The fallacy of Free Agency AAV @ 8M per WAR

[amjgt]

What is a free agent worth? $8M AAV per WAR. That's what they all tell me. It never felt right because it never seems to work out that way, ESPECIALLY for the top end of the FA market.

It is based on this article ( https://blogs.fangraphs.com/the-cost-of-a-win-in-free-agency-in-2020/ ) as well as an older article that he reference a couple times

There are two problems here.

1) He is relying on future WAR projections, attempting to quantify the Qualifying Offer silliness (not his silliness... the system's silliness), as well as some other assumptions. All of these things might seem logical on their own but once you roll them all together things get messy and lack real world context.

2) That's not how people are using his work. They are looking at past WAR and saying "based on his 2.3 WAR average the last two seasons he's worth 20M in free agency." -- Spolier Alert: 2.3 WAR players are lucky to get half of that in free agency --. Even for the people that might claim that they are actually saying that player provided 20M in VALUE .... That's not true either. In 2021 MLB payrolls were about $4 Billion and Players provided about 650 positive WAR. So really in that context a "WAR" is worth $6M. ($4B/650), but that's not really what I'm after here. I'm after what is actually happening in free agency and how it correlates to past performance. 

 

Here it is.

 

I looked at the top 20 free agents (according to MLB Trade Rumors) from two recent offseasons, looked at their free agent contract AAV, then looked up their WAR from the previous three seasons (fWAR in this case). I looked at it two similar ways. First was just their WAR from the season before free agency, and second I looked at it based on the average of their previous two seasons.

Key points:

The average is right around $6.0M/WAR (There's that number again)

Almost nobody gets 8.0/WAR. If they do it's usually one of two special circumstances. a) They're a RP, or b) they missed a bunch of time which suppressed their WAR in a given season

The top end free agents definitely don't get $8/WAR. They are more around $5/WAR

 

Conclusion: We can project future value, make assumptions, and try to account for market factors all we want, but at the end of the day, the numbers are the numbers. We have baseball-wide economics telling us that the value of 1.0WAR is about $6M ($4B/650WAR) and we have front offices signing free agents at about $6M per WAR from previous seasons. 

Maybe the number we should start using for projecting free agent AAV is $6M, not $8M

 

[Otto von Ballpark]

I'm a little confused. You say in point #1 that the figure is based on future projected WAR, then describe in #2 how people misuse it by applying it to past performance instead. But then you proceed to make a bunch of calculations and conclusions based on that same assumption in #2.

This kind of calculation has to be based on future projected WAR because players age and we're looking at a lot of longer-term contracts.

Take the Josh Donaldson deal: $92 mil guaranteed over 4 years, age 34-37. He was coming off a 4.9 fWAR / 5.4 bWAR season, but here were his ZiPS projections going forward:

Age 34: 3.8 WAR
Age 35: 2.9
Age 36: 2.1
Age 37: 1.0

That was 9.8 projected WAR, or $9.4 mil per. Now, the Twins aren't just using ZiPS and probably liked the odds of Donaldson beating such projections, but if these figures tend to fall in the same ballpark for FA contracts league-wide, then it's probably a decent estimate for the overall market.

[ashbury]

I've never looked deeply into it, but I've often wondered if these analyses and discussions would be better served by using Wins Above Average instead of WAR.  The market for free agents gets set by the deep-pockets teams like the Yankees, Red Sox and Dodgers, but they don't pull out all the stops to get a perceived 1 WAR or 2 WAR player - if they Twins offer a Happ type of pitcher $8M, the Yankees don't bother trying to outbid them to get him back.  It's the Gerrit Cole types whom they covet - difference makers who on any given day are an advantage over their counterparts on the opposing team's lineup.

A full-time player (let's consider catchers and relievers separately) needs about 2 WAR to be average.  Those first couple of WAR may net the player $3M or $4M apiece.  It may turn out that the third Win is what brings $12M, and the next Win even more.  That behavior is going to skew simple averages, and cloud understanding.

In other words, the Twins ought not pay $16M a season for a 2-WAR player, but maybe should pay $32M for a 5-WAR player who really fills a need they couldn't fill in-house.

[Mike Sixel]

  On 10/4/2021 at 8:31 PM, ashbury said:

I've never looked deeply into it, but I've often wondered if these analyses and discussions would be better served by using Wins Above Average instead of WAR.  The market for free agents gets set by the deep-pockets teams like the Yankees, Red Sox and Dodgers, but they don't pull out all the stops to get a perceived 1 WAR or 2 WAR player - if they Twins offer a Happ type of pitcher $8M, the Yankees don't bother trying to outbid them to get him back.  It's the Gerrit Cole types whom they covet - difference makers who on any given day are an advantage over their counterparts on the opposing team's lineup.

A full-time player (let's consider catchers and relievers separately) needs about 2 WAR to be average.  Those first couple of WAR may net the player $3M or $4M apiece.  It may turn out that the third Win is what brings $12M, and the next Win even more.  That behavior is going to skew simple averages, and cloud understanding.

In other words, the Twins ought not pay $16M a season for a 2-WAR player, but maybe should pay $32M for a 4-WAR player who really fills a need.

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IIRC, studies show that it is linear, but that teams SHOULD make it like you suggest.....but I could be remembering that wrong. 

[Cap'n Piranha]

Generally speaking, MLB players post about 1,000 WAR a year, according to Fangraphs, so with MLB total salaries in the $4B range, 1 WAR is worth about $4M.  If there is 1,000 WAR posted, then that's 33ish WAR per team, which means a team with 0 WAR (that is, every pitch thrown and plate appearance taken is done by  a replacement level player), would win 58 games.

From there it follows that if a team spends $120M at the average 1 WAR/$4M rate, they will win 88 games.  For a team to win 95 games while spending at average efficiency, they will need to spend $148M.  Since it is unlikely the Twins will spend that much, that means for the Twins to return to competitiveness, they will need to be more efficient than that $4M/WAR threshold.  As such, for every FA deal the Twins complete where they don't anticipate hitting that mark, they have to complete another deal below that threshold, or get production from pre-Arb 2 players.

[amjgt]

  On 10/4/2021 at 8:18 PM, Otto von Ballpark said:

I'm a little confused. You say in point #1 that the figure is based on future projected WAR, then describe in #2 how people misuse it by applying it to past performance instead. But then you proceed to make a bunch of calculations and conclusions based on that same assumption in #2.

This kind of calculation has to be based on future projected WAR because players age and we're looking at a lot of longer-term contracts.

Take the Josh Donaldson deal: $92 mil guaranteed over 4 years, age 34-37. He was coming off a 4.9 fWAR / 5.4 bWAR season, but here were his ZiPS projections going forward:

Age 34: 3.8 WAR
Age 35: 2.9
Age 36: 2.1
Age 37: 1.0

That was 9.8 projected WAR, or $9.4 mil per. Now, the Twins aren't just using ZiPS and probably liked the odds of Donaldson beating such projections, but if these figures tend to fall in the same ballpark for FA contracts league-wide, then it's probably a decent estimate for the overall market.

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Good questions...

There are two ways to project the AAV.

1) Future protected WAR. A perfectly good way to do it and what the $8M number is based on (the fangraphs article).

2) Previous actual WAR.

The problem with #1, from a fan's point of view, is that projecting WAR is done differently by everyone. Of course that's how TEAMS should think of it but they probably all do it differently. ZiPS does it different that Steamer who does it differently than The Bat, and so on They all have their own assumptions.

So, #1 is a complicated way to do it and requires a TON of assumptions. And where it fails here, is that most people in casual discussion, apply #1 like its as simple as #2. It's a very complex calculation that's being applied very non-critically.

So, my goal here was to see if there was a much simpler correlation. People want to apply a simple formula so let's see if we can give them one. 

As it turns out, I believe $6M for the average WAR of their previous two seasons is a pretty good rule of thumb. It doesn't require aging curves, projected WAR, complex algorithms, etc....  It just looks at a) what teams are actually paying for FA, and confirmed with b) what the actual league-wide value of 1.0 WAR is ($4B/650) over the course of a season. 

 

[Mike Sixel]

  On 10/4/2021 at 9:09 PM, Cap'n Piranha said:

Generally speaking, MLB players post about 1,000 WAR a year, according to Fangraphs, so with MLB total salaries in the $4B range, 1 WAR is worth about $4M.  If there is 1,000 WAR posted, then that's 33ish WAR per team, which means a team with 0 WAR (that is, every pitch thrown and plate appearance taken is done by  a replacement level player), would win 58 games.

From there it follows that if a team spends $120M at the average 1 WAR/$4M rate, they will win 88 games.  For a team to win 95 games while spending at average efficiency, they will need to spend $148M.  Since it is unlikely the Twins will spend that much, that means for the Twins to return to competitiveness, they will need to be more efficient than that $4M/WAR threshold.  As such, for every FA deal the Twins complete where they don't anticipate hitting that mark, they have to complete another deal below that threshold, or get production from pre-Arb 2 players.

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Not exactly.....they don't have to pay market rate for several years, so we can't conclude from non-free agent salaries what free agent salaries are worth. That said, there is some merit in your second paragraph.

[amjgt]

  On 10/4/2021 at 9:09 PM, Cap'n Piranha said:

Generally speaking, MLB players post about 1,000 WAR a year, according to Fangraphs, so with MLB total salaries in the $4B range, 1 WAR is worth about $4M.  If there is 1,000 WAR posted, then that's 33ish WAR per team, which means a team with 0 WAR (that is, every pitch thrown and plate appearance taken is done by  a replacement level player), would win 58 games.

From there it follows that if a team spends $120M at the average 1 WAR/$4M rate, they will win 88 games.  For a team to win 95 games while spending at average efficiency, they will need to spend $148M.  Since it is unlikely the Twins will spend that much, that means for the Twins to return to competitiveness, they will need to be more efficient than that $4M/WAR threshold.  As such, for every FA deal the Twins complete where they don't anticipate hitting that mark, they have to complete another deal below that threshold, or get production from pre-Arb 2 players.

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This year players accumulated a little more than 650 positive fWAR. The actual number was 650, but I pulled that on Friday night, so it went up a little from there

[Otto von Ballpark]

  On 10/4/2021 at 9:14 PM, amjgt said:

There are two ways to project the AAV.

1) Future protected WAR. A perfectly good way to do it and what the $8M number is based on (the fangraphs article).

2) Previous actual WAR.

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#1 is basically just #2, with an aging curve applied. There's not a whole lot that's controversial about public projection systems, unless you're looking at a FIP or BABIP outlier or something.

And if you're just looking at projected WAR for the upcoming season, based on the previous season(s), then you're not accounting for that aging curve. In a long-term deal, a team expects more WAR out of a player in year 1 & 2 of a FA contract than they do in later seasons.

What you describe as "$6 mil per WAR" for a guy like Harper could mean $6 mil per WAR for the first few seasons, gradually hitting $8 mil per WAR for the middle years, and then $10 mil per WAR near the end. What's the best way to describe that? $8 mil per WAR isn't perfect, but I think it's better than saying $6 mil per WAR. You're generally paying in years to get the lower $/WAR rate today.

[Cap'n Piranha]

  On 10/4/2021 at 9:16 PM, amjgt said:

This year players accumulated a little more than 650 positive fWAR. The actual number was 650, but I pulled that on Friday night, so it went up a little from there

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I think you're only looking at hitters--I pulled all hitters, and filtered out anyone with less than 0 WAR, and got 664.  The same methodology for pitchers shows 495.6 WAR.  If you include all players, even those with negative WAR (who need to be included, as they were still paid), it goes to 572.1 for hitters and 430.1 for pitchers.

