Fantasy: Making Joseph Hands a Mortal, Part 2
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The reason I went through the exercise of categorizing every player—and did so for each of the prior two seasons, as well—is to simplify the estimated risk of attrition. A star in his prime at any position has the chance to be a star, again, the next season. He also could become a star in decline, a star with reservations, or a below-replacement-level player. I have to include the probability of each situation and the value of that situation in order to calculate an expected value.
In order to find the probability of each change in category, I simply added up all the examples of each transformation and divided by the total number of them. I did that over the last three seasons and across all positions.
| Category | Pot. star | Star in prime | Star in decl. | Star with res. | RORA | P&Q | Non-star | Below repl. | Retired |
| Rookie prospect | 50% | 5% | 0% | 0% | 0% | 5% | 0% | 40% | 0% |
| Potential star | 28% | 24% | 0% | 7% | 0% | 14% | 3% | 24% | 0% |
| Star in prime | 0% | 70% | 12% | 3% | 0% | 0% | 0% | 15% | 0% |
| Star in decline | 0% | 0% | 35% | 0% | 0% | 0% | 0% | 52% | 13% |
| Star with res. | 0% | 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0% |
| RORA | 0% | 20% | 0% | 27% | 0% | 7% | 13% | 33% | 0% |
| P&Q | 0% | 0% | 0% | 0% | 10% | 40% | 0% | 50% | 0% |
| Non-star | 0% | 0% | 0% | 0% | 2% | 1% | 40% | 56% | 0% |
The left column of the table represents the category of a player in year y. The data shows the percentage of players who then became the possible categories in year y + 1. For example, 50% of rookie prospects became potential stars. 5% became stars in prime. 5% became P&Qs. And 40% became below-replacement-level players.
| Pot. star | Star in prime | Star in decl. | Star with res. | RORA | P&Q | Non-star | Below repl. | Retired | |
| QB | $10.23 | $22.03 | $8.74 | $20.60 | $28.61 | $5.01 | $2.06 | $0.00 | $0.00 |
| RB | $12.56 | $30.43 | $8.64 | $11.54 | $29.75 | $9.37 | $5.39 | $0.00 | $0.00 |
| WR | $13.27 | $25.84 | $9.82 | $12.17 | $31.33 | $6.99 | $5.37 | $0.00 | $0.00 |
| TE | $6.99 | $15.89 | $5.43 | $10.34 | $2.83 | $0.00 | $0.00 |
Next, I calculated the average prices of a player in each category at each position. Those averages will not replace the true value estimates of individual players. They will simply help to approximate percent changes from one category to another. Over the three seasons, no tight ends were labeled as stars with reservations or P&Qs, which is why they are blank.
| Category | Pot. star | Star in prime | Star in decl. | Star with res. | RORA | P&Q | Non-star | Below repl. | Retired | |
| QB | Rookie prospect | $5.12 | $1.10 | $0.00 | $0.00 | $0.00 | $0.25 | $0.00 | $0.00 | $0.00 |
| QB | Potential star | $2.82 | $5.32 | $0.00 | $1.42 | $0.00 | $0.69 | $0.07 | $0.00 | $0.00 |
| QB | Star in prime | $0.00 | $15.37 | $1.02 | $0.72 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| QB | Star in decline | $0.00 | $0.00 | $3.04 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| QB | Star with res. | $0.00 | $0.00 | $0.00 | $20.60 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| QB | RORA | $0.00 | $4.41 | $0.00 | $5.49 | $0.00 | $0.33 | $0.28 | $0.00 | $0.00 |
| QB | P&Q | $0.00 | $0.00 | $0.00 | $0.00 | $2.86 | $2.00 | $0.00 | $0.00 | $0.00 |
| QB | Non-star | $0.00 | $0.00 | $0.00 | $0.00 | $0.68 | $0.06 | $0.84 | $0.00 | $0.00 |
| RB | Rookie prospect | $6.28 | $1.52 | $0.00 | $0.00 | $0.00 | $0.47 | $0.00 | $0.00 | $0.00 |
| RB | Potential star | $3.47 | $7.34 | $0.00 | $0.80 | $0.00 | $1.29 | $0.19 | $0.00 | $0.00 |
| RB | Star in prime | $0.00 | $21.23 | $1.00 | $0.40 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| RB | Star in decline | $0.00 | $0.00 | $3.01 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| RB | Star with res. | $0.00 | $0.00 | $0.00 | $11.54 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| RB | RORA | $0.00 | $6.09 | $0.00 | $3.08 | $0.00 | $0.62 | $0.72 | $0.00 | $0.00 |
| RB | P&Q | $0.00 | $0.00 | $0.00 | $0.00 | $2.98 | $3.75 | $0.00 | $0.00 | $0.00 |
| RB | Non-star | $0.00 | $0.00 | $0.00 | $0.00 | $0.71 | $0.11 | $2.18 | $0.00 | $0.00 |
