Valuing Gerrit Cole’s Opt Out
Last night, Gerrit Cole signed a record-breaking contract with the Yankees. Jay Jaffe broke down the signing, and mentioned one important part: the contract includes a player option after five years. In a contract as lengthy and lucrative as Cole’s, an opt out might seem like mere ornamentation. That’s not the case, though: as Stephen Strasburg’s earlier contract shows, sometimes the market in the future is simply better for a pitcher than we think. With that in mind, I took a stab at valuing the player option.
We use two player projection systems here at FanGraphs, and I ran both of them through the option pricing tool, as well as a hybrid. First, let’s take a look at the most optimistic: Steamer projects Cole for 6.3 WAR this year. From there, I applied a standard 0.5 WAR/year aging penalty and ran the numbers. You can read the methodology here, but as a quick refresher, I take an aging-inclusive projection, then bump each year by a random, normally distributed number to account for fluctuations in talent level.
The bumps persist year-to-year; if Cole improves to a 7 WAR projection for 2021, his mean projection for 2022 would be 6.5 WAR after the aging penalty, and I then apply another random talent bump to that projection. I do the same thing with the cost of a win in free agency; it generally trends upward, but jumps around, and the jumps persist year-to-year.
Cole opts out a surprising amount of the time under these projections:
| Condition | Odds | WAR | Salary ($m) | $/WAR |
|---|---|---|---|---|
| Opts Out | 0.374 | 31.9 | 180 | 5.6 |
| Stays | 0.626 | 29.1 | 324 | 11.1 |
| Total | 1 | 30.1 | 270.1 | 9.0 |
But perhaps more surprising is how much better he is in the scenarios when he opts out than he is when he stays. It might sound counterintuitive, but Cole projects for more WAR over five years when opting out than he does over nine years when staying. Why? In many of the scenarios where he declines, the last four years of the deal dip towards replacement level. For him to leave, on the other hand, he has to outperform expectations significantly (or the cost of a win has to spike higher).
How significantly are we talking? Take a look at Cole’s performance and pay in the two scenarios:
| Condition | Odds | WAR (Year 6) | Cost of 1 WAR | New Contract |
|---|---|---|---|---|
| Opts Out | 0.374 | 6.5 | 9.4 | 214 |
| Stays | 0.626 | 2.2 | 9.2 | — |
On average in the worlds where Cole opts out, he defies aging, looking as good in six years as he does now. In some, he’s a 10 WAR player; in some, a mere 5 WAR, 36-year-old player. You could quibble with the caps teams would be willing to pay for four years of a 10 WAR pitcher, which would tinker with his expected windfall upon opting out, but using a linear cost of a win and the odds of Cole opting out, the option to become a free agent again in five years is worth $26 million to Cole.
Steamer’s projections are the rosiest. If we instead use ZiPS, which starts with a 5 WAR projection but declines more slowly, an early departure becomes less likely:
| Condition | Odds | WAR | Salary ($m) | $/WAR |
|---|---|---|---|---|
| Opts Out | 0.268 | 27.5 | 180 | 6.5 |
| Stays | 0.732 | 22.9 | 324 | 14.2 |
| Total | 1 | 24.1 | 285.4 | 11.8 |
Even in this scenario, however, Cole leaving involves him significantly beating his projections, and the opt out is worth $16 million:
| Condition | Odds | WAR (Year 6) | Cost of 1 WAR | New Contract |
|---|---|---|---|---|
| Opts Out | 0.268 | 6.2 | 9.4 | 205 |
| Stays | 0.732 | 1.8 | 9.2 | — |
Finally, I ran a blend of the two projections. The results, as expected, were somewhere in between:
| Condition | Odds | WAR | Salary ($m) | $/WAR |
|---|---|---|---|---|
| Opts Out | 0.318 | 29.7 | 180 | 6.1 |
| Stays | 0.682 | 26.0 | 324 | 12.5 |
| Total | 1 | 27.2 | 278.2 | 10.2 |
And this time, Cole’s opt out is worth $21 million:
| Condition | Odds | WAR (Year 6) | Cost of 1 WAR | New Contract |
|---|---|---|---|---|
| Opts Out | 0.318 | 6.4 | 9.4 | 210 |
| Stays | 0.682 | 2 | 9.2 | — |
So there you have it. I believe the player option part of Cole’s contract is worth around $20 million. You can disagree with pieces of it; maybe my particular style of random variation doesn’t handle pitchers as well as it does for position players, or maybe the assumption of a linear $/WAR doesn’t work for some extreme outcomes. The overall conclusion, however, seems straightforward: Cole’s player option isn’t a mere trinket, but it also doesn’t significantly change the terms of the deal. Gerrit Cole got paid; and he got paid slightly more due to the exact design of his contract.
