then there are stars. Most teams struggle to fill out their rotations and lineups with quality players.

 

For most clubs the question isn't oh well how do I fit this star into my lineup it's how do I pay this star 20 30 million and still round out the rest of the roster.

Edited February 15, 2018 by wrathofhahn

[Dam8610]

They already take most of this into account via the position adjustment. So for example if a player plays a position where there is scarcity of good players like SS or CF for example they get a positive adjustment if they play one where there are more options like say DH or 1B they are adjusted as such.

 

Which is the right way to account for what you are talking about. I also disagree with the premise you made there isn't a deluge of good players anymore then there are stars. Most teams struggle to fill out their rotations and lineups with quality players.

 

For most clubs the question isn't oh well how do I fit this star into my lineup it's how do I pay this star 20 30 million and still round out the rest of the roster.

 

There are a lot more 2-3 WAR players than there are 6+ WAR players. Also, the positional adjustment is only designed to equalize WAR values between positions, it has nothing to do with the incremental value of WAR itself, it more accounts for teams being more willing to tolerate less productive bats at positions like CF, SS, and C than positions like LF, 1B, and DH.

[wrathofhahn]

There are a lot more 2-3 WAR players than there are 6+ WAR players. Also, the positional adjustment is only designed to equalize WAR values between positions, it has nothing to do with the incremental value of WAR itself, it more accounts for teams being more willing to tolerate less productive bats at positions like CF, SS, and C than positions like LF, 1B, and DH.

 

The point I was making is that WAR isn't linear. It accounts for scarcity via the positional adjustment. So if you are a star SS and there is a lack of quality SS in the league that is accounted for. The same goes for CF and so on.

 

The rest of your post I don't agree with. You keep saying that stars are more valuable because they only take up one position but like I stated earlier I don't take that view.

 

In my opinion when you look at FA and how fangraphs does the dollar per war figure often it's inflated versus what they get in FA. Thats because teams recognize they need to fill out the rest of the roster and thats hard to do in a 152 million dollar payroll (league average last year) while still paying stars what they are worth.

 

I could break it all down but I already have in other threads b. I actually make the case the opposite is true for example Baseball reference indicates there were 153 players with 300 PA or more with WAR less then or equal to 2. 89 less then or equal to 1.

 

Lets go with 1. That means on average teams carried three players who received significant amount of PA who contributed 1 WAR or less. Thats just positional players not even taking into account your bullpen or starting pitching.

 

Lets say they instead got 2 WAR from those players. Thats at minimum an extra 3 WAR production in some cases more depending on who they are replacing. What is 2 WAR going for in FA?

 

 

 

EDIT:

I just googled when typing up this post should have known fangraphs already did a similar study. Could have saved myself some time it confirmed much of the research you can read it here: https://www.fangraphs.com/blogs/the-lineari...f-cost-per-win/ and https://www.fangraphs.com/blogs/the-recent-...-agent-pricing/

 

And these articles don't even get into the regression and return on investment that these players provide in the latter half of their deals.

Edited February 16, 2018 by wrathofhahn

[Dam8610]

The point I was making is that WAR isn't linear. It accounts for scarcity via the positional adjustment. So if you are a star SS and there is a lack of quality SS in the league that is accounted for. The same goes for CF and so on.

 

The rest of your post I don't agree with. You keep saying that stars are more valuable because they only take up one position but like I stated earlier I don't take that view.

 

In my opinion when you look at FA and how fangraphs does the dollar per war figure often it's inflated versus what they get in FA. Thats because teams recognize they need to fill out the rest of the roster and thats hard to do in a 152 million dollar payroll (league average last year) while still paying stars what they are worth.

 

I could break it all down but I already have in other threads b. I actually make the case the opposite is true for example Baseball reference indicates there were 153 players with 300 PA or more with WAR less then or equal to 2. 89 less then or equal to 1.

 

Lets say they instead got 2 WAR from those players. Thats at minimum an extra 3 WAR production in some cases more depending on who they are replacing. What is 2 WAR going for in FA?

 

Lets go with 1. That means on average teams carried three players who received significant amount of PA who contributed 1 WAR or less. Thats just positional players not even taking into account your bullpen or starting pitching.

 

EDIT:

I just googled when typing up this post should have known fangraphs already did a similar study. Could have saved myself some time it confirmed much of the research you can read it here: https://www.fangraphs.com/blogs/the-lineari...f-cost-per-win/ and https://www.fangraphs.com/blogs/the-recent-...-agent-pricing/

 

And these articles don't even get into the regression and return on investment that these players provide in the latter half of their deals.

