fWARconomics and the value of a win

AbbyNoho · Oct 2, 2015

Isn't part of this dynamic that a team probably can't field a successful team paying full FA value per win? You have to knowingly overpay for veteran wins and hope to make up that difference with pre-FA players and maybe some over-performing FA contracts.

nvalvo · Oct 2, 2015

(By the way, you sum this team's current WAR, and you get 30.5. Add that to 47, and you get 77.5. The system works.)

alwyn96 · Oct 2, 2015

Talking about "value of a win" always gets into weird arguments because no one really agrees what value means, or from what perspective one should look at it from. Can a 3 WAR player have more "value" to one team than another, or is a 3 WAR player just worth 3 WAR, end of story. You see this a lot in MVP debates - otherwise the MVP would always just go to the best player in the league. But of course, it sometimes doesn't. It's often been "best player on a playoff contender" since some people argue that if team isn't good then a great individual performance doesn't have as much "value". I don't know if there's really a right answer.

Like kiecker mentioned, if you make a number of economisty-type assumptions, building a team should be easy. You just maximize the number of WAR from a set of players based on a given budget. You could just plug your list of players with your WAR estimates and salaries and positions into R and you should easily be able to figure out a your best team given your assumptions. But of course, it's way more complicated than that. Players' performances can be wildly variable. Assumptions about value can be wrong. Young players' salaries are artificially lower than what they would be on the open market. In some cases players make in arbitration nearly what they would be making in FA. Teams have different needs and can value players very differently. Buchholz might not bring back an equivalent 3 WAR player because teams might not value Buchholz at that level, or actually require their 3 WAR player in order to compete, or the money doesn't add up, or they just don't need him to reach their goals, or the team is a competitor and has no interest in helping you get better, or maybe your GM made a joke at a party once that the other GM didn't get and he hates you now.

I think a rough $/WAR valuation can be useful in judging whether FA deals are crazy overpays or underpays, but it's limited, and it's usually post-hoc. We often don't know how much money teams are willing to spend. The market of good players available in FA is very limited. Teams are in different circumstances and deals make more sense for some teams than others. The Yankees and Dodgers can afford to spend a ton on FA and not have that overly hurt their ability to make other moves in a way that would hurt a poorer team. The Scherzer deal was a lot but not insane for the Nats, but the exact same deal for the Phillies would have been weird, despite the same $/WAR.

tl;dr, I guess $7M/WAR is a decent sort of rule of thumb about whether a deal is insane or not, but obviously it's more complicated than that.

finnVT · Oct 2, 2015

Plus, it's not as simple as "under 4.25 good, above 4.25 bad", because simply being efficient isn't enough. You also have a accumulate enough wins/WAR within the limit of a 25 man roster, with a fixed number of innings/plate appearances. So a single player that gets you 5 WAR might be worth overpaying for on an efficiency basis, because he provides a significant portion of the total that you need to accumulate.

Put another way, roster building is really about optimizing two equations, one maximizing team WAR, and one maximizing salary efficiency. Doing one or the other alone is not likely to work: you'll either end up with a 300m payroll, or a 75 win teams full of pretty good, but very cheap players. The 4.25 cutoff considers only the 2nd equation, whereas signing a huge WAR player regardless of the contract considers only the first. By trying to optimize the series (of 2) equations, you should have a better chance of success. But the key here is that these two equations apply at the team level, so it's difficult to assess a single player's value out of context, because while they might help for one part or the other, you need to understand the rest of the team to know if that's a net plus or not. (A player that helps on both equations is, of course, easy to evaluate-- they're awesome; this tends to be the really good pre-FA guys, who provide a lot of WAR and are highly efficient, but they're uncommon and easy to evaluate).

Savin Hillbilly · Oct 2, 2015

kieckeredinthehead said:
You need about 88 wins to at least make the play-ins. The luxury tax threshold is $189 million, so a team looking to spend above and beyond major league minimum to get 40 wins above replacement could spend about $170 million. That's $4.25 million per WAR. On average, any player the Red Sox hire that is lower than that is good. Any player making more than that is bad.

But this is only true if they are paying market rate for everybody. Every win they get from a player making less than market rate is equivalent to a certain amount of money deposited in an account that can be used to pad that $4.25 million figure. This in a nutshell is why it's so crucial, in the luxury tax era, to develop good young players.

This year the Sox are getting, according to FG, 19 fWAR from 24 players making the major league minimum--call that $13M. So if we call the tax limit (allowing for benefits etc.) $175M, that means the Sox have over $160M to spend on 21 market-rate wins, or not quite $8M per win. In a $7M/win market, this should put them in the driver's seat, except that they wound up spending $57M of that $160M on about -4 combined wins from Hanley, Panda, Porcello, Craig, and Breslow, so to win 90 they needed 25 wins for $100M from the rest of the roster, and instead they got about 12.