[Cap'n Piranha]

  On 10/4/2021 at 9:14 PM, amjgt said:

Good questions...

There are two ways to project the AAV.

1) Future protected WAR. A perfectly good way to do it and what the $8M number is based on (the fangraphs article).

2) Previous actual WAR.

The problem with #1, from a fan's point of view, is that projecting WAR is done differently by everyone. Of course that's how TEAMS should think of it but they probably all do it differently. ZiPS does it different that Steamer who does it differently than The Bat, and so on They all have their own assumptions.

So, #1 is a complicated way to do it and requires a TON of assumptions. And where it fails here, is that most people in casual discussion, apply #1 like its as simple as #2. It's a very complex calculation that's being applied very non-critically.

So, my goal here was to see if there was a much simpler correlation. People want to apply a simple formula so let's see if we can give them one. 

As it turns out, I believe $6M for the average WAR of their previous two seasons is a pretty good rule of thumb. It doesn't require aging curves, projected WAR, complex algorithms, etc....  It just looks at a) what teams are actually paying for FA, and confirmed with b) what the actual league-wide value of 1.0 WAR is ($4B/650) over the course of a season. 

 

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I think there's merit here--if the FO wants to give someone a $40M contract, do they anticipate being able to get 10 WAR over the course of that contract?  If no, it's an inefficient way to acquire WAR.

That said, if you have no choice but to overspend to acquire WAR (like the 2022 Twins and the shortstop position), it can still be an acceptable method, provided you have a clear roadmap on which pre-arb/arb-1 players will be able to offset that player getting $6M-$8M/WAR.

[Cap'n Piranha]

  On 10/4/2021 at 9:15 PM, Mike Sixel said:

Not exactly.....they don't have to pay market rate for several years, so we can't conclude from non-free agent salaries what free agent salaries are worth. That said, there is some merit in your second paragraph.

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Oh for sure, I wasn't trying to peg a FA-only value of WAR, simply stating that teams should assume $4M/1 WAR is the going rate across the entire roster, and adjust their win expectancy and payroll capacity accordingly.  That is, a team that wants to win 95 games, but is only approved for a $130M payroll will need to overdeliver, whether by signing FAs who outperform their contract, or having multiple pre-FA players performing at 1 WAR or more.

Apply this to the Twins and the Buxton scenario--I don't think you can reasonably expect more than 4 WAR/yr from him, giving the injury risk (he certainly could provide 7-8 WAR if healthy for 150 games).  Therefore, if you need to pay Buxton $20M next year, but you only get 2 WAR due to injuries and some decline, do you have 3 guys on rookie contracts who can produce between them 4 WAR?

[amjgt]

  On 10/4/2021 at 11:16 PM, Cap'n Piranha said:

I think you're only looking at hitters--I pulled all hitters, and filtered out anyone with less than 0 WAR, and got 664.  The same methodology for pitchers shows 495.6 WAR.  If you include all players, even those with negative WAR (who need to be included, as they were still paid), it goes to 572.1 for hitters and 430.1 for pitchers.

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I’m 100% sure I saw a pitcher on the last page before the 0.0 group, because I was specifically worried about this. However, I acknowledge that it’s possible that I saw a pitcher that managed to accumulate a slightly positive WAR from the plate.

[amjgt]

I went back and looked. That WAS just hitters. I think I just got unlucky by noticing a pitcher in the hitter stats

[amjgt]

Doesn’t REALLY change my point. It just doesn’t line up exactly at $6M like I thought it did. To your point earlier, it actually moves the real value of $/WAR down

[amjgt]

It was Bailey Ober at +0.1 offensive fWAR that tripped me up.

Two plate appearances. One hit... 0.1 fWAR