How Much is Edwin Worth?

Mandatory Credit: Nick Turchiaro-USA TODAY Sports ORG XMIT: USATSI-327368 ORIG FILE ID: 20161004_pjc_bt2_113.JPG

Image Via: Nick Turchiaro – USA TODAY; Oct 4, 2016

There are lots of things for Jays fans to worry about this off-season, and Edwin Encarnación is near the top of that list. Here’s a brief look at what Edwin has given the Blue Jays in terms of value during his tenure with the organization, and some estimates of what he might sign for (scroll to last table for contract projections).

Over the last five seasons, Edwin averaged just over 4 wins above replacement according to Fangraphs. Using estimates for the market value of a win in each year, (subtracting the league minimum salary since it is the least a player can receive and is therefore not a relevant cost), I calculated Edwin’s estimated value-added based on what he produced compared to what he was paid. It seems that we have approximately 81 million reasons to thank him.

Season Age fWAR Est. League $/WAR Value ($) Salary ($) League Min ($) Value Added ($)
2010 27 1.7 4,250,000 7,225,000 5,175,000 400,000 2,450,000
2011 28 0.7 4,500,000 3,150,000 2,500,000 414,000 1,064,000
2012 29 4.3 4,750,000 20,425,000 3,500,000 480,000 17,405,000
2013 30 4.0 5,000,000 20,000,000 8,000,000 490,000 12,490,000
2014 31 3.6 5,500,000 19,800,000 9,000,000 500,000 11,300,000
2015 32 4.5 6,250,000 28,125,000 10,000,000 507,500 18,632,500
2016 33 3.9 7,000,000 27,300,000 10,000,000 507,500 17,807,500
  22.7         81,149,000

Although he is currently showing no real signs of slowing, we should expect his production to decline in the coming years because no one can escape age (except maybe David Ortiz).

In order to project Edwin’s future performance, I took a sample of Fangraphs batting WAR leaders between 2011 and 2016, for the age range 30 to 40, so that I could get an idea of how he stacked up against other players of the same age(s). The sample consisted of 175 players, and could be summarized and explained as follows:

Age 30 31 32 33 34 35 36 37 38 39 40 Slope
# Players 173 158 149 121 93 69 45 30 17 10 4  
Mean fWAR 2.8 2.3 2.0 1.6 1.4 1.9 1.4 1.1 0.9 0.7 1.9 -0.143
StDev fWAR 2.0 2.0 1.9 1.9 1.9 2.1 1.9 1.7 1.4 1.7 2.0 -0.028
Max fWAR 8.2 9.6 7.7 6.5 5.8 6.9 7.1 6.1 2.6 2.8 4.4  
  • Two players who were on the WAR leaderboard for their ages 31-35 seasons did not play in the MLB at age 30
  • As age increases, we would naturally expect fewer and fewer players to remain in the league, and though it would be reasonable to assume that only the better players are able to continue to play at an older age, they still appear to create fewer WAR relative to younger players
  • “Mean WAR” represents the average of all players of that age between 2011 and 2016 (for example, between 2011 and 2016, 34 year-olds averaged 1.4 WAR)
  • “StDev WAR” and “Max WAR” represent the standard deviation and the highest value for that age group, respectively
  • “Slope” describes the linear rate of increase/decrease from age 30 to age 40; the negative value for Mean WAR is in line with our expectation of lower production as a player ages
  • Surprisingly, the standard deviation of WAR at all ages is very close to 2, despite fewer players at each increasing age

Using these figures, I put together a very crude estimate of Edwin’s future production as follows:

Age 30 31 32 33 34 35 36 37 38 39 Slope Avg
Z-Score 0.29 0.33 0.70 0.63             0.138 0.49
Proj. Z-Score (s)         0.63 0.74 0.76 0.80 0.87 0.92    
Proj. WAR (s)         2.6 3.4 2.8 2.4 2.1 2.3    
Proj. Z-Score (m)         0.49 0.49 0.49 0.49 0.49 0.49    
Proj. WAR (m)         2.3 2.9 2.3 1.9 1.5 1.5    
  • “Z-Score” calculates how many standard deviations Edwin was above the mean WAR in that age group; note that it seems to be increasing as he ages, which indicates that he produced more than other players his age (or maintained a high level of play while other players got worse)
  • “Slope” describes the rate of increase of Edwin’s Z-Score from age 30 to age 33
  • “Avg” is the mean Z-Score from age 30 to age 33
  • “Proj. Z-Score (s)” is the projected Z-Score based on the previous three seasons (as a moving average), multiplied by the Slope, to represent Edwin’s increasing separation from players of his age group; this method expects Edwin to reach almost one full standard deviation higher than other players at age 39
  • “Proj. Z-Score (m)” is the projected Z-Score using Edwin’s average Z-Score over his age 30 to 33 seasons
  • Together, “Proj. Z-Score (s)” and “Proj. Z-Score (m)” form the upper and lower boundaries for Edwin’s projected WAR
  • Projected WAR for each age is simply calculated as: [mean + (StDev * Z-Score)]

I also made assumptions regarding how much value the league might place on a win over the next six years (Edwin’s age 34 to 39 seasons) in order to factor this into his future value:

Age 34 35 36 37 38 39
Est. League $/WAR 7,750,000 8,500,000 9,500,000 10,500,000 11,500,000 12,500,000
Projected Value (s) 20,219,350 28,976,421 26,907,468 25,235,362 23,873,634 28,601,089
Projected Value (m) 18,156,017 24,474,518 21,969,083 19,678,150 17,796,616 19,092,744
  • By multiplying the estimated league value per win by the projected WAR previously calculated, I came up with a range of annual dollar values consistent with my earlier assumptions
  • The table above shows the annual value in terms of production, and the table below provides a summary by contract length:
  4 Years 5 Years 6 Years
Projected Value ($) – High 101,338,602 125,212,236 153,813,324
Average Annual Value (AAV) ($) – High 25,334,650 25,042,447 25,635,554
Projected Value ($) – Low 84,277,768 102,074,383 121,167,127
Average Annual Value (AAV) ($) – Low 21,069,442 20,414,877 20,194,521

In summary, this is just one way to produce a valuation, and it does not consider dozens of other relevant stats that may be more highly-regarded by the team, let alone intangible factors that may also be valued (not to mention the fact that these projections are heavily dependent upon the league value per win).

Other notes:

  • Because these WAR projections are fairly conservative (in my personal opinion, they seem a bit low, especially for the next 2-3 years), I would expect Edwin to exceed them
  • Edwin may have an advantage over other players of his age in future years if he were to be limited to the DH position; because he wouldn’t produce negative WAR through sub-par fielding, he may see a slower decline in WAR than other players

Adam

Adam likes baseball and uses Instagram mainly for the Joe Biden memes.