If Hanley/Panda/Porcello provide the 10-11 wins they were expected to, instead of combining for about -2 wins, that solves the problem right there. A better bullpen would have helped, but if those three guys had been what they were projected to be, a better bullpen would have been icing on the cake--maybe the difference between a wild card team and a division champ.

alwyn96 · Oct 2, 2015

I think something that hasn't gotten a lot of discussion but probably should is that the current CBA is ending soon, and the luxury tax level seems almost certain to rise in 2017. There's no telling what it would go up to, but I imagine the union will be pushing hard to get it higher. That probably has some implication for backloading long-term contracts. The Red Sox could go over the luxury tax in 2016, but might be able to get comfortably under in 2017 if the tax level goes up.

HangingW/ScottCooper · Oct 3, 2015

Am I the only one that thinks nobody really has any idea how to value defense in WAR? I did a study on defensive statistics in college and referred a lot to James' Win Shares. One thing that kept coming up is the concept we now refer to as the value over a replacement player. I think even that is floating.

The goal of normalizing everything into a single statistic has been attempted since baseball began and I still don't believe anyone has succeeded. WAR may be able to more accurately compare player's offense to another player's offense but when trying to factor in defense as well as the relative value of a pitcher all in the same statistic, I really think it's misguided.

Sure it's a nice exercise, trying to determine the value of a win, but we're all looking at trying to find the latest moneyball inequality here. While there obviously still has to be inequalities in paying for wins, I still don't think statisticians have correctly identified where wins come from.

Savin Hillbilly · Oct 3, 2015

HangingW/ScottCooper said:
Am I the only one that thinks nobody really has any idea how to value defense in WAR?

Hardly. "Nobody really has any idea" is putting the case a bit more starkly than usual, but the idea that the defensive side of WAR is a globby mess, and pretty much useless in one-year-or-smaller slices, is SoSH boilerplate at this point.

lexrageorge · Oct 3, 2015

HangingW/ScottCooper said:
Am I the only one that thinks nobody really has any idea how to value defense in WAR? I did a study on defensive statistics in college and referred a lot to James' Win Shares. One thing that kept coming up is the concept we now refer to as the value over a replacement player. I think even that is floating.

The goal of normalizing everything into a single statistic has been attempted since baseball began and I still don't believe anyone has succeeded. WAR may be able to more accurately compare player's offense to another player's offense but when trying to factor in defense as well as the relative value of a pitcher all in the same statistic, I really think it's misguided.

Sure it's a nice exercise, trying to determine the value of a win, but we're all looking at trying to find the latest moneyball inequality here. While there obviously still has to be inequalities in paying for wins, I still don't think statisticians have correctly identified where wins come from.

Defensive WAR is garbage masquerading as a statistic.

It is probably correct that if you rank players based on dWAR, you would see most of the best defenders on top, the worst on the bottom, etc. The other major stat for defense, UZR and its brethren, works much the same way. But UZR has a huge amount of season-to-season variability for a given player, as does dWAR, mainly due to the methodology used to calculate it. And I've yet to see a coherent argument that we've figured out how to isolate the win value of a fielder from all of the other variables that affect how many contacted balls become hits in any given season.

iayork · Oct 3, 2015

HangingW/ScottCooper said:
Am I the only one that thinks nobody really has any idea how to value defense in WAR? I did a study on defensive statistics in college and referred a lot to James' Win Shares. One thing that kept coming up is the concept we now refer to as the value over a replacement player. I think even that is floating.

There are rumors, or maybe more than rumors, that individual teams have proprietary ways of measuring defense that are more sophisticated than the tools we plebeians have. Of course we don't have access to those tools, so we don't know if or how well they work. My guess is that they're closer to detailed scouting, human-input, approaches than the sort of generic zone-based tools that are publicly available.

Probably the various StatCast things that are gradually becoming available will help, and I think teams have had access to that sort of thing for a while. Even knowing the actual starting position (instead of the assumed generic position) of a fielder would help. So in the next few years, there may be new stats that are better for evaluating fielders.

The stats that are available today aren't completely useless, but even as descriptive stats, let alone predictive, they have such wide error bars that they don't tell you any more than the eyeball test does. I suspect that the most accurate descriptive fielding stats are Tango's scouting reports, which rely entirely on the eyeball test spread out over many people.

Devizier · Oct 3, 2015

Individual player cameras is a thing, right? Honestly, looking at those during fielding plays would be the best way to "quantify" defense.

As for WAR -- people point out that it matches team totals very well. This is true, which indicates that WAR, including the defensive component, is accurate. But I would argue that it's not very precise. For each individual fielder, you're going to have large errors. With enough N, those errors tend to cancel out to yield an accurate estimate.

The thing is, general managers sign players, not teams. So you need more precision. and that's setting aside nailing the actual predictive value of performance, which is what matters, right?

Scoops Bolling · Oct 3, 2015

I wrote my thesis in economics on this topic. The TL;DR version is that the value of wins (in marginal revenue) varies dramatically. I don't have my numbers handy so these are just ballpark figures, but the first 70 or so wins bring very little marginal revenue, the next 10 or 15 or so are non-negligible, and then the wins as you approach a playoff level win total are worth a substantial amount. The free agent price paid, per win, most closely aligns with those playoff level wins. From an economic perspective, you would never pay free agent prices for lower level wins; the marginal revenue would not come close to matching the cost. At the end of the day, it comes down to the cost-control of pre-arb and arb level players that lets the system works as it currently does, and you can't really use the free agent market price for wins to assign "value" to anything else.

