What's Edwin Encarnacion worth to the Jays?

With the Blue Jays having signed Kendrys Morales and Steve Pearce after their early four year, $80-million dollar offer to Edwin Encarnacion was rejected, his market is somewhat in disarray after he was seeking up to five years and $25-million per season. But with reports he prefers to return to Toronto, the Blue Jays could conceivably still have or make room for him if his market fell and the price was right. So what is that price?

Fundamentally, player value is tied to forecasted production. Steamer is projecting a further decline in hitting for Encarnacion in 2017, to a 125 wRC+ and 2.3 WAR. With normal aging would imply something like just 6-7 WAR for his next contract. ZiPS on the other hand forecasts a 137 OPS+ in 2017, driving 3.6 WAR which implies 11-13 WAR over the contract. Needless to say, that's a huge difference in value.

Before the season began, I tried to estimate an extension for Edwin based on the career progression of similar players to Encarnacion over his ages 29-32 seasons (2012-15), the years after his breakout. The results were as follows:

A few important takeaways:

1. Production wise, Edwin was actually very close in 2016 to the overall age-33 expectation, with his 134 wRC+ very close to the average of 136 (median 139)
2. He really outperformed in terms of staying on the field. His 702 plate appearances were exceeded by only six of the 50 comparable players in their age-33 seasons. His is positive for the longer term outlook, but only modestly so
3. As discussed earlier this year, there's a skew in terms of the distribution of outcomes over time. The significant minority of players who collapse drag down the average, but those who don't collapse are fairly productive with a tail of very productive players.

With 2016 now in the books, the comparison set can be further refined to reflect Edwin's age 33 season, essentially removing players who didn't decline or those who really broke down. Fangraphs took a shot at performing a similar exercise a few weeks ago, and came up with a comparison set of 14 players and a pretty pessimistic outlook for Encarnacion. Over the next four years, he would only be expected to produce a 115 wRC+, with an average of 500 PA and 1.5 WAR. Not a player to whom you want to commit $20-million a year for four or five years.

However, I have a few problems with the criteria that were used. First and foremost was screening for players with a similar WAR (within 3 WAR). At this point in his career, Encarnacion's value is essentially entirely tied up in his bat. He can play a decent first base and is not a total liability on the basepaths, but his value in these areas is negligible and basically already bottomed out. What we really care about is how his bat can be expected to age, and what makes more sense in projecting value is use that as an input.

Comparable Historical Hitters to EE

My screen for similar hitters to Encarnacion were players since WWII (integrated era) within 10 points of wRC+ over either their age 31-33 seasons (min 1500 PA) or age 29-33 season (2500 PA). In their age-33 seasons, I required a substantially full season (min 450 PA), and eliminated players whose production spiked above their previous trend by more than 10 points of wRC+. Finally, I eliminated a handful of players who were basically broken down (eg, Albert Belle played a full season but never played again due to hip injuries known at the end of that season).

That left a group of 42 players, and below is how they compare to Encarnacion:

Overall, the group matches Encarnacion's track record very well, with very almost identical amounts of playing time over the past three and five years. As a group, they were slightly worse hitters but more valuable by WAR since there's no restriction on defensive value (I'll get to that below). The age-33 comparison is pretty good too: Encarnacion had more PA (702 vs. 625) but very similar production (134 v. 136 wRC+).

Over the next three years (which is what any team signing would mostly be paying for), the average player put up about 525 PA, with a 122 wRC+. Again, because of how the sample was selected we can't really use the WAR numbers, but assuming -15 runs for defence and baserunning, that would work out to a little over 2 WAR/year. Over the last two years, ages 37-38, we can expect about 625 more PA at about 108 wRC+, so for a 1B/DH there's little expected value.

However, the caveat is that again the distribution of value is skewed, with the median above the average. In other words, there's significant chance that Encarnacion will be a total flop (7 of the 42 players didn't make it to 4 WAR, 14 of 42 or one-third were at 110 wRC+ or below for their careers). But if he doesn't flop, he should deliver pretty strong production over the next couple years, and potentially into the fourth and/or fifth year of the deal.

Do sluggers like Edwin age the same?

Above, all players were considered regardless of position. But that includes a number of players who in addition to being excellent hitters, retained the athleticism to have strong defensive and/or baserunning value. Might their batting abilities age better? Of the original 42, 14 were tossed who either played premium positions, or graded well in the outfield corners. That left 28, essentially first basemen or non-premium corner infielders.

Surprisingly, the difference is pretty small. This subset were slightly better hitters from ages 29-33, though slightly less valuable. They were identical in their age-33 season. But what's interesting is that they had more value as hitters as they aged, with about 25 more PA per season, and a couple of extra points of wRC+ for their age 34-36 seasons. We can use the WAR data now, and they average about 2.5 WAR per season, but there's even more skew with a median of 3.0 WAR per year.

If Encarnacion followed the average of this group, his year-by-year projection would be as follows:

This looks pretty reasonable to me, and basically ends up right in between the Steamer and ZiPS projections.

So what's that worth?

With a veteran team that is built to win over the next couple years and coming off back-to-back ALCS appearances, the Blue Jays are positioned to pay a premium for near term wins. Fangraphs assumes a win on the market is worth $8.5-million, increasing by 5% a year thereafter. Interestingly, Mark Shapiro back in 2012 put the value of marginal wins at closer to $9-million for a team around the 89-90 win mark, and that would only have gone up since then.

Let's be pretty aggressive and assume $10-million/win in 2017 and 2018, and then $9-million thereafter. This looks weird, but it's basically the combined effect of assuming about 5% inflation as well as a very high marginal value of wins in 2017, regressing thereafter as the forecast gets hazier.

This would give Encarnacion annual value of about 80-million over four years, or $85-million over five years. That happens to be right in line with what the Jays apparently offered in the quiet period, before they signed Kendrys Morales. However, there is one final piece, which is the value of the draft pick they won't get if they re-sign Edwin compared from another team signing him. That has a value of something like of $5-10 million, so I'd say fair value will max out at $75-million over four years or $80-million over five years.