Ben is a writer at FanGraphs. He can be found on Bluesky @benclemens.
Two articles in a row on the blog roll? Love to see it
The part missing from the equation is how is the opt valued at the point of negotiation. In other words, if the Yankees insisted on no opt out, would Cole have countered with a higher amount to compensate? It seems as if we all assume opt outs are just thrown into the mix after the deal is negotiated, but if players desire them, and teams extract concessions for them, the dynamic changes considerably. Under those conditions, an opt out is in the team’s best interest (i.e., non cash compensation is a nice way for team’s to lower costs). After all, the Yankees would have gladly signed Cole to only a 5 year deal, so if he remains good enough to opt out (meaning the Yankees have gotten more than their money’s worth to that point), both parties are in the same place as if that scenario played out. Similarly, if Cole isn’t up to par and doesn’t opt out, the Yankees are no more on the hook than they’d be if there wasn’t an opt out. Essentially, the risk to the team is they lose the opportunity to have more years of a good contract, but that also means they’ve already enjoyed great production and still have the opportunity to determine if they want to continue the relationship. Unless the opt out is given freely and provides an escape when the player is too young, teams should be quite happy to put opt outs in long-term free agent contracts.
There isn’t a single person I’ve spoken to, specifically on FG that thinks opt outs are throw ins, why would you think that people think this? Is this a common assumption I missed?
Second there is more to an opt out then the team getting out of the back end of a contract, rarely if ever is a team happy to lose a player that opts out. If the player opts out then it is assumed that his open market value is worth more then the back end of the contract. Meaning the team loses value in either player performance or trade value, and have to be replaced, I don’t know if any front offices that like losing value.
The likeliest thing is that the opt out at negotiating times may cost a player a guaranteed year at the end or a higher AVV or perhaps it’s used to put a team over the top but i don’t think anyone thinks it’s a throw in.
In almost every discussion about opt outs, the negotiated value is completely ignored. That’s why I think most people regard it as a throw-in. I am glad you think differently.
+1 here for looking at the negotiated value. Guessing the “throwin” concept is more from sports radio, where they tend to struggle with economics, numbers, and math.
What if the player option is a form of hedging by the Yankees?
Even IF the guy has dominated for 5 years, such that going into year 6 he is worth more on the FA market than the remainder of his contract provides, in that scenario you’ve still had him for 5 dominant years and he’s chosen to walk away for his year 35 (34?) season, leaving the 4 most likely injury & decline years off your books. Someone else pays the extra money to lock him in for the riskiest years.
See Alex Rodriguez. If that is the case the Yankees would much rather have him not opt out then do so. There is never a situation where the team is happy a player opts out, only situations where hindsight makes it a good thing. If Cole opts out it’s because the last 4 years on his contract are a relative bargain.
sadTrombone makes this dumb argument all the time — that the team who GIVES the player an option somehow wins by the player exercising the option because there’s some very dumb other team who wants to throw away $180M.
This is a player option which the player would only exercise if he deemed the market conditions (ie, teams who have $180M would deem his future performance worthy) and his recent performance would reap a bonanza — as it did for Strasburg 2 days ago in garnering him an extra $120M. If Cole wasn’t on the market, I’m sure NYY would have bid for Strasburg.
Ben’s analysis here features a nice random bump in performance that I wouldn’t have thought of. A simple analysis 5 years out where Cole thinks he can get 4*$45M vs he doesn’t exercise the option and receives 4*$36M at equal probabilities results in the option value coming to $18M, just a bit short of Ben’s average of $20.5M. Raise that to 5*$45M and you get $40M – (what Cole could get on a 1 year deal after his 9 year contract expires).
I don’t think the argument is dumb at all. If someone has an opt out after several big seasons, and he exercises it then sure, he (and prospective teams that might pay him) are working on the assumption that his projected value is going to exceed the value of the contract he’s opting out of. BUT you’ve already banked the huge seasons, you’ve *realized* a profit. Maybe you’re missing out at a chance at being even more in the green, but you’re also avoiding the chance of going negative.
I just don’t see how a contract that stipulates “We lose you if you’re awesome for five years” doesn’t have value to the team because, well, it implies the player was awesome for five years. It is, in short, *guaranteeing* a profit on the contract if the player performs well.