AB in DC · Oct 4, 2015

alwyn96 said:
I think something that hasn't gotten a lot of discussion but probably should is that the current CBA is ending soon, and the luxury tax level seems almost certain to rise in 2017. There's no telling what it would go up to, but I imagine the union will be pushing hard to get it higher. That probably has some implication for backloading long-term contracts. The Red Sox could go over the luxury tax in 2016, but might be able to get comfortably under in 2017 if the tax level goes up.

This seems very important to the 2016 discussion. All else being equal, 2016 would be a good year to get under the LT threshold, because the Sox have a whole bunch of young players making close the minimum. But if the threshold is going to go way up in 2017-2018, then the benefit of going under may be very small. And if the current rules for resetting the tax (after one year) under goes away, then all bets are off.

In my lifetime · Oct 4, 2015

AB in DC said:
This seems very important to the 2016 discussion. All else being equal, 2016 would be a good year to get under the LT threshold, because the Sox have a whole bunch of young players making close the minimum. But if the threshold is going to go way up in 2017-2018, then the benefit of going under may be very small. And if the current rules for resetting the tax (after one year) under goes away, then all bets are off.

I would have agreed before the season, but this year's performance + last year's big signings that haven't worked out well (Panda, HRam + extension to Porcello) have given the RS little room to stay under and also pay a top of the line starter and closer-type. I have them currently at ~165M incl player benefits and the full 40 man roster (not including Craig). If the RS go the way most think they will go ---- get a top of the line starter and a very reliable BP arm (closer or closer in the waiting), the choice will be either spend $ on a #1 starter and likely be over or spend the assets of a few prospects, cost-controlled players on the #1 starter. Then after they get the starter staff set, they will probably go the opposite way (using prospects instead of free agency) and get the closer they need. So pick your poison: over the luxury tax threshold or good bye to several of the following: Owens, Devers, Margot, Benintendi, JBJ, Johnson or Vazquez (the latter 2 on sell low with the injuries) in order to get that #1 starter and reliable reliever. I would assume Moncada, ERod and Swihart are not going to be moved.

If they really wanted to get under, they should have done it this year when they faded from contention and moved players a little earlier. The only way that was happening was if Koji was one of the guys to go (prior to injury), maybe with some dead money (Napoli/Victorino) to get some other team to pick up enough (or all) of the salary to drop below the threshold number for this year. But that shipped has sailed.

lxt · Oct 4, 2015

No. It's voodoo economics. Investing based on WAR is not the way to build a team. There are plenty of teams going into the playoffs that have teams value well below the WAR estimate of $7million/win. Think about it a moment. Are Betts and Bogaerts each worth $35million/year? The only ones who benefit from using WAR as an indicator of a players value are the agents and the players. And only for those players who have posted a significant WAR for a season or two.

Savin Hillbilly · Oct 4, 2015

lxt said:
No. It's voodoo economics. Investing based on WAR is not the way to build a team. There are plenty of teams going into the playoffs that have teams value well below the WAR estimate of $7million/win. Think about it a moment. Are Betts and Bogaerts each worth $35million/year? The only ones who benefit from using WAR as an indicator of a players value are the agents and the players. And only for those players who have posted a significant WAR for a season or two.

I can't make head or tail of the bolded. Can you elaborate?

Devizier · Oct 4, 2015

Savin Hillbilly said:
I can't make head or tail of the bolded. Can you elaborate?

My guess is that he's arguing that plenty of teams are winning 90+ games without spending ~300 million on their payroll.

Of course, it goes without saying that there isn't a team in the league that signed every single player via free agency.

alwyn96 · Oct 5, 2015

Devizier said:
My guess is that he's arguing that plenty of teams are winning 90+ games without spending ~300 million on their payroll.

Of course, it goes without saying that there isn't a team in the league that signed every single player via free agency.

There isn't, although I'm always kind of amazed at how close the 2004 Red Sox were to that. Obviously not all the players came from free agency, but the Red Sox didn't develop all that many of the key players on that roster.

This year's Blue Jays are sort of similar - Goins and Pillar came up through the Toronto org, but most of Toronto's big stars came from elsewhere. It's not impossible to build a team that way, but it takes getting guys before they hit FA, a good amount of luck with trading prospects for stars, and better luck with random pickups.

lxt · Oct 5, 2015

Sorry, must be me not communicating well. I was simply stating that teams presently in the playoffs did not necessarily get their by purchasing players based on WAR. Their are so many things that go into selecting a player that trying to find one number such as WAR makes minimal sense. there are Metrics/Old School variables that come in to play when trying to find the right players for a team. If teams buy players strictly based on the WAR then I think you'd find a Yankees team with many once great players being paid huge contracts for decent seasons of play in the twilight of their careers.

Hagios · Oct 6, 2015

kieckeredinthehead said:
So, I guess my question is: is the $7 million / WAR metric meaningful at all when thinking about team building? Does it just provide a target for players that are under-valued? Is "value" determined by the market or by what the team can afford?

