By Atul Venkatesh '27
Evaluating player performance is one of the most critical concepts in pro football. One method to do so is Approximate Value (AV), where players are given a seasonal score based on accolades and statistics that accumulate throughout their careers. While AV reflects a player's performance historically, it lacks insight into their current worth. To address this issue, I have modified AV to create the Present AV (PAV) statistic, which shows the current value of over 1800 players through the 2022 NFL season. I have also created a draft value chart which gives the expected PAV of every draft pick. With both of these metrics, it is now possible to evaluate past trades, determine the appropriate draft compensation for a player, and use a statistics-based method to determine the most valuable players in the league.
Introduction
Since its inception in 2008, Pro Football Reference’s Approximate Value (AV) has been pivotal in assessing player value on a season-to-season basis [1]. Each offense is given a certain number of points based on the team’s points per drive compared to the league average. These points are then distributed among players at each position. Players can earn these points based on statistics and accolades. AV is calculated based on the team’s playstyle and league averages [2]. For example, if a team were more run-heavy, then the team’s running back would hold more value. PFR also includes the career AV statistic: the total AV a player has accumulated throughout their career. There have been several adaptations of AV and career AV, including average career AV for every draft pick [3], determining positional value [4], and analyzing the draft using an AV per game metric [5].
While AV offers valuable insights, there are limitations. Most notably is assigning positional weight. The metric puts more weight on basic statistics such as tackles, interceptions, and touchdowns, which emphasizes the linebacker and running back position. However, this does not reflect league-wide trends toward nickel/dime defenses and pass-heavy offenses, which diminish the value of the respective positions [5]. Moreover, a reliance on box score statistics undervalues positions such as lockdown cornerbacks whom QBs simply choose not to throw to.
Another shortfall of AV is its neglect of the role of age in determining player value. An older and younger player with the same AV, despite their age difference, would be valued equally. However, the younger player should be more valuable due to their untapped potential. Similarly, career AV favors players with longer careers as they have more chances to accumulate AV. The top 10 active players in career AV came into the league in 2014 or earlier [Figure 1]. AV seems to fall short in determining how valuable a player truly is.
Figure #1: The top ