I think I’ve read this whole thread and have yet to see someone layout anything like how economic net present value is calculated in discussing how to evaluate different contracts under conditions of risk.
We should bring back The Sandbox just so we have a forum to move this thread into.
You're absolutely right, and this is the first thing (as a community) that we should have done. Below is a back of the envelope NPV analysis of the contract. Numbers below reflect millions not thousands.
For starters, I'm assuming that the market price is $10/WAR, mostly because I don't have the time to estimate
the approximate change from 2017. I suspect the market contracted this offseason, so I expect the FA to be around 10 anyways. However, given that the FA next year contains some high-value players, it is possible that the FA market may be closer to $11/WAR.
Second, for the purpose of this evaluation, I'm
using "Depth charts" from fangraphs to assume an optimistic projection of 3.4 fWAR and "steamer" for a pessimistic projection of 2.4 WAR. Yeah, yeah fWAR sucks, but its one of the few ways to do an analysis while making few assumptions about the context of the team. This selection has the advantage of an adjusted number, but is limited in its ability to evaluate defense and the context of whether we even need defense from JDM. In other words, the red sox likely price the components that drive fWAR very differently than this analysis does; however, this analysis will likely underrate JDM's contributions because it weighs defense more than the red sox likely do. On the other hand, I'm not a prophet, and using WAR benefits from the fact that I'm not assuming anything about what happens to the outfield over the next 5 years.
Third, I'm assuming growth charts from
this recent analysis of aging curves on wOBA, which suggests that JDM will lose approximately 3 points of wOBA/year over the next 5 years. As above, JDM is not being counted on for defense, and will likely play a majority of his games at the DH position. Therefore, his WAR fluctuation will be driven by his offense. Since his value is tied to the bat, wOBA decline will give a good estimation as to the decline in WAR. As an aside, I have an interesting approach for characterizing heterogeneity in player trajectories and development, if anyone's interested; I just don't have the time to prepare MLB data to test it on. I'll be honest, this is the weakest part of the analysis below. I'd be happy to revisit it when I have any time.
To summarize, I am assuming that JDM will produce 3.4 or 2.4 WAR in 2018, on a wOBA of 384 or 377 in 145 or 128 games. These WAR will be worth $10/WAR per season; though one might want to adjust to 11 in 2020. With a three point drop per year, you're looking at a slow decline in WAR. A change in 46 wOBA points from 2016 to 2017 was worth about 15 batting runs to JDM -- so you're looking at a loss of about 1 run a year (or 0.1 WAR per year). To be fair, I'll assume a tradiional 0.5 WAR drop per year as well, though I think that's pessimistic for DH's (hitter declines tend to be much slower) and JDM in particular (who has improved over the last 4 years, which is the opposite of the
expected trend). As a result, below are the expectations for the positive (not net) value JDM will produce under these differing assumptions:
2018: 34/34/24/24
2019: 33/29/23/19
2020: 32/24/22/14
2021: 31/19/21/9
2022: 30/14/20/4
TOTAL: 160/120/110/70
Based on these assumptions, JDM should produce somewhere between 70 and 160 million dollars over the course of this contract. Now, we can assume the cost and see what the expected net value will be for each year. The cost per year is as follows: 25/25/20/20/20. I'll tackle the player options after:
2018: 9/9/-1/-1
2019: 8/4/-2/-4
2020: 12/4/2/-6
2021: 11/-1/1/-11
2022: 10/-6/0/-16
Already we can see something interesting. My quick and dirty DH aging analysis suggests that JDM may never produce negative value throughout the contract, regardless of whether the initial projection is optimistic or pessimistic. In fact, the sum value of the third approach equals the salary projected from his contract. In three of the four projections, the last three years of the contract have little negative value (-3 million), even in the most pessimistic projection, the cost is minimal (-33 million -- which is tiny compared to cherington's many expensive mistakes).
Now the net present value is usually the sum of the cumulative net value derived from the analysis. In other words, we just sum the net value over the years. However, we must also keep in mind the possibility that net value depends on whether the player chooses to remain with the team. Naturally, the player's projections will also differ at those points, since we will have more information as to how the player will perform in 2020+. To keep things simple, I'll point out the project sums for three timepoints, the total (NPV), the total after year 2 (NPV-2), and the total after year 3 (NPV-3), which are three of the most possible outcomes from this contract.
NPV: 50/10/0/-40
NPV-3: 29/17/-1/-11
NPV-2: 17/13/-3/-5
I hope the analysis shows how a simple set of assumptions can produce a wide range of valuations. One can always adjust the starting numbers or aging curves to estimate value differently. Other limitations to this analysis abound. I haven't taken into account factors that could affect future projects (such as any injury risk to JDM), I haven't utilized projections specific to the DH spot (which may age differently than non-DH), nor for players similar to JDM, since he surged offensively in his later years. I'm not sure how these options are valued from the player perspective. We can see that the Martinez went from 7/200 to 5/110 with the two opt-outs, suggesting that the opt-outs are worth no more than 90 million in net value to the player. Finally, I did these calculations in my head, so there could easily be a stupid mistake somewhere.
Out of the 12 possibilities (3 contract outcomes by 4 projections), 6 provide positive value while 5 provide negative value. Of the five that provide negative value, only two have a negative value over 10 million. On the other hand, all 6 of the positive value projections are worth over 10 million. I think this is what Average Reds meant by structuring the contract to mitigate risk. Even if one of the negative outcomes occurs, the cost of the negative outcome is likely to be mitigated.