I've been thinking along similar lines for a while. The $7 million per win is definitely important because it is still the best approximation of what you pay on the free agent market. And it is clear that you can't build a playoff team entirely out of free agent talent anymore. Getting the 40 wins above replacement would cost you $280 million. Even the Yankees can't do that.

This also shows the value of home-grown talent. The salient cutoff is not at 4.25 million per win. The salient cutoff is free agents vs. players under team control. Take Mookie Betts and Cole Hamels. They were both projected to produce about 2.5 WAR for the 2015 season (actual WAR was 4.8 and 1.7 respectively). But Cole Hamels' AAV was a market rate $17million whereas Betts hasn't even reached arbitration. Given the actual numbers put up by Betts and Hamels, there is also the whole "paying for past production" factor at work as well.

Draft picks are worth more than ever. Drafting well, developing talent, and having luck in the draft is what will separate good and bad teams in the future.

Savin Hillbilly · Oct 6, 2015

lxt said:
Sorry, must be me not communicating well. I was simply stating that teams presently in the playoffs did not necessarily get their by purchasing players based on WAR. Their are so many things that go into selecting a player that trying to find one number such as WAR makes minimal sense. there are Metrics/Old School variables that come in to play when trying to find the right players for a team. If teams buy players strictly based on the WAR then I think you'd find a Yankees team with many once great players being paid huge contracts for decent seasons of play in the twilight of their careers.

I think you're conflating two things here--relying on free agency and relying on WAR--that are very different. ESPN did an interesting article last winter where they rated teams on who did the best and worst job of incorporating analytics into personnel decisions. You can see that there's little correlation between how high teams rank on the list and their payroll status. Some of the teams in the top tier are among the poorest--but the Sox and Yankees are also in there.

Of course there probably aren't any teams basing their decisions on WAR in the off-the-rack, FG or BBref forms--but I assume most teams have some sort of proprietary system for figuring out how many wins their roster projects to provide, and how many wins a potential acquisition would be likely to add to that. Ultimately, what other yardstick is of any use?

ALiveH · Oct 6, 2015

I have a bunch of questions that have bugged me on this topic...

In player valuation is the value of a WAR linear? Is a 6-WAR player automatically worth 3x a 2-WAR player? There are only so many roster spots. A roster full of 2-WAR players only takes you to 0.500. So, is the incremental WAR over 2 worth more than the first 2 WAR?

czar · Oct 6, 2015

People continue to conflate the $6-8m figures with pre-arb players by applying it to the entire roster.

It's well accepted that it is extraordinarily difficult for a team to perform well (given current payroll constraints) with a roster devoid of pre-arb or even post-arb players. The $/WAR figure is used to describe the marginal cost of a win on the free market, but everyone accepts that the market isn't free, which is why young, cost-controlled players are generally a cornerstone of most modern day rosters (including Boston's), even when they have significant payroll flexibility.

ALiveH said:
I have a bunch of questions that have bugged me on this topic...

In player valuation is the value of a WAR linear? Is a 6-WAR player automatically worth 3x a 2-WAR player? There are only so many roster spots. A roster full of 2-WAR players only takes you to 0.500. So, is the incremental WAR over 2 worth more than the first 2 WAR?

Generally, we assume the valuation is linear, but as you pointed out, the roster constraints add an implicit non-linearity. However, with the talent pool distributed as such around the league, it's somewhat difficult for me to envision constructing a roster where this is too problematic...

lxt said:
Sorry, must be me not communicating well. I was simply stating that teams presently in the playoffs did not necessarily get their by purchasing players based on WAR. Their are so many things that go into selecting a player that trying to find one number such as WAR makes minimal sense. there are Metrics/Old School variables that come in to play when trying to find the right players for a team. If teams buy players strictly based on the WAR then I think you'd find a Yankees team with many once great players being paid huge contracts for decent seasons of play in the twilight of their careers.

This is actually somewhat the point mentioned above -- you cannot simply "buy WAR" and expect to be elite. Teams have clearly done well with a significant fraction of their value coming from free market acquisitions, but I think most would accept that is the exception rather than the rule at this point.

alwyn96 · Oct 6, 2015

ALiveH said:
I have a bunch of questions that have bugged me on this topic...

In player valuation is the value of a WAR linear? Is a 6-WAR player automatically worth 3x a 2-WAR player? There are only so many roster spots. A roster full of 2-WAR players only takes you to 0.500. So, is the incremental WAR over 2 worth more than the first 2 WAR?

David Cameron definitely thinks $/WAR is linear. I think he makes a pretty good case that this is so.

Buzzkill Pauley · Oct 6, 2015

czar said:
People continue to conflate the $6-8m figures with pre-arb players by applying it to the entire roster.

It's well accepted that it is extraordinarily difficult for a team to perform well (given current payroll constraints) with a roster devoid of pre-arb or even post-arb players. The $/WAR figure is used to describe the marginal cost of a win on the free market, but everyone accepts that the market isn't free, which is why young, cost-controlled players are generally a cornerstone of most modern day rosters (including Boston's), even when they have significant payroll flexibility.

Generally, we assume the valuation is linear, but as you pointed out, the roster constraints add an implicit non-linearity. However, with the talent pool distributed as such around the league, it's somewhat difficult for me to envision constructing a roster where this is too problematic...