Because the assumption is that both the player and the team are rational actors who can correctly value the player’s contributions, likely future results, and market value. Obviously this is a mental model and not real world, but for your version to be true — that the team “wins” if the player opts out — we have to assume the player / agent makes a valuation mistake. So the question to ask is: how likely are Cole / Boras to misread the market? After the last few offseasons, and considering Boras has some true duds on his resume (Stephen Drew’s declined QO is the first one to come to mind but I think there are more), it seems fair to at least say that the chances are non-trivial. But even if this happens 10% of the time, 90% of the time Cole declines the remaining (bargain) years on his contract and gets more money, when the Yankees would’ve preferred to keep him at the original price.
tl;dr 5 great years followed by an opt out isn’t BAD, it’s just less GOOD than 5 great years followed by 4 bargain/market value years.
Oh and Cole’s 10/5 rights vesting at the time of the opt out seems like an underdiscussed point in his favor
What you wrote here has a lot of good points, but this is where the model goes wrong: Cole doesn’t need everyone to believe he’s worth more than the contract he already has. He only needs one team to believe it. This is the flaw in the rational actor model, where everyone agrees on what the value of a player is–not everyone agrees, not everyone has the same information, and not everyone has the same needs.
Besides, there aren’t really many scenarios where he’s going to be worth $144M in his age 35-38 seasons, even if he’s been good leading up to it. I don’t think people take the relative likelihood of him actually being worth the back end of the contract into account enough.
If there’s still a team thinking 35-year-old Gerrit Cole is worth more than 4/144, the Yankees are better off trading him to that team than watching him walk and sign a bigger contract with no compensation.
With those 10/5 rights (and maybe an NTC in there), good luck with that.
Why would a team that has “banked” 5 great Cole years suddenly become risk-phobic and want him off the team when his remaining 4+ years have positive trade value even at $36M/year? Why didn’t the Diamondbacks just give Greinke away for free last summer? They could have avoided the last 2 years of risk of a 33-year old pitcher. Answer: They’re not stupid, he was pitching great and still had trade value. (There are cases in the past in August waiver claims where a team would give away a player because his contract was an albatross, but I don’t think that player would have opted out and particularly not in WAR-efficient today.)
Thus, the Yankees do not benefit by giving Cole a free option. They mitigated their option cost by having the option not kick in until year 5. I’m sure Boras asked for an option after year 2 or 3 where it would have a lot more value, but was politely declined.
Because it’s not whether you can bank a profit in the years under contract — it’s comparing it to different options.
It might be more risk averse, but sub-optimal economically. You would have a positive value asset (gap between contract and market value) that you’re losing the rights to.
The “you could make more money” argument is difficult to understand intuitively, but it’s the correct way of looking at the problem. Just because it’s not so bad to have banked those years, doesn’t mean it’s the optimal decision. And just because it could work out (player opts out then sucks) doesn’t mean that’s the right way to evaluate the decision.
This stuff is difficult. I recommend Annie Duke’s “Thinking In Bets” to develop more intuitive understandings.
Yeah, I make that dumb argument a lot. The reason why is because virtually every analysis makes a totally inappropriate comparison: The world where the player performs well (and opts out) versus the one where the player does not (and does not). In the real world, a team will never confront this choice. The only choice the team has is to give the opt-out; the player’s performance isn’t out of the team’s control, but is is not likely affected by the presence of the opt-out.
You can see how this plays out in a 2×2 table:
A) In the world where Cole has the opt-out and performs well enough to opt-out (and leaves), the team loses if Cole would have continued to outperform the money remaining in the back half of the contract. The team wins if Cole opts-out and then is worth less than the remaining amount of cash on the contract.
B) In the world where Cole has the has the opt-out and performs badly (and doesn’t opt out as a result), the team has won a little bit because they traded the opt-out for something else of value (see williamnyy’s point elsewhere in this thread).
C) In the world where Cole doesn’t have the opt-out and performs well enough to opt-out, the team wins if Cole continues to outperform the money remaining on the back-end of the contract. The team loses if Cole underperforms the money on the back end of the contract.
D) In the world where Cole doesn’t have the opt-out and performs badly, the team has won a little bit because they because they traded the opt-out for something else of value (see williamnyy’s point elsewhere in this thread).
A quick perusal of the 2×2 table, which I don’t think anyone could disagree with, shows that that in scenarios B and D the team saves a little bit of money by giving the opt-out. It’s not a big win, but if Cole doesn’t perform enough to ever opt-out, giving the opt-out is always good for the team because it was traded for something else of value.
