20 January 2016

Taking Another Cut At The Chris Davis Contract

by Jake Brintzenhofe

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.

The Process
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.

The Model
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

Financial Analysis
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 million
He 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.


Anonymous said...

All these analyses look blindly at the cold statistics without taking everything else to account. Suppose Angelos thinks that the $42M in deferred money over 22 years is chump change and has no value whatsoever. I'll bet that's why he structured the contract this way. It is HIS money. Why don't we value the contract in terms of the actual hit the annual payroll takes? Isn't that what really affects what players can be retained each year and which ones can't? That's how we played our roster game in October/November. That would make the contract more in the $119M range which is where all you guys' comfort range is.

Also, I don't see much credit being given for his jump-off year with the O's in 2012 (33HR, 85RBI). I know it's only 1.6 WAR but it sure had everyone excited for the next season it produced. And there is no factor adjustment for the suspension. Davis was starting to have a pretty good Sept/Oct when he got suspended. He has traditionally had good fall production as the weather got cooler. The season might not have looked so bad with a good fall for Davis.

Davis just produced 15.1 WAR over four years. Can we not expect him to produce 15.1 WAR over the next seven if he keeps his head straight, gets his TUE, and stays in shape? There are other similarity comps out there that don't show up because they did not produce AS WELL as Davis up to this point but were better later (see the Baylor example).

Just for reference, the Upton contract dwarfs this one in AAV. And Cespedes seems to be expecting more of the same. Davis was the only one of the three available this cheap.

Jon Shepherd said...

If you want more consideration to more recent performance then you use my comp model.

Also if you go through your query, do you notice how you seem to be try to find every single positive angle? The above methodology does not look for any positive or negative angles. I think by assuming performance with respect to suspensions or TUEs is going off into wish fulfillment bias. Unless we have solid reasons to lean in those areas and make corrections, it is better to have a sober read of it.

Matt's article on Monday discussed payroll issues and how Davis money might only be for him.

Anonymous said...

Cost per win at $7M is low, and using the similarity scores has some merit; but Davis' athleticism makes him unique in some ways. Conservatively, give me the average of his fWAR & rWAR over 2012-2015, and I'll take him sustaining that level for the next 4 years.

I believe he will provide surplus value to this contract rather easily.

Jon Shepherd said...

If you recall our post from yesterday, our 7 MM per win estimate is playing out well for the position player market.

Anonymous said...

I try to find some positive angles because it seems to me statisticians are only looking a negative angles. You can make these statistics come out however you want by choosing different comps, different years, different values to rank similarity. It IS true that Davis was on an upswing when he was suspended and has performed well historically in the fall. Have you seen what happens to ADHD types when they go off their meds? Adderall doesn't help you build muscle (it's not a steroid); it helps you focus your energies on the task at hand. Hitting takes a heckuva lot of concentration. Flinch and you just missed a strike. Plus Adderall is an appetite suppressant. Do we have any idea if Davis was keeping as fit and eating properly during 2014? The TUE is a HUGE factor (note: I resent all the random commentators talking about him like he's just another cheating sonuvabitch which I don't believe he is).

Mike Bonsiero said...

What is the annual rate of inflation for a win on the market, or is there one? Even a modest increase over the 7 years gets him at least to the halfway mark. Which isn't particularly reassuring.

Another thing I think is worth noting is how many of the Davis comps just completely and randomly fell off a cliff, value-wise. A lot of those guys went from 3 or 4 WAR players one year to replacement or below the next, even those whose performance previously had less variability than Davis. That's where the gamble is on Davis: where exactly is his cliff? If it's in the next year or two, this contract is a disaster. If they can get 3 or 4 2015 caliber years out of him, it ends up being worth it (though projecting him to do that well is admittedly wishful thinking rather than analysis)

Anonymous said...

Lemme give you another angle on the money. Consider Davis to be your next house purchase and you have a choice of loans - 30 year fixed or 15 year fixed. I think Angelos chose a 30 year fixed so he could buy more houses now rather than a 15 year fixed to buy fewer houses now and more in the future. At 86, maybe he wants to win before he dies.

Jon Shepherd said...

"I try to find some positive angles because it seems to me statisticians are only looking a negative angles." Think about that statement, Anon. What statistics work literally does is strip away bias as best as it can. Neutral statements and conjecture can look negative if one is being hopeful. For instance, looking at a single month is an optimistic view. Why? Because we have absolutely no indication that single month performances are indicative of overall performance. All it tells us is that he flashed exceptional value, but the sample size simply is not powerful enough. What you are do there is providing a narrative so that the data from that season works with the overall narrative of the two shouldering seasons. I do not think your rationale is strong enough to toss out the majority of the 2014 season as an outlier. To me, it makes more neutral sense to consider the whole package.

Also, as someone with a doctorate in toxicology and having worked with toxicokinetics...yes, I understand the chemicals that are used. I understand what they do to the body.

Bonzi - I generally use a 5% mark. You can argue anything between 3-8%. Obviously, that can make a considerable difference.

Matt Perez said...

"What is the annual rate of inflation for a win on the market, or is there one? Even a modest increase over the 7 years gets him at least to the halfway mark. Which isn't particularly reassuring."

I found a 7% annual increase from 2004-2013.

But this case presumes an equal amount of WAR each year. What are the chances of that happening really? Given the parameters, I expect factors to even out.

Jon Shepherd said...

Matt - I agree. WAR should be divied out by expected year because I think we should be interested on yearly impact of value and cost.

Anonymous said...

Positive or negative, have you adjusted for the time value of money - particularly on the deferred money. $42 million now is obviously worth a lot more than $42 million 22 years from now.

Jon Shepherd said...

Yes, read the column.

Jon Shepherd said...

Oh, I got you. No, it does not appear Jake commented on that. My article from Saturday pegs the value at 138 MM. I have seen ranges of 128 to 146 MM.

Unknown said...

I had heard that we are entering a period of lots of pitchers and fewer hitters, coming up from the minor leagues. Doesn't that make Davis more valuable?

The age of the pitcher and how we got here

Also, when the NL adds the DH at the next CBA, won't that make hitters like Chris even more valuable?

Is there any calculation for scarcity of hitting on the market? I mean, sure, perhaps Chris' ability declines, but if there simply isn't any hitter replacement available on the market, then the O's would have to settle for a lower-quality replacement.

I guess what I'm saying is, perhaps the "Average" in the WAR calculation declines, based on the items I've identified above, in which case Chris' relationship to the average increases and therefore your future WAR predictions are under-estimated.

Matt Perez said...

"I had heard that we are entering a period of lots of pitchers and fewer hitters, coming up from the minor leagues. Doesn't that make Davis more valuable?"

That was the conventional wisdom. It appears to have just been a fluke for a few years.