This is actually somewhat the point mentioned above -- you cannot simply "buy WAR" and expect to be elite. Teams have clearly done well with a significant fraction of their value coming from free market acquisitions, but I think most would accept that is the exception rather than the rule at this point.

The biggest single problem with team-building by "buying WAR" - as well as the reason that $7MM = 1 WAR is now the going rate instead of nearer to the $4-5MM it was just a few short years ago - is revenue sharing and the recent influx of RSN money. More money flowing to small market teams allows more teams to lock in a few of the first (and usually best) years of free agency for 2-3 of their 4-5 best players. And if a big-market team or two should try to "buy WAR" at the market rate, their revenue sharing tax hit means gives even more latitude for other teams to lock up more of their better players.

That flow impacts more than just the disappointment from other teams' fans that those players aren't on the market to be signed.

Not only do fewer elite players hit free agency, a lot of the best ones are hitting free agency later. The scarcity of elite talent increases the price paid to other, often lesser, players. And the truly elite who hit free agency can aim for super-long contracts (with or without player opt-out provisions). Because teams on the playoff margin are more willing to pay higher premium rates for higher premium performance.

Can one ever reasonably compare the team-construction environment now to 2003? I think the marketplace has been too altered by design.

alwyn96 · Oct 6, 2015

kieckeredinthehead said:
So then why do you continue to point to the $7m/WAR figure as a reason to retain Buchholz? That seems to me to be exactly the conflation you're talking about. Yes, Clay should be cheaper than a comparable starting pitcher on the free agent market. That says nothing about the details of the Red Sox' specific needs given their current roster construction and payroll.

You didn't ask me, but $/WAR is the just the only measure of the market available, which is why people use it. I would say in Buchholz' case, if you think he's a 2-4 WAR pitcher, his contract is cheaper than what you could get on the free market. If they can get a better pitcher for cheaper should they do it? Sure. But that's what you should always be doing. $/WAR just kinda lets you know how hard it's probably going to be to do that. Acquiring a new $0.5M/WAR SP from outside the org is going to be tougher to get than a $8M/WAR pitcher and is probably going to have to come in trade, because those guys just aren't on the open market.

This example may make no sense, but if you compare it to another market, like say for TVs or something, knowing how much a new TV is worth on the open market is useful. If you have 3 tvs, and a guy you know has none and wants to trade you a fancy chair for your tv, you're probably going to want to know what that chair and the tv are worth on the open market before you trade him a tv for it. Even if the guy inherited the fancy chair from his grandfather, it's still "worth" the open market price even though he paid nothing for it. Of course, what that chair is worth "to you" might be very different. Maybe above the market if you just love that chair more than average, or below if you like it less than average. Or you could just get a replacement-level folding chair from the Ikea, but you aren't going to win any sitting championships that way.

ALiveH · Oct 6, 2015

In Clay's specific case, since the Sox have the option on his contract, assuming similar production to what he's shown over the last few years (even considering all the injuries) the contract seems to clearly undervalue the AAV he'd get if he were a free agent hitting the market. Therefore, the Sox lose nothing by exercising the contract. If they decide he's not a great fit for roster construction, they should be able to trade his net positive expected value contract for another contract that has net positive expected value.

That Cameron article was a great read, especially the comments section. Due to scarcity value & roster constraints, I still think there is some argument for nonlinearity if high-WAR players always perform as expected, but in the free agent market other considerations probably drag it down to what a linear model would predict, e.g., concentrating too much value-at-risk (injury risk) into a smaller number of players and the fact that only a very small number of teams even have the financial resources to bid for high-WAR players. Anyway, I'm coming around to the view that linearity is a good approximation of reality.

AB in DC · Oct 6, 2015

Savin Hillbilly said:
I think you're conflating two things here--relying on free agency and relying on WAR--that are very different. ESPN did an interesting article last winter where they rated teams on who did the best and worst job of incorporating analytics into personnel decisions. You can see that there's little correlation between how high teams rank on the list and their payroll status. Some of the teams in the top tier are among the poorest--but the Sox and Yankees are also in there.

What's most interesting to me is that the eight teams least interested in analytics, as of last year, will be drafting #1, #2, #3, #4, #7, #9, #13, and #17 based on this year's performance..

Pilgrim · Oct 6, 2015

kieckeredinthehead said:
So then why do you continue to point to the $7m/WAR figure as a reason to retain Buchholz? That seems to me to be exactly the conflation you're talking about. Yes, Clay should be cheaper than a comparable starting pitcher on the free agent market. That says nothing about the details of the Red Sox' specific needs given their current roster construction and payroll.

Almost any player worth multiple wins is also getting quite a few years, so you are paying for expected wins further down the road the better the player is. Good luck getting Jordan Zimmermann to sign a 1 year deal with an option at normal $/WAR figures.

czar · Oct 6, 2015

kieckeredinthehead said:
So then why do you continue to point to the $7m/WAR figure as a reason to retain Buchholz? That seems to me to be exactly the conflation you're talking about. Yes, Clay should be cheaper than a comparable starting pitcher on the free agent market. That says nothing about the details of the Red Sox' specific needs given their current roster construction and payroll.