 

The positional adjustment doesn't account for scarcity at the position, it accounts for, essentially, the "difficulty" of the position, i.e. SS is a lot more difficult to play good defense consistently than 1B. As for the linearity argument, all he's saying is that in practice teams just use the strategy I gave in the example. If a team is actually trying to win, having 6 WAR out of one roster spot is more valuable than having 3 WAR. I don't think even the author of those articles would dispute that. What is disputed is the value of roster spots, and I don't agree with his premise that most teams just have 4-5 roster spots they could improve at any given moment, at least not the ones trying most to win. Also, the market is going to give bad data points. For example, Bryce Harper is going to get $400 million over 10 years from some team next offseason. Does that mean that team thinks he'll average being a 5 WAR/year player over those 10 years, or does that mean the market price for WAR has gone up? Of course, that question gets stickier if the contract is closer to 12 years and $500 million as some have speculated. I suppose surplus value works by measuring each individual contract against the market average, but then all it's really telling you is whether the contract was negotiated well or not. It's not actually telling you anything about value. It's essentially an index stat at that point, like OPS+ or wRC+, and it's not actually telling you anything about the value of WAR. They should call it the market price of WAR based on what it actually measures, not the value. Many things have far more value than what the market is willing to pay for them. I think I see that I'm looking to measure a different thing than what Fangraphs is measuring, though, and this their linear market price of WAR makes much more sense. They should just call it that, though, because they're measuring market price of WAR, whereas I'm more looking for the intrinsic value of WAR. To me, the surplus value of a contract would be the intrinsic value of the WAR provided less what was actually paid to the player, and what Fangraphs measures is the price the team should've paid for the WAR produced based on market average against what they actually paid. It seems more a measure of good (or poor) contract negotiation and less a measure of how much more (or less) valuable a player was to a team than what they were paid on their contract.

[Jerksticks]

So what does it mean when say the Astros racked up about 52 total team WAR in 2017 but only had an opening day payroll of 125M? Did they really get $340M in surplus value?

 

The bottom two teams record wise, the Tigers & Giants break down as follows:

Giants: 37 team WAR, opening day payroll $172M: $161M surplus value

Tigers: 20.6 team WAR, opening day payroll: $199M: -13.6MM

 

 

The Dodgers had about $210 million in surplus value, putting up essentially the same WAR as the Astros with double the payroll.

 

 

What does all this mean? Nothing?

 

 

[Dam8610]

So what does it mean when say the Astros racked up about 52 total team WAR in 2017 but only had an opening day payroll of 125M? Did they really get $340M in surplus value?

 

The bottom two teams record wise, the Tigers & Giants break down as follows:

Giants: 37 team WAR, opening day payroll $172M: $161M surplus value

Tigers: 20.6 team WAR, opening day payroll: $199M: -13.6MM

 

 

The Dodgers had about $210 million in surplus value, putting up essentially the same WAR as the Astros with double the payroll.

 

 

What does all this mean? Nothing?

 

From what I can tell, it means Friedman and Luhnow are relying on a lot of young stars AND they're pretty good at negotiating contracts.

[Chicago White Sox]

The point I was making is that WAR isn't linear. It accounts for scarcity via the positional adjustment. So if you are a star SS and there is a lack of quality SS in the league that is accounted for. The same goes for CF and so on.

 

The rest of your post I don't agree with. You keep saying that stars are more valuable because they only take up one position but like I stated earlier I don't take that view.

 

In my opinion when you look at FA and how fangraphs does the dollar per war figure often it's inflated versus what they get in FA. Thats because teams recognize they need to fill out the rest of the roster and thats hard to do in a 152 million dollar payroll (league average last year) while still paying stars what they are worth.

 

I could break it all down but I already have in other threads b. I actually make the case the opposite is true for example Baseball reference indicates there were 153 players with 300 PA or more with WAR less then or equal to 2. 89 less then or equal to 1.

 

Lets go with 1. That means on average teams carried three players who received significant amount of PA who contributed 1 WAR or less. Thats just positional players not even taking into account your bullpen or starting pitching.

 

Lets say they instead got 2 WAR from those players. Thats at minimum an extra 3 WAR production in some cases more depending on who they are replacing. What is 2 WAR going for in FA?

