As we head into the Winter Meetings and the hotter portion of the “Hot Stove Season,” we will surely be asked to evaluate trades. How does one compare two sides of real or prospective deals to each other?
In one popular method of making that comparison, baseball analysts reduce the value of a baseball player’s on-field contributions to a single number (Wins Above Replacement, or WAR), establish how much one WAR is worth in dollars, then compare that to how much a player is owed over the life of his contract. The result of this reduction is commonly called “Surplus Value.”
Surplus Value has been around for a very long time. Much of the ideas were pioneered by Vincent Gennaro in his book, Diamond Dollars. I was introduced to it in 2009 by Sky Kalkman’s Trade Value Calculator. Over time, many other analysts have refined the idea, and I don’t know that I can hope to give them all credit.
For your use during the season, here’s an update on the calculator, in Google Doc form.
Make a copy for yourself. If you want it in Excel, from inside the Google Doc click “File,” then “Download as,” and choose to download it as an excel file. The great thing about this is that if you don’t like my numbers, you can change them!
Explanation of Columns
This column is self explanatory. A good source for data is Cot’s Baseball Contracts, now hosted by Baseball Prospectus. Enter this data yourself.
Salary (in present value)
This column is based on the idea that a dollar now is worth more than a dollar later. Generally in economics this is driven by inflation and by the possibility of investing. In baseball, it means that the scary big number at the end of an escalating multi-year baseball contract isn’t going to be quite as scary when you get there as it sounds right now.
I’ve assumed a discount rate of 6% per year. You can change that in the worksheet by changing the value of the “Discount on future $” field located below the main worksheet.
Enter this data yourself.
One commonly used method of doing this is to use a projection (I like the combined Steamer and ZiPS projections on FanGraphs) for the upcoming year, and then to lower it by a half WAR for every year after that to account for aging and the risk of injury. There is lots of research on aging curves out there, though, so if you want something more precise or less conservative, feel free to experiment.
Projected WAR (in present value)
Much like the discounted future value of money, this column accounts for the fact that a win now is worth more than a win later. There are lots of reasons to think this way, and some of them, evident in Gennaro’s research, have to do with how wins now can help organizations gain fans (which lead to more sales, more money, higher payroll, and an easier time winning later). Some of them have to do with increased uncertainty the farther out you project, and the hidden cost of that uncertainty (it’s negative, not neutral).
I’m discounting future WAR at a steeper rate than I am future money, and here’s an admission—while I can justify it to myself well enough, I’m not totally sure why. Back in 2015, I did a bunch of these calculations at the trade deadline, and at that time I used different rates. Former me was a better, more in-practice baseball analyst than current me, and I’m guessing he had a good reason!
You can debate this choice if you’d like, and I’m interested in what you’ll say. For your own use, if you don’t like the rate, change it (by changing the “Discount on future WAR” value located below the main worksheet).
Salaries go up. When I first started looking at this, teams paid around $5 million for every win above replacement. Now, in 2018, it will probably be around $11 million.
I really liked Matt Swartz’s writing on the topic during his FanGraphs residency, which stated that baseball salaries have gone up slightly faster than Nominal GDP. I took the 6% number used in the spreadsheet from his work.
Surplus and Discounted Surplus
These final columns are your answers.
The first column, called “Surplus,” is based off of actual salary and WAR projection numbers, applying no discounts for future value. It does include the projected growth of baseball salaries.
The second one, “Discounted Surplus,” incorporates those discounts on future value in an attempt to give a more realistic picture of backloaded contracts.
Generally, I would use “Discounted Surplus” if I’m looking for a single number, but as long as you understand what you’re doing and are doing it intentionally, I don’t think you’re wrong to use either one.
- Use this tool to your heart’s content. Surplus value calculations aren’t magic. Any baseball fan can do them.
- Give credit. Not to me, if you use this tool, but to the folks who did the research. I think that means Gennaro and Swartz (and the creators of ZiPS and Steamer, based on the numbers I’m using), but I’m very sorry if I’ve left someone out. If you also talk about prospect values, credit goes to Victor Wang, and the many people who have updated his research (like these fine folks at The Point of Pittsburgh).
- Do not let the precision of the calculation fool you into thinking it’s more accurate than it is. Projections are a best guess.
- Enjoy, and once more, if you don’t like my numbers or assumptions, change them.