In scenarios A and C, the question becomes whether Cole will outperform the back-end of the contract. Do we think that Gerrit Cole is going to be worth $144M in his age 35-38 seasons? (or whatever it is?). More importantly, do we think that if Gerrit Cole is still a star at age 34 and he’s likely to opt-out, that portends he’s going to be worth $36M a year anyway? As far as I can tell in this simulation, Gerrit Cole will never lose more than 0.5 wins in a year, and often much less, and sometimes even improve regardless of age.
What this means is that in a simulation like this–which is similar to how a lot of people think about player performance–it’s impossible to come to a conclusion where a player is good enough to opt-out and somehow not worth the back end of the contract; the simulations and mental models completely exclude the idea that someone could be good enough to opt out and yet not worth the back end of the contract*. In both those situations, people come to the conclusion that opt-outs are always bad for the team. But historically, we know that in virtually every single one of those big-money deals, the back end of the contract subsidizes the front end. Max Scherzer and Zack Greinke are exceptions rather than rules.
(*Other people use mental models where everyone is a rational actor and knows what the actual value of a player on the free agent market is, so in those situations no one ever makes bad decisions on the free agent market, which is also obviously false. You can get to the same wrong conclusion that opt-outs are always bad using that logic as well).
To be fair, Ben literally says “it’s okay if you don’t believe the exact parameters of this simulation” in this piece and in the previous piece says “this method probably won’t work for pitcher aging because pitchers are too weird” but I’d caution people away from extrapolating too much from the findings here about the value of opt-outs in general.
One more point, and then hopefully I’m done: I sincerely doubt this opt-out ever gets exercised. I sincerely doubt any of these opt-outs except for Xander Boegarts gets exercised. Pretty much everyone knows the back ends of these deals subsidize the front end. And this is the main reason why opt-outs are good for the team: You probably just got to save a little money on something the player will never use.
Exactly, and part of the point I made above. In the worst case scenario (a still valuable player opts out), the team still has the opportunity to assess whether maintaining the relationship is worthwhile. Although in most cases teams would likely have preferred that the player not opt out, losing out on a potential future benefit is not the same as incurring a loss. That’s why it’s important to consider what was negotiated for the opt out in the first place. If teams are saving money because players covet them, it tilts the balance and actually compensates teams for taking long-term risk.
williamnyy: The $21M option value seems not so significant on a $324M contract. I mean, so what if the NYY would have had to pay him $346M without it.
1 point I forgot to mention in the “Player Option is somehow good for the team who gives it argument”: If NYY somehow experience penury 5 years from now and find the Cole contract unaffordable, his willingness to opt out indicates that the contract has positive trade value since he thinks he could get an even better contract than he already has. The team could then trade Cole 5 years out…unless he opts out. The Opt Out is a gift to the player and a small detriment to the team.
So what if the Yankees saved $21M? Well, if they did, and Cole opts out, that means they could offer him an additional $5M per year for a four-year extension ($164/4 instead of playing out the remaining $144/4) and still come out even. And, if Cole doesn’t opt out, they end up saving $21M over what they would have otherwise paid. The trade off for the opt out is very significant, and without knowing it, we can’t really say who benefits most and by how much.
Regarding your last point, whenever teams dump salary, they are often forced to eat money. We’ve seen that time and again. Even if Cole’s contract is friendly after five years, if the Yankees needed to trade it, they would likely have to absorb some of the cost, and probably a significant amount if they want prospects of any value.
It is significant in that it’s hypothetical money rather than actual money.
If it were me, I’d rather offer someone a few words saying they could leave after awhile than another 6.5% of the contract amount in actual dollars.
If it costs more than that to re-sign the player afterward, you worry about it then, when the 21 million dollars you saved has accrued interest or allowed you to sign another player that you might not have otherwise.
“Not significant” was a poor choice of words on my part. “Obvious” would have been better in that it’s obvious that the Opt-Out has value to the player and the player would negotiate for equivalent additional money if the team wouldn’t give an opt-out.
“If teams are saving money because players covet them, it tilts the balance and actually compensates teams for taking long-term risk.”
This makes sense to me. Teams can afford to take on more risk, because they have a larger pool of players. A single player can’t spread the risk around. There’s a premium for that.