 

 

 

EDIT:

I just googled when typing up this post should have known fangraphs already did a similar study. Could have saved myself some time it confirmed much of the research you can read it here: https://www.fangraphs.com/blogs/the-lineari...f-cost-per-win/ and https://www.fangraphs.com/blogs/the-recent-...-agent-pricing/

 

And these articles don't even get into the regression and return on investment that these players provide in the latter half of their deals.

I have no idea what that fangraphs study even means. GMs may very well pay on a linear $/WAR basis, our argument is they should not and value each incremental WAR more than the previous.

 

The best example I have of this would be fantasy football related. David Johnson was predicted to outproduce all other players by a f***ton last year (ignore the injury for argument’s sake). Anyone fortunate enough to get him would of theoretically had a huge advantage. In auction leagues, you should have paid a huge premium to land him because there is a finite number of roster smarts and he’s an absolute difference maker. The goal is any sport is to get the most overall value out of your finite number of spots and there’s a theoretical limit of much value (or WAR) that can be generated based on the number of superstars in the game. Every time you miss on a superstar you’re team is theoretically capped off a little bit more. It’s exactly why a 8 WAR player four 2 WAR players. There has to be a premium for elite talents whether or not those players ultimately receive it as free agents. Unfortunately for them, there is a ton of risk inteams signing to guys to 8+ year deals that they may not ultimately get their fair share.

[Dam8610]

I have no idea what that fangraphs study even means. GMs may very well pay on a linear $/WAR basis, our argument is they should not and value each incremental WAR more than the previous.

 

The best example I have of this would be fantasy football related. David Johnson was predicted to outproduce all other players by a f***ton last year (ignore the injury for argument’s sake). Anyone fortunate enough to get him would of theoretically had a huge advantage. In auction leagues, you should have paid a huge premium to land him because there is a finite number of roster smarts and he’s an absolute difference maker. The goal is any sport is to get the most overall value out of your finite number of spots and there’s a theoretical limit of much value (or WAR) that can be generated based on the number of superstars in the game. Every time you miss on a superstar you’re team is theoretically capped off a little bit more. It’s exactly why a 8 WAR player four 2 WAR players. There has to be a premium for elite talents whether or not those players ultimately receive it as free agents. Unfortunately for them, there is a ton of risk inteams signing to guys to 8+ year deals that they may not ultimately get their fair share.

 

The argument boils down to the value of roster spots. His (and the author's) argument is that they essentially hold no value based on supply and demand. My argument is that those spots are highly valuable to a contender, who is going to want too pack as much WAR as they can manage into 25 roster spots.

[bmags]

So couple thoughts:

 

I don't think people are paying on a linear $/WAR basis. I think that number is largely shorthand and also recall it is backed into, it's an average.

 

Two examples: Wellington Castillo was worth 2.1 WAR last year at a scarce position. Making 8mill/year. That's only 4 mill/WAR, half the 8.

 

Cashner just got the same deal. K, probably unlikely to get the 4 bWAR season again, honestly he's likely to get 0, but he got 8 million.

 

Darvish, let's pencil him in for 3 WAR and say last year was aberration.

 

He is getting 7 mill / WAR.

 

Lorenzo Cain! Okay so maybe project less than 5 WAR, let's go 4. He's getting? $4 mill/WAR.

 

So anyway my point is, I agree that the "surplus value" stuff for trades is frivilous because it's based on a backed into number that isn't that illustrative. But it's a model and there is some consistency, so it's better than nothing.

 

However, I also just brought up the above because I don't think teams actually do use $/WAR linearly. And I think pitchers and position players are valued different on a $/WAR basis.

 

In heart of hearts, I see pitchers viewed closer to 6-7 mill /WAR and position players $4 mil/WAR, with hitters seeing that escalator when you hit a predictive 3 WAR and above.

 

 

 

Maybe they are predicting both Castillo and Cashner are 1 WAR players in each year, and thus their contract, but I doubt it.

 

Now, Carlos Santana got 20 mill a year, and is a more likely 3.5 WAR player. He got 5.7 mill/WAR. Incremental improvement.

 

Darvish

 

[Dam8610]

So couple thoughts:

 

I don't think people are paying on a linear $/WAR basis. I think that number is largely shorthand and also recall it is backed into, it's an average.

 

Two examples: Wellington Castillo was worth 2.1 WAR last year at a scarce position. Making 8mill/year. That's only 4 mill/WAR, half the 8.

 

Cashner just got the same deal. K, probably unlikely to get the 4 bWAR season again, honestly he's likely to get 0, but he got 8 million.