I'm unclear what you are asking.

The reason why I use $/WAR with Buchholz is two-fold. One, because that is what Buchholz would be worth on the open market if he was not tendered a contract, as many around here seem to desire. That, therefore, is his marginal value to a team with that deal.

Two, because you'd have to replace that value if you let Buchholz go, likely on the free market.

Snodgrass'Muff · Oct 6, 2015

WAR is designed to be linear when comparing one player to another. As we are seeing in this thread, that gets really messy and loses a lot of its usefulness when talking about roster construction because of the fact that player value doesn't exist in a vacuum and is impacted by a number of factors that most people don't consider when thinking about free agent signings, trades, or other roster moves.

So for me, even if we could trust WAR in smaller samples in the first place, it's not terribly useful in most discussions we, as fans, tend to get into when we want or need a figure that represents a player's holistic value.

We can either talk about player value in the micro sense or about roster construction in a general sense (value at a macro scale) but we don't really have good tools for mixing the two.

SumnerH · Oct 6, 2015

ALiveH said:
I have a bunch of questions that have bugged me on this topic...

In player valuation is the value of a WAR linear? Is a 6-WAR player automatically worth 3x a 2-WAR player? There are only so many roster spots. A roster full of 2-WAR players only takes you to 0.500. So, is the incremental WAR over 2 worth more than the first 2 WAR?

Apparently (and surprisingly to me) the value seems to be linear in practice. I would've thought that higher-WAR players would be paid more per WAR for the same reasons you outline, but it doesn't seem to be the case.

http://www.fangraphs.com/blogs/albert-pujols-and-linear-dollars-per-win/
http://www.fangraphs.com/blogs/linear-dollars-per-win-again/
http://www.ussmariner.com/2008/02/14/2008-win-values/

(There are other ways in which contracts are non-linear that aren't related to what we're talking about)

czar · Oct 6, 2015

kieckeredinthehead said:
Maybe read the thread again, then? The economic decisions that the Red Sox need to make regarding Clay's option is not made in a vacuum with regard to how much a starting pitcher costs on the free agent market. It's made in relation to the amount of money the team has to spend to get to 88 wins, or about 48 wins above replacement. They have more than five potential starters for next year (Buchholz, Porcello, Miley, Kelly, Johnson, Rodriguez, Owens, Wright). There is little question that, if healthy, Buchholz projects to be cheaper than what they could purchase on the free agent market. That alone, as people have said, means that if nothing else he would be a valuable trade chip. Beyond that, how do the Red Sox decide whether Clay Buchholz is the best $/WAR that they're going to get? You can't use $/WAR from the free agent market because if they did that for every player they'd blow past not only the luxury tax but, presumably, their own budget.

-The cost of purchasing Buchholz on the free agent market is more than his option. By that criterion, they should pick it up.

-The amount the Red Sox can afford to pay per WAR to get to 88 wins is approximately $4.25/WAR. By that criterion, it's less clear because we don't know how well or how long Clay will perform.

-The amount the Red Sox can afford to devote to a starting pitcher who will give them 2-3 WAR (based on his three year average) is even less clear given the in-house alternatives.

I agree that it's a no-brainer to pick up the option because of his trade value. The question is then whether to trade him or keep him? Now that we've agreed not to conflate free agent market value with other ways of valuing players, how do you decide whether Clay is a "bargain" or not that will help the Red Sox get to 88 wins while staying within their (assumed) budget of ~$189 million?

I think you are misconstruing my arguments if you think I've been arguing for the Red Sox to not even consider moving Buchholz. e.g.,

czar said:
Again, it is ludicrous to think that Clay Buchholz (provided "healthy") is possibly not worth 1/$13 on the open market. Even with his craptacular start to the season (and caveats about valuation aside), FG has him worth $25m this year (which assumes $/WAR ~ $8m) in like half a season. He is still the 19th most valuable pitcher in 2015 (out of 690 to appear in an MLB game) and he hasn't pitched in a month.

Last offseason, Jake Peavy got 2/$24 after posting half of Buchholz's 2015 WAR in twice the innings last year. Yovani Gallardo got 1/$13 and his rates have been trending the wrong way for years. Brett Anderson got 1/$10 and he hadn't thrown more than 100 innings in FIVE YEARS. Clay Buchholz will have non-negligible trade value on a 1/$13 + option for 1/$13. As Plympton pointed out, he has even MORE value (aside from the 1/$13) tied up in the fact that a team has the OPTION of keeping him around at $13m in 2017 (i.e., it's either ends up being a cheap 1/$13 roll of the dice if he sucks, or a 2/$26 steal if he pitches anywhere close to what he did this season).

The Sox will pick up the option unless his elbow falls off. There is no reason not to. The Sox can then decide whether to keep or trade him, but that's a totally separate question.

There is zero reason (health-permitting) for the Sox not to pick up his (Buchholz's) option. However, one could easily envision many ways to move Buchholz and create net positive value for the team. Is that what you are asking? I don't think anyone is arguing "we must keep Buchholz at all costs due to his WAR/$ ratio." That would be the equivalent of saying "we cannot trade JBJ for Mike Trout because JBJ's WAR/$ ratio is higher." It all comes down to what Buchholz could net in a trade. If Buchholz could help you get Carlos Carrasco? Sure. If you are going to move Buchholz because he's "injury prone" and get a couple A-ballers back -- well, I'm not sure how that creates net value for the team.