This isn’t really what hedging means. They aren’t exchanging upside in exchange for downside protection — the way the contract doesn’t work out for them is if Cole is awful and stays. Team options are hedges: if they had offered him, say, 5/42 with a team option for 4/25 on the back end, then they would be hedging the disastrous Cole scenario.
The only person hedging in this deal is Cole; he gets paid $144 million for the last four years if he turns into a pumpkin, but can still dip into the market for another shot if he remains great. Now, he’s presumably paying for that hedge with a lower AAV, so it’s not as if the Yankees get nothing for it, but a 9/36 contract with an opt out is inherently and strictly better for a player than one without an opt out.
How can you say the opt out is inherently and strictly better without knowing what the deal would have been without it? Take the CC Sabathia deal as an example (that is more analogous than Strasburg because his contract was not a free agent deal). He originally signed for $161mn and leveraged the opt out into an extension that added 1 year and $30 million. So, in total, he went from $23 per year to $23.75 per year. Now, let’s imagine the Yankees shaved $10 million from the original deal by including the opt out. All of sudden, the net difference between the two deals is only $20 million, but that includes an extra year. Essentially, it would be as if Sabathia had not opted out and then signed a $20mn extension (actually $20mn less whatever accrual the Yankees would have earned on the $10mn in cumulative lower payments). As it turns out, FG has Sabathia’s WAR-based value at $21mn in what turned out to be year-8, so it’s not clear that the opt was inherently and strictly better.
Obviously, the above is just one example, but the overarching point remains. Without knowing how these opt outs are valued at the point of negotiation, we can not definitively determine to whose benefit they end up being.
I agree with this, and stated it above: “Now, he’s presumably paying for that hedge with a lower AAV, so it’s not as if the Yankees get nothing for it, but a 9/36 contract with an opt out is inherently and strictly better for a player than one without an opt out.”
I’m saying that for the same contract in monetary terms with and without one of these, the player option strictly benefits the player. I think you have the right idea that there’s some cost the team saves that makes this make sense. But people love to say ‘the opt out works for the team because the player will opt out and save them the bad half of the contract’ and that’s not how it works. If your argument is that opt outs are mutually beneficial, then I agree – but I think many people think they are worthless and might actually help the team (given the same dollar terms) and that’s simply not true.
Gotcha…didn’t realize your point was all else being equal, in which case the opt out clearly benefits the players. However, in some cases, I think opt outs can help teams, particularly smaller market ones who may be uncertain about their ability to compete long-term. In those cases, the team’s thinking may be they want the player for the short-term, but think over the longer span they will stop being competitive, in which case they wouldn’t even want the player regardless of how productive he remained. Granted, such a player could be trade bait, but rarely do large salary dumps come without subsidy. For example, I am guessing the Marlins might have preferred a Stanton opt out over having to send the Yankees $30mn and take Castro in exchange for prospects.
Yeah, I agree. Opt outs are things that make a lot of sense for both players and teams, which is why they exist – I just think it’s useful to show rough indifference points. If this analysis is roughly right, the Yankees would have been indifferent between 9/344 with no opt out and the actual deal. That sounds about right to me, and has particular value for them because non-dollar sources of value for players are useful for teams with luxury tax hits. Just worth spelling out what that extra value Cole gets is worth, and where it comes from.
I’m guessing Cole was in such high demand (especially after Strasburg signed), he didn’t have to lower his AAV to include the opt out.
Let’s say the Yankees were at $324mn/9 years with no opt out and another team matched the money and added the opt out. The Yankees could then ask Boras what would it take in money to trump the opt out. His answer would be the negotiated value of the opt out.
This assumes that money and opt-out are the only inputs he considers. I understand your question, but I don’t think it’s knowable — how does a team and player value it? We will never know, but the $/WAR regression models are a reasonable broad strokes advisement.
williamnyy, that’s a great example. Here’s another hypothetical. The bidding war led to the Angels having the best offer on the table with 9/$320M and 4 player opt out years, but Cole preferred the Yankees (again, just hypothetical) and the Yankees really, really wanted Cole. Boras checked back with the Yankees one more time and they offered 9/$324M. Boras said if you include 4 player opt out years, I’ll run it by Gerrit. Yankees say okay and Cole says done deal.
I’m guessing so too, just based on the total of the contract. Very fair logic. Im gussing the Angels made it close, or raised the price.
I’m trying to understand the Nationals situation where they give stras an opt out in one contract (or he demands one). And then there isn’t one in the second contract.
The other thing the opt out does is that it hedges against large changes in the luxury tax. Should that increase substantially, $/war almost certainly must also increase, right?
