Over the past several weeks, the writers at Camden Depot have taken multiple looks at Chris Davis and his contract. During this process, we became aware of Jake Brintzenhofe taking on the same question, but from a slightly different perspective. He currently is part of the expanded roster (feel free to email us with a sample article if you are interested in being a part of that) and may be joining the stables. Click here for the Chris Davis archives.
For two out of the last three years, Chris Davis played outstanding baseball. Per Baseball Reference, Davis tallied WARs of 6.5, 1.8, and 5.2 WAR in this three-year period – two all-star caliber seasons and one borderline everyday player caliber season. This winter, Davis hit the free agent market with the expectation of cashing in long term on those two years of success. This post examines what a team could reasonably expect to get out of Davis over the next seven years and what that means regarding the seven-year, $161 million contract that the Orioles gave him.
It is within the realm of possibility that Chris Davis could produce a simply Bondsian late career stretch where he harnesses power and plate discipline to become a dangerous hitter through his 30s. It is also within the realm of possibility for him to do what most players do and decline rather rapidly beginning in his early 30s. To determine where Davis's future lies, we have a process.
The approach is a comparison model based on the performance of similar players in the past in their age 30-36 seasons. Baseball Reference’s similarity score feature lists the 10 most similar players in baseball history through their age 29 seasons – a similar, but ultimately different method than what Jon Shepherd used. Using those similar players, we’ll calculate their total WAR over their age 30-36 season, attach a linear weight to it based on the degree of similarity to Davis, and calculate our projection from there.
Weights were calculated by dividing each individual similarity score by the average similarity score of the group and then dividing that number by 10 – the number of players we’re comparing to Davis. Dividing by 10 makes it so that when we add up our equation, we get our total projection with each player contributing a little more or a little less than 10% to the total. For example, Richie Sexson’s weight was his 944 similarity score over the 924.6 average and then we divided that number by 10. We then multiplied that number by Sexson’s age 30-36 total WAR.
The top 10 most similar players to Chris Davis through their age 29 seasons were, in order: Richie Sexson, Cecil Fielder, Mark McGwire, Glenn Davis, Lee May, Dave Kingman, Tino Martinez, Tony Clark, Nick Swisher, and Willie Stargell. This motley mix of steroid era mashers, overweight first basemen, journeymen, and borderline Hall of Famers feels about right for Davis’s career arc to me. He has had two seasons at the plate that jump directly off the page in the midst of an otherwise forgettable career characterized by strikeouts, forgettable defense, and splashes of raw power.
Let’s get to the math.
Based on the similarity score weighting detailed above, we get the following equation:
Projected WAR = .1020982(SexsonWAR)+.1016656(FielderWAR)+.1011248(McGwireWAR)+.1006922(DavisWAR)+.1000433(MayWAR)+.0992862(KingmanWAR)+.0989617(MartinezWAR)+.0989617(ClarkWAR)+.0986372(SwisherWAR)+.0985291(StargellWAR)Subbing in each player’s WAR from his age 30-36 seasons we get our calculation of Projected WAR = 10.618
On the open market each WAR that a player accrues is worth $7 million. That leaves us with the quick little calculation below:
10.618 Projected WAR * $7 million per win = $74.326 millionHe almost got halfway to $161 million in projected value. Almost. What this calculation says is that our projection puts Davis as being worth $74.326 million in baseball productivity over the next seven years of his career.
A reasonable point to raise would be that this calculation doesn’t examine the revenue aspect of the game – that’s completely true; it doesn’t. To mend this, I ran a quick regression of team wins on revenue while correcting for year and got the following output. Team wins were taken from 2001-2014 from eight teams to match with available revenue data.
If you’re not familiar with regression output, this chart says two main things that we really need to look at. First, for every additional win a team accrues, it can expect $2.75 million in additional revenue when holding the year constant. Second, this calculation is statistically significant at the 95% level. This means that we’re almost completely sure the additional revenue per win is between $1.74 million and $3.77 million and that our best estimate is $2.75 million.
Adding in our new revenue data and extrapolating a bit onto the next seven years, we get that Davis will be worth an additional $29.2 million.
$2.75 million per win*10.618 Projected WAR = $29.2 million in expected revenue
Adding the $29.2 million to the $74.326 million in market value, we get that Davis is projected to be worth a total of $103.526 million over the next seven years.
We’re not quite done though. Because the Orioles will not be paying him upfront, but instead on a year-by-year basis, we need to do a present value calculation on his value that way. The idea is that paying someone $10 million today looks a lot different than paying them $10 million in 1916 or in 2116. To do this, we’ll assume an annual inflation rate of 3% - the long-term historical average. The calculation will break down Davis’s expected annual value and modify it with the expected inflation.
7 year value=14.79+1.03(14.79)+〖1.03〗^2 (14.79)+〖1.03〗^3 (14.79)+〖1.03〗^4 (14.79)+〖1.03〗^5 (14.79)+〖1.03〗^6 (14.79)
Seven-year value = $113.328 million
The reason for the additional size of the exponent in each term is that inflation happens every year. Next year will inflate 3% over this year and the following year will inflate 3% over next year – we need to assess this every year.
So our conclusion is that in baseball performance and revenue dollars added, we can project Chris Davis to be worth $113.328 million over the next seven years.
10.618 wins over seven years does not measure up to the contract. Even with increased revenue from the wins, the Orioles could perhaps find those 10 wins in a cheaper way with a few smaller contracts on a roster that still has a couple gaping holes.
If I were a GM, I would have stayed far away from Davis. You could probably have talked me into a somewhat inflated contract of seven years for about $120 million where we gamble with the idea that maybe those two great years are the real Chris Davis going forward. I could live with throwing away several million dollars in expected value in that bet with the hopes of hitting it big.
That said, seven years for $161 million is asking the GM to gamble $50 million of his owner’s money on the possibility that an old and slow first baseman will somehow manage a few more years of peak performance and then age gracefully. This is pretty much like a kid blowing $200 of his parents’ money at a carnival and coming away with a slew of teddy bears that they could have snagged at the local Wal-Mart for $100.
The Orioles gave Davis a huge deal and that was always the likeliest outcome. Robinson Cano got paid, Prince Fielder got paid, Anaheim will be direct depositing checks into Albert Pujols’s account for the next five years – these things happen. If you’re an Orioles fan, just hope that the real Davis is the power hitting monster that we’ve gotten to watch for two years and that Orioles fans aren’t explaining the importance of frugality to their kids with this contract as an example in three years.