Some believe in the idea that there are infinite parallel universes out there in the yonder. Carbon copies doing different things, living different lives, in similar worlds. We’re familiar with the concept via 1970’s science-fiction writing, but today I wanted to focus on just two of these universes. In Universe A we have calm, cool, mild-mannered Chris Archer. He is focused, he is unemotional, he carries the swagger of a killbot designed for one purpose, to kill batters without once taking pleasure in his mission.
In Universe B we have wildman Chris Archer. He starts bar fights and gets fired up when the Jets turn the ball over. This Chris Archer is the emotional one that is prone to snap before begging your forgiveness. He’s polite, but that doesn’t stop him from enjoying a cigar after taking your mama out for a spin. This Chris Archer is liable to do anything, as he once sang along, probably, “As long as I got my beretta, I’m down for whateva.”
These Chris Archers will never meet. They will never know each other exists. They will go on to have wildly divergent career paths due to mental maturity, physical luck, and those Gottdang dinosaurs that we thought were extinct, but in one of these universes they are brought back into existence by a totes mean necromancer named Jabari Parker (parallel universes, brah).
Yesterday, I mocked up what some different scenarios would look like for Chris Archer……based on how he performs under his new deal in this very universe that we live in, but it’s very important to emphasize that this isn’t some deal in a vacuum. The options aren’t pay Chris Archer all this guaranteed money or tell him to frig off. The alternative to signing this contract was that Chris would go year to year as a highly likely Super 2 so I wanted to show what that would look like compared to the stuff from yesterday:
Starting with the mediocre path we see that he’s basically a league average pitcher over the next five years before beginning a decline phase in what would be his walk year. In the first scenario where he has signed the deal he would make his $44.5M while providing around 13 WAR or $84M in production value for a Present Value Surplus of around $50.5M. In this scenario the cost of a win is roughly $2.5M, which is incredible, but you have to compare to the alternative universe where he went year-to-year with similar production.
Note that arb figures in 2016 – 19 are based on a shoot from the hip formula of:
Arb 1 = 20% of previous year’s value
Arb 2 = 40% of previous year’s value
Arb 3 = 60% of previous year’s value
Arb 4 = 80% of previous year’s value
So he would make some reasonable figures in arbitration ending up with around $27M before waving good bye, while racking up 11.5 WAR or close to $73M in production value. This leaves a Present Value Surplus of a little over $51M. I will come back to this stuff in a summary format later, but know that it’s really close, though a slight edge to Y2Y from the team’s perspective if he’s averagish. How about if he’s really good, like David Price good:
Price’s first five full seasons were at 1.3, 3.9, 4.3, 4.8, and 4.4 WAR. Archer was worth 1.2 last year and if everything goes right it’s not crazy to see him on this similar path. This is the best-case scenario. Under the deal all options are picked up because he’s crazy good. He makes the full $44.5M accruing 28 WAR and providing $185M in value for a PV Surplus of $152M.
If he goes year-to-year you’re looking at steeply escalating arbitration values, much like we’ve seen with Price, but with a dose of inflation factored in. We would actually pay him more for these six years than the full eight of the contract by almost $10M and we would lose two pretty good seasons off the end leaving the total value at $143M and a surplus of “only” $101M. This is the scenario that you hedge against by locking him up. You save money in the short term, and the long term because he’s just so freaking good and the dollars are puny in comparison. Now let’s take a look at the worst-case scenario. He doesn’t develop showing ineffectiveness and ultimately getting injured never to pitch again (I hate you parallel universe you piece of crap):
You end up buying out the option(s) and paying the guaranteed minimum of $25.5M. He provides 3 WAR as a bad starter/low lev relief arm before he gets kicked in the head by a mule never to pitch again. He provides around 17M in value for a surplus (loss) of $-3M. Meanwhile, if he had gone year-to-year the Rays would have simply cut bait after the fourth year abandoning all hope of him ever panning out. In that scenario they actually make around $14.4M simply because of how valuable those two essentially free years are. So we see a lot of different figures here, it kind of runs the gamut between good and bad, much like you’ll find with our run of the mill infinite parallel universes. Let’s bring it all together to try to glean a little more:
So this gives us some bottom line figures for each scenario. The yellow-highlighted averages are simple, while the blue-highlighted averages shows what this looks like if we try to assign some risk to these things. Let’s say that there’s a 20% chance that he’s really good or really bad and a 60% chance that he’s mediocre. You can adjust these figures however you like, this is simply a hypothetical with no actuarial analysis attempted, but if you could nail down those figures, that’s where the real margins lay.
Right off the bat we know that we’re likely to lay out more money, and nearly $13M more focusing on the Adj. Avg. as I will throughout the rest. In real dollars this works out to something like $9M more guaranteed. This is the team’s risk. We see that he’s likely to put up around two more wins taking the deal, but at a higher price of $2.2M per win while the Y2Y side sees $/WAR at something like $1.8M. For the extra price you are getting a couple more wins, total, which manifests itself in the value at $91M for the deal and roughly $76M for the Y2Y. Taking it to the last step we see that under the deal you’re looking at a greater PV surplus at a skoje over $60M while taking the deal leaves surplus of almost $54M.
So taking all this risk into account and the different performance outcomes we can see that taking the player taking the deal is worth around $6M in the favor of the team. Another measure that says it’s probably not worthwhile is to look at the ROI:
The law of diminishing returns means that more investment is going to come with a price and we see that here as each extra marginal dollar spent becomes slightly less effective. This also shows up in the $/WAR, but I don’t think ROI should be the end all, be all here, because the goal is to amass WAR, responsibly, not become the most efficient $/WAR machine possible. Getting roughly 14 WAR over the next 8ish years at $2.2M per win represents a coup for this team, one that they could not just go out and buy at the store.
Luckily, we do not have to put our 5D glasses on to see multiples of Chris Archer, because we get the one that compiles all the qualities on the scale. We get the stoic young man that can snatch your eyes before you know they’re gone. We get the intelligent philosopher questioning how much does one man really need. We get the prideful lion yelling and gesticulating upon achievement. We get all these things because parallel universes may or may not exist, but the one and only Chris Archer certainly does and Rays fans like myself should be overjoyed that we get to see this young man for the better part of his career.