They are exchanging upside (the player is great for his entire contract) for downside (the player meets or exceeds his contract value for five or six years, then the contract becomes an albatross) protection. In fact, when put like that, I would bet on the downside being more likely!
I wonder to what extent the opt out is protection in case the new CBA (or other factors) change the landscape to the point that those last few years turn out to be cheap more than Cole outperforming his contract. We don’t really know what the relative value of $36 million in the 2024 off-season is compared to now.
Seems like the value of the opt out should be weighted by the likelihood of it occurring. If it results in $20m more to Cole only 30% of the time, really it’s value in today’s negotiations is about $6m.
It’s weighted. The value of the new contract is listed in each case – the value to him is the extra money he’d make relative to the contractual terms weighted by the odds of opting out.
Thanks!
Question: Is the 0.5 aging penalty appropriate at such a high projected WAR value? I know we use this standard aging technique as a means of doing quick and easy math (although I do really like your random shocks/bumps!), but I’m not sure I buy that given where we are along the distribution of projected WAR totals. For example, If you apply the -0.5 WAR bump to two players, let’s say a 10-WAR player and 5-WAR player, a 0.5 WAR penalty reduces the WAR total by 5% for the 10-WAR player, but 10% for the 5-WAR player. Is that a sensible assumption? Would a percentage decrease penalty be more sensible? I’m really not sure, so interested to hear peoples’ thoughts.
In an analysis like this, it may also be useful to model the probability of some catastrophic injury that sucks away more than 0.5 WAR of value. In normal FA valuation exercises that may not be necessary, but when trying to find the value of the opt-out, the decision to opt-out is significantly impacted by the health of the player.
Really, my two points are saying that the variation in outcomes is fairly wide here and I’m not sure your aging/random bumps exercise properly mimics the true potential set of outcomes that could face Cole. There are different ways to look at this contract. One way is to see it as a 5-year contract with insurance covering 4-years if the optimal outcome does not happen (i.e. he is dominant for the next 5 years). Well, the hindsight value of that insurance would be super valuable if Cole gets significantly hurt. Are you capturing enough of those worst-case scenarios in your aging penalty method? Maybe you are and I simply overlooked it in the methodology, but it would seem like the distribution of potential aging outcomes is more crucial in this sort of analysis than in the normal free agent valuation article where the mean is a sufficient first-moment analysis.
To add on to your point – is this the right model for starting pitchers, who tend to break more than they decline? Maybe a simulation model with a “% chance he breaks each year” is superior.
This is an excellent point. I would need to do a more in-depth look at pitcher breaking and expected recovery from serious injury. Offhand, I’m not tremendously worried that this model captures things wrong, because there are already events like a 2-stdev decline (2.7 WAR counting for the aging penalty) that probably behave a lot like an injury. There’s definitely merit to looking more at starting pitcher aging curves, and that’s a worthy offseason project, just one I haven’t started yet.
As to your first question, about aging happening as a ratio rather than as an absolute, I haven’t found a ton of evidence of it in the aging studies I’ve looked at, but one big problem with that is that looking at the aging of people with really outlandishly high WAR is necessarily a small sample size problem. This would probably fall into the same aging study; but most of the delta method stuff I’ve seen hasn’t really shown a much different effect for stars versus scrubs. I’d be interested to delve more into this as well.
Thanks for the reply. I definitely agree that this is a “small sample” problem as it relates to injuries for outlandishly high WAR players. And it would be interesting to see if, after delving more into aging curves for starting pitchers of different starting ability levels, the assumptions made in the model fit reality.
Definitely interesting stuff though and I like the general approach you took to analyze the question. Simulating a more realistic distribution of performance aging considering injury would be the next step in improving the methodology (that’s if the current aging methodology actually is off, which may not actually be the case). But the general approach makes a lot of sense.
I think that one variable that would be difficult to quantify, but extremely relevant will be the changes forthcoming in the new CBA. It would appear that the Players’ Union is moving towards a more “egalitarian” distribution of the wealth within baseball, both between the players and owners and amongst the players (which has typically been the tenor of labor negotiations in almost all industries.) Thus, one might see a future world where a $36mm annual salary will become even more rare than it appears to be today, with more players (i.e. minor leaguers, <3 years service, 3-6 years service) earning at a higher rate and the "top end" earning at a lower rate and with less frequency. If the curve is severe it could very well make the "opt-out" worth much less and it is difficult to see an outcome where the "opt-out" is worth more than you calcs.