 

Darvish, let's pencil him in for 3 WAR and say last year was aberration.

 

He is getting 7 mill / WAR.

 

Lorenzo Cain! Okay so maybe project less than 5 WAR, let's go 4. He's getting? $4 mill/WAR.

 

So anyway my point is, I agree that the "surplus value" stuff for trades is frivilous because it's based on a backed into number that isn't that illustrative. But it's a model and there is some consistency, so it's better than nothing.

 

However, I also just brought up the above because I don't think teams actually do use $/WAR linearly. And I think pitchers and position players are valued different on a $/WAR basis.

 

In heart of hearts, I see pitchers viewed closer to 6-7 mill /WAR and position players $4 mil/WAR, with hitters seeing that escalator when you hit a predictive 3 WAR and above.

 

 

 

Maybe they are predicting both Castillo and Cashner are 1 WAR players in each year, and thus their contract, but I doubt it.

 

Now, Carlos Santana got 20 mill a year, and is a more likely 3.5 WAR player. He got 5.7 mill/WAR. Incremental improvement.

 

Darvish

 

It is backed into using the actual data to determine what teams are actually paying per WAR, which makes the "surplus value" they present nothing more than an indexing stat like OPS+, ERA+, wRC+, etc. because the data of each contract is in the average they calculate. It says nothing about the actual value of WAR, just what teams are paying for it. Any good business makes more off of their product than what they pay for it, though.

[wrathofhahn]

The positional adjustment doesn't account for scarcity at the position, it accounts for, essentially, the "difficulty" of the position, i.e. SS is a lot more difficult to play good defense consistently than 1B. As for the linearity argument, all he's saying is that in practice teams just use the strategy I gave in the example. If a team is actually trying to win, having 6 WAR out of one roster spot is more valuable than having 3 WAR. I don't think even the author of those articles would dispute that. What is disputed is the value of roster spots, and I don't agree with his premise that most teams just have 4-5 roster spots they could improve at any given moment, at least not the ones trying most to win. Also, the market is going to give bad data points. For example, Bryce Harper is going to get $400 million over 10 years from some team next offseason. Does that mean that team thinks he'll average being a 5 WAR/year player over those 10 years, or does that mean the market price for WAR has gone up? Of course, that question gets stickier if the contract is closer to 12 years and $500 million as some have speculated. I suppose surplus value works by measuring each individual contract against the market average, but then all it's really telling you is whether the contract was negotiated well or not. It's not actually telling you anything about value. It's essentially an index stat at that point, like OPS+ or wRC+, and it's not actually telling you anything about the value of WAR. They should call it the market price of WAR based on what it actually measures, not the value. Many things have far more value than what the market is willing to pay for them. I think I see that I'm looking to measure a different thing than what Fangraphs is measuring, though, and this their linear market price of WAR makes much more sense. They should just call it that, though, because they're measuring market price of WAR, whereas I'm more looking for the intrinsic value of WAR. To me, the surplus value of a contract would be the intrinsic value of the WAR provided less what was actually paid to the player, and what Fangraphs measures is the price the team should've paid for the WAR produced based on market average against what they actually paid. It seems more a measure of good (or poor) contract negotiation and less a measure of how much more (or less) valuable a player was to a team than what they were paid on their contract.

 

You are misinterpreting what that means. When they say difficulty of position they referring to scarcity (the lack of quality defensive and offensive players) and the amount remains fluid. Say for example all of sudden the market gets flooded with catchers who are hitting .900 the amount of runs added to the positional adjustment would change.

 

You can read more here: https://www.baseball-reference.com/about/wa..._position.shtml

 

CTRL + F : Rpos, Positional Adjustment Runs

 

As far as the rest goes I can't disprove your theory mainly because I don't want to do the work for an internet argument. You are just going to have to put two and two together from the numbers I posted earlier. Like I said there were 135 players who had 2 WAR or less with 300 PA. 89 with 1 WAR or less. That is without going into starting pitching.

 

There are certainly outliers of teams with relatively full lineups the Yankees situation comes to mind but for the vast majority of teams when you look at their lineups they'd be better off with using the cheaper $/WAR figure I provided earlier on two three players rather then overspending on a single elite FA.

 

That's before even getting into the weeds of regression and length

Edited February 16, 2018 by wrathofhahn

[Dam8610]

You are misinterpreting what that means. When they say difficulty of position they referring to scarcity (the lack of quality defensive and offensive players) and the amount remains fluid. Say for example all of sudden the market gets flooded with catchers who are hitting .900 the amount of runs added to the positional adjustment would change.