| WR | Rookie prospect | $6.63 | $1.29 | $0.00 | $0.00 | $0.00 | $0.35 | $0.00 | $0.00 | $0.00 |
| WR | Potential star | $3.66 | $6.24 | $0.00 | $0.84 | $0.00 | $0.96 | $0.19 | $0.00 | $0.00 |
| WR | Star in prime | $0.00 | $18.03 | $1.14 | $0.42 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| WR | Star in decline | $0.00 | $0.00 | $3.41 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| WR | Star with res. | $0.00 | $0.00 | $0.00 | $12.17 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| WR | RORA | $0.00 | $5.17 | $0.00 | $3.24 | $0.00 | $0.47 | $0.72 | $0.00 | $0.00 |
| WR | P&Q | $0.00 | $0.00 | $0.00 | $0.00 | $3.13 | $2.80 | $0.00 | $0.00 | $0.00 |
| WR | Non-star | $0.00 | $0.00 | $0.00 | $0.00 | $0.75 | $0.08 | $2.17 | $0.00 | $0.00 |
| TE | Rookie prospect | $3.50 | $0.79 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| TE | Potential star | $1.93 | $3.84 | $0.00 | $0.00 | $0.00 | $0.00 | $0.10 | $0.00 | $0.00 |
| TE | Star in prime | $0.00 | $11.08 | $0.63 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| TE | Star in decline | $0.00 | $0.00 | $1.89 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| TE | Star with res. | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| TE | RORA | $0.00 | $3.18 | $0.00 | $0.00 | $0.00 | $0.00 | $0.38 | $0.00 | $0.00 |
| TE | P&Q | $0.00 | $0.00 | $0.00 | $0.00 | $1.03 | $0.00 | $0.00 | $0.00 | $0.00 |
| TE | Non-star | $0.00 | $0.00 | $0.00 | $0.00 | $0.25 | $0.00 | $1.14 | $0.00 | $0.00 |
Finally, I combined the two to create expected values by category. I will return to the rookie prospect example to explain. A QB that is a potential star is worth, on average, $10.23. A rookie prospect has a 50% chance of becoming a potential star that next season, so the expected value from the potential star category is:
EVQB-potential star = .5 * $10.23 = $5.12
The total expected value is simply the sum of all the expected values by category. In the case of QB rookie prospects, that is the $5.12 from potential star, $1.10 from star in prime, and $0.25 from P&Q, which rounds to $6. Since below-replacement-level players are worth $0, the probability of that category is irrelevant to the calculation.
| Category | BeforeEV | AfterEV | %Change | |
| QB | Rookie prospect | $0 | $6 | |
| QB | Potential star | $10 | $10 | 0.01 |
| QB | Star in prime | $22 | $17 | -0.22 |
| QB | Star in decline | $9 | $3 | -0.65 |
| QB | Star with res. | $21 | $21 | 0.00 |
| QB | RORA | $29 | $11 | -0.63 |
| QB | P&Q | $5 | $5 | -0.03 |
| QB | Non-star | $2 | $2 | -0.24 |
| RB | Rookie prospect | $0 | $8 | |
| RB | Potential star | $13 | $13 | 0.04 |
| RB | Star in prime | $30 | $23 | -0.26 |
| RB | Star in decline | $9 | $3 | -0.65 |
| RB | Star with res. | $12 | $12 | 0.00 |
| RB | RORA | $30 | $11 | -0.65 |
| RB | P&Q | $9 | $7 | -0.28 |
| RB | Non-star | $5 | $3 | -0.44 |
| WR | Rookie prospect | $0 | $8 | |
| WR | Potential star | $13 | $12 | -0.10 |
| WR | Star in prime | $26 | $20 | -0.24 |
| WR | Star in decline | $10 | $3 | -0.65 |
| WR | Star with res. | $12 | $12 | 0.00 |
| WR | RORA | $31 | $10 | -0.69 |
| WR | P&Q | $7 | $6 | -0.15 |
| WR | Non-star | $5 | $3 | -0.44 |
| TE | Rookie prospect | $0 | $4 | |
| TE | Potential star | $7 | $6 | -0.16 |
| TE | Star in prime | $16 | $12 | -0.26 |
| TE | Star in decline | $5 | $2 | -0.65 |
| TE | Star with res. | $0 | $0 | |
| TE | RORA | $10 | $4 | -0.66 |
| TE | P&Q | $0 | $1 | |
| TE | Non-star | $3 | $1 | -0.51 |
All of that work provides the foundation for this final table, which shows the year y and year y + 1 expected values. The percent change column shows the rate of attrition for every position and category. For example, the average QB star in his prime is worth $22. I calculated that I should expect him to be worth $17 next season. That -0.22 percent change is the manifestation of the probability that the star player will no longer be a star because of injury or decline. Rookie prospects are listed without percent changes because they have no history of value.
Continued in Part 3.
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Questions and comments are always welcome via Twitter – @PFF_ScottSpratt
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