I think your second and third bullets need to be merged. In aggregate the team needs to extract $4.25m/WAR, for example, but you already have in-house, under-control options like Betts, Bogaerts, Swihart, etc. that get you ahead of that figure. At that point it comes down to how/where you make up the extra wins at the margins. If having enough young talent gets you to a situation where you can afford to spend $10m/WAR to get to whatever benchmark you need, you are in a very enviable position. It means you are extracting arbitrage from your young players such that you can be either more inefficient (aggressive?) w/r/t the FA market or you can acquire even more surplus value for the same dollar mark.

Hagios · Oct 6, 2015

czar said:
I think your second and third bullets need to be merged. In aggregate the team needs to extract $4.25m/WAR, for example, but you already have in-house, under-control options like Betts, Bogaerts, Swihart, etc. that get you ahead of that figure. At that point it comes down to how/where you make up the extra wins at the margins. If having enough young talent gets you to a situation where you can afford to spend $10m/WAR to get to whatever benchmark you need, you are in a very enviable position. It means you are extracting arbitrage from your young players such that you can be either more inefficient (aggressive?) w/r/t the FA market or you can acquire even more surplus value for the same dollar mark.

Good point. Another way of looking at it is that if you used the $4.25/WAR as an iron law, you'd be stuck with only home grown talent, and it's unlikely that any team would have enough home grown talent to make the playoffs without a lot of luck. Most teams are going to need to hit free agency, and that means going well above the $4.25/WAR threshold.

lxt · Oct 7, 2015

Good article ... fun read.... you'd think Miami would be knee deep in analytics ... thanks Savin.

The whole discussion about WAR is most confusing and wrought with inaccuracies and misconceptions. It is just another metric to combine with others to help decide who is the best player from a teams perspective. Someone I may find acceptable and a plus to my team another may not. Does it provide a price tag, No. It's used by agents to a players advantage when it is up and down played when its down. Does WAR provide an answer to who to hire and who to not, NO. It is another tool in the large bucket of analytics.

HangingW/ScottCooper · Oct 13, 2015

iayork said:
There are rumors, or maybe more than rumors, that individual teams have proprietary ways of measuring defense that are more sophisticated than the tools we plebeians have. Of course we don't have access to those tools, so we don't know if or how well they work. My guess is that they're closer to detailed scouting, human-input, approaches than the sort of generic zone-based tools that are publicly available.

Probably the various StatCast things that are gradually becoming available will help, and I think teams have had access to that sort of thing for a while. Even knowing the actual starting position (instead of the assumed generic position) of a fielder would help. So in the next few years, there may be new stats that are better for evaluating fielders.

The stats that are available today aren't completely useless, but even as descriptive stats, let alone predictive, they have such wide error bars that they don't tell you any more than the eyeball test does. I suspect that the most accurate descriptive fielding stats are Tango's scouting reports, which rely entirely on the eyeball test spread out over many people.

They talk about it in Moneyball when evaluating Terrance Long vs. Johnny Damon. They look at trajectory and location of similar hits and assign a result. A line drive hit to a certain location at a certain trajectory results in a double 90% of the time, a single 5% of the time and an our 5% of the time. When an outfielder turns it into a single or an out that's positive on their record for run prevention.

alwyn96 · Oct 14, 2015

HangingW/ScottCooper said:
They talk about it in Moneyball when evaluating Terrance Long vs. Johnny Damon. They look at trajectory and location of similar hits and assign a result. A line drive hit to a certain location at a certain trajectory results in a double 90% of the time, a single 5% of the time and an our 5% of the time. When an outfielder turns it into a single or an out that's positive on their record for run prevention.

The Inside Edge stuff on fangraphs breaks this down even further, although their system is proprietary and we have no idea how Inside Edge is actually classifying it. Presumably with eyeballs, but it's all a trade secret, so who knows.

At any rate, I think the Inside Edge stuff is good to look at as a reminder that the overwhelming majority of defensive plays are routine, and that defensive WAR is weighted a lot by opportunity.

Plympton91 · Oct 15, 2015

And even those systems are dependent on positioning of the fielder you are evaluating and the skills and positioning of the players at adjacent positions. Defensive statistics are no better than RBI, which will be very highly correlated with the best hitters over large samples, but measure what you want to measure only highly imperfectly.

More generally, I would argue absolutely that any attempt to maximize wins by maximizing WAR/$ has to account for multiple nonlinear constraints in the system. You have to maximize subject to overall roster limits, as well as the obvious but overlooked limits of one player at each position in the starting lineup, and that having more than 5 heathy effective starters provides heavily diminished marginal returns.

Savin Hillbilly · Oct 16, 2015

Plympton91 said:
More generally, I would argue absolutely that any attempt to maximize wins by maximizing WAR/$ has to account for multiple nonlinear constraints in the system. You have to maximize subject to overall roster limits, as well as the obvious but overlooked limits of one player at each position in the starting lineup, and that having more than 5 heathy effective starters provides heavily diminished marginal returns.