 

You can read more here: https://www.baseball-reference.com/about/wa..._position.shtml

 

CTRL + F : Rpos, Positional Adjustment Runs

 

As far as the rest goes I can't disprove your theory mainly because I don't want to do the work for an internet argument. You are just going to have to put two and two together from the numbers I posted earlier. Like I said there were 135 players who had 2 WAR or less with 300 PA. 89 with 1 WAR or less. That is without going into starting pitching.

 

There are certainly outliers of teams with relatively full lineups the Yankees situation comes to mind but for the vast majority of teams when you look at their lineups they'd be better off with using the cheaper $/WAR figure I provided earlier on two three players rather then overspending on a single elite FA.

 

That's before even getting into the weeds of regression and length

 

We're saying the same thing on the "difficulty" concept, just looking at it different ways. You're saying the positional adjustment is based on scarcity of quality hitters at the position, whereas I'm saying that teams are willing to put up with poorer hitters at those positions because they're harder to play defensively. It's a philosophical difference of source that leads to the same conclusion that defensive adjustments are (and should be) made based on the difficulty of the position. I can understand your point about an influx of .900 OPS catchers, my argument is the likelihood of that happening is nearly zero because catcher is a hard position to play good defense. Apparently, this is also a point of contention between Fangraphs and Baseball Reference, as well.

 

ETA: My argument is not and was never about the market price of WAR. Based on the example I gave in my original post, it's clear that I agree with you on what the common practice of teams is when trying to replace a player, and how they might be best served. The point I'm actually trying to discern is what the VALUE of WAR is, not the market price. I'd also contend that without a true value of WAR, you can't really know what the surplus value of a contract is, just how well you negotiated a contract relative to the market. That's a good thing for GMs to know, but I don't think it provides much information beyond that, and certainly not the information it purports to provide.

Edited February 16, 2018 by Dam8610

[GreenSox]

I don't think that any serious observer has argued otherwise. I haven't read anyone suggest that 3 2-War players = 1 6 war player.

 

No one would trade Chris Sale for 3 Melkys.

Edited February 16, 2018 by GreenSox

[wrathofhahn]

We're saying the same thing on the "difficulty" concept, just looking at it different ways. You're saying the positional adjustment is based on scarcity of quality hitters at the position, whereas I'm saying that teams are willing to put up with poorer hitters at those positions because they're harder to play defensively. It's a philosophical difference of source that leads to the same conclusion that defensive adjustments are (and should be) made based on the difficulty of the position. I can understand your point about an influx of .900 OPS catchers, my argument is the likelihood of that happening is nearly zero because catcher is a hard position to play good defense. Apparently, this is also a point of contention between Fangraphs and Baseball Reference, as well.

 

ETA: My argument is not and was never about the market price of WAR. Based on the example I gave in my original post, it's clear that I agree with you on what the common practice of teams is when trying to replace a player, and how they might be best served. The point I'm actually trying to discern is what the VALUE of WAR is, not the market price. I'd also contend that without a true value of WAR, you can't really know what the surplus value of a contract is, just how well you negotiated a contract relative to the market. That's a good thing for GMs to know, but I don't think it provides much information beyond that, and certainly not the information it purports to provide.

 

 

I think though if you look at the WAR dollars of fangraphs they are already widely inflated for example going off their figures prior to last year Donaldson previous two years was worth 70 million and 60 million. At what point does it become more of a theoretical exercise rather then useful data?

 

I would much rather if the goal is to have a useful stat is for the market value of the player to be calculated. Spotrac already does it to some extent but it's clumsy. Opportunity cost should always be a factor in surplus value and right now it isn't.

[Dominikk85]

100% agree and have been arguing this for a while. Each incremental WAR should be worth more given there are a finite amount of spots on the field and the scarcity of stars in the game.

 

I get the idea but it isn't really true. There is a finite amount of spots but the amount of spots is much larger than for example in basketball and every team has some bad players. Real world analysis shows that war is indeed linear and that it doesn't make a difference whether a team has more star players or more depth as long as overall war of the team is the same. Teams also value war linearly in contracts according to almost all available resources.

[Eminor3rd]

Two things to add:

 

1) $/WAR is constantly misused; its only purpose is as a descriptive statistic that refers to what the free agent market is actually paying per WAR in a given time frame. It is not intended to, nor was it ever intended to, nor has anyone ever made an argument that it should or could be used to claim what WAR should be worth in dollars. They sound like the same thing, but they aren't because half or more of all WAR is tied up in non-free agent eligible players, so the economics break down entirely.