Of course positional value adjustments are designed to account for exactly this. If it wasn't true that you have to have a shortstop in the lineup whether you can find one who's a good hitter or not, there would be no logic behind assigning shortstops extra value points just for being shortstops. So this constraint is already embedded in WAR.

Plympton91 · Oct 16, 2015

Savin Hillbilly said:
Of course positional value adjustments are designed to account for exactly this. If it wasn't true that you have to have a shortstop in the lineup whether you can find one who's a good hitter or not, there would be no logic behind assigning shortstops extra value points just for being shortstops. So this constraint is already embedded in WAR.

Agreed, I'm not saying that SS aren't inherently more valuable than an otherwise equivalent LF. What I'm saying is that you have to account for the fact that having three great SS doesn't help you as much as having a great SS, a good 2B, and a good 1B, because only one of the SS can play SS at a time. If you pay the market rate for a great SS, and then move him to 2B, you've overpaid.

HangingW/ScottCooper · Oct 18, 2015

alwyn96 said:
The Inside Edge stuff on fangraphs breaks this down even further, although their system is proprietary and we have no idea how Inside Edge is actually classifying it. Presumably with eyeballs, but it's all a trade secret, so who knows.

At any rate, I think the Inside Edge stuff is good to look at as a reminder that the overwhelming majority of defensive plays are routine, and that defensive WAR is weighted a lot by opportunity.

Win Shares looked at this as well. While it's an old book it breaks down the relative value of each position on the field and the effect of various types of pitching staffs. Definitely a good read.

redsox3g2 · Oct 19, 2015

kieckeredinthehead said:
Okay, the principle that teams can afford to over-pay free agents because of their young pre-arb talent is obvious, but the actual details of how you work out how much a team can afford to pay for WAR is still unclear in my head. So here's back of the envelope calculations, team payroll for next year and a quick estimate of WAR:

Catcher: Swihart ($0.5M, 2.5-3 WAR); Hanigan ($3.5m, 0.5 WAR); Vazquez ($0.5M, 1 WAR)
1B: Hanley ($22.7m, 1 WAR)
2B: Pedroia ($13m, 4 WAR)
SS: Bogaerts ($0.5M, 4-5 WAR)
3B: Sandoval ($17.6m, 1 WAR)
LF: Castillo ($11.2m, 0-1 WAR)
CF: JBJ ($0.5M, 1-2 WAR)
RF: Betts ($0.5M, 4-5 WAR)
UT: Holt ($0.5M, 2 WAR)

Position Players: $71M, 19-24 WAR

Pitchers:
Buchholz ($13M, 2.5 WAR)
Porcello ($20M, 2.5 WAR)
Miley ($6M, 2 WAR)
Kelly ($1M in arb?, 1 WAR)
Rodriguez ($0.5M, 2 WAR)

Starting Pitchers: $40.5M, 10 WAR

Relief:
Koji ($9M, 2 WAR)
Taz ($3M in arb?, 1 WAR)
Ross ($1M in arb?, 0.5 WAR)

Relief: $13M, 3.5 WAR

Again, this is just because I want to see how these calculations actually work. Feel free to quibble with arbitration estimates, WAR expectations, etc. But bottom line, based on the above the team has about $124M committed to 18 players that will likely be on the 25 man roster to start the season (as of now). Those players might be expected to put up about 37 WAR. That's 11 wins short of the playoffs. They're currently spending ~$3.35M/WAR, leaving ~$60M to acquire/retain an additional 11 wins, or ~$5.5M/WAR. Even with all the incredible, cost-controlled talent on the roster the Red Sox still can not acquire the remaining 11 WAR by paying market rate without blowing past the luxury tax.

The real offenders, obviously, are Hanley and Sandoval. At least one of them has to bounce back or the Red Sox are very unlikely to be able to make up the difference elsewhere. Castillo is next in terms of $/WAR, although league average play would bring his costs down pretty quickly. Porcello and Hanigan are costly, but for different reasons. Porcello's costly because his contract is expensive; Hanigan's costly because he's not that good (again, subject to large error bars around WAR in general and my guesstimates specifically). Hanigan is obviously worth keeping around because the total cost of his contract is not that large and he provides incredible depth at a critical position.

Buchholz is next - he's right in the middle in terms of $/WAR. I suspect that he's the guy that could bring back something of value in trade or offer salary relief (say package Buchholz and Panda). Trading Buchholz really might free up money to sign a true "ace."

I think this is a useful look at where the roster stands. Although I believe you missed one addition.

David Ortiz: $16M (2.5-3 WAR)

Which brings the total to roughly $44M left to add 8-8.5 wins based on your other assumptions. ($5.17M-$5.5M/WAR left)

Savin Hillbilly · Oct 19, 2015

I think a mistake may have crept into the conversation here, which is the assumption that a replacement level team is worth 40 wins and therefore you need 48 WAR to contend. It's the other way around. A replacement level team, according to FG, is worth 47.7 wins, so 40 WAR gets you into contending territory. 37 WAR is not "11 wins short of the playoffs"; it's maybe five at the most, or less with a bit of luck.

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