 

2) The linearity of WAR value was a hot topic many years go. Essentially, "is a 4 WAR player worth more, less, or the same as two 2 WAR players?" There are a ton of really attractive hypotheses and logical reasons to think one way or the other, but studies occurred, and everyone concluded that despite what seems like it makes sense, WAR IS essentially linear. I cannot tell you why, as it's been a long time since I've read anything on it, but know that it has been studied and consensus reached.

[Dam8610]

Two things to add:

 

1) $/WAR is constantly misused; its only purpose is as a descriptive statistic that refers to what the free agent market is actually paying per WAR in a given time frame. It is not intended to, nor was it ever intended to, nor has anyone ever made an argument that it should or could be used to claim what WAR should be worth in dollars. They sound like the same thing, but they aren't because half or more of all WAR is tied up in non-free agent eligible players, so the economics break down entirely.

 

2) The linearity of WAR value was a hot topic many years go. Essentially, "is a 4 WAR player worth more, less, or the same as two 2 WAR players?" There are a ton of really attractive hypotheses and logical reasons to think one way or the other, but studies occurred, and everyone concluded that despite what seems like it makes sense, WAR IS essentially linear. I cannot tell you why, as it's been a long time since I've read anything on it, but know that it has been studied and consensus reached.

 

1) This is what I learned from this exercise, that the "surplus value" Fangraphs publishes measures a different thing than what I'm looking to measure, namely, as you put it, what WAR should be worth, essentially the intrinsic value of WAR. Since figuring out the difference, I've been thinking of ways to attempt to measure and quantify this. If I come up with anything, I'll share the results.

 

2) For market valuation purposes, I totally understand why that conclusion makes sense. It's because teams will replace a star player with several quality players, hoping that works in their favor. That is what makes the market value of WAR linear. That said, I feel that the intrinsic value is likely nonlinear. I'm certain, for example, the incremental WAR that puts a team in the postseason is more valuable than most, as is the one that wins a divisional championship, as is the one that provides home field advantage throughout the playoffs. The question then becomes how to quantify and measure this? I don't think I have the answer to that question, nor do I think anyone does at this time.

[Eminor3rd]

1) This is what I learned from this exercise, that the "surplus value" Fangraphs publishes measures a different thing than what I'm looking to measure, namely, as you put it, what WAR should be worth, essentially the intrinsic value of WAR. Since figuring out the difference, I've been thinking of ways to attempt to measure and quantify this. If I come up with anything, I'll share the results.

 

2) For market valuation purposes, I totally understand why that conclusion makes sense. It's because teams will replace a star player with several quality players, hoping that works in their favor. That is what makes the market value of WAR linear. That said, I feel that the intrinsic value is likely nonlinear. I'm certain, for example, the incremental WAR that puts a team in the postseason is more valuable than most, as is the one that wins a divisional championship, as is the one that provides home field advantage throughout the playoffs. The question then becomes how to quantify and measure this? I don't think I have the answer to that question, nor do I think anyone does at this time.

 

Ah, I see. Have you read up on "win curve" research?

 

https://www.fangraphs.com/tht/rethinking-the-win-curve/

https://www.fangraphs.com/blogs/win-curves-...player-pricing/

http://grantland.com/the-triangle/what-is-...n-curve-anyway/

[Dam8610]

Ah, I see. Have you read up on "win curve" research?

 

https://www.fangraphs.com/tht/rethinking-the-win-curve/

https://www.fangraphs.com/blogs/win-curves-...player-pricing/

http://grantland.com/the-triangle/what-is-...n-curve-anyway/

 

That first article is fascinating, and solved the surplus value issue I was having, though with a HUGE level of uncertainty to it. I think what the information in that article would address is the team variance component of the matter. But there are still other factors at play, I think, in coming up with a value for WAR. When a team has a prospect develop into a superstar, for example, that commodity is valuable and will be a big draw whether the team was projected to win 60, 80, or 100 games without that player. Obviously of those three, that development would affect the projected 80 win team the most, but the other two would still likely get a boost from it (the 100 win team likely minimally due to the law of diminishing marginal utility). I still think the intrinsic value of WAR is nonlinear, this research strongly suggests team win projection as a dependent variable, individual player value seems to also be a fairly obvious dependent variable...it seems like further research is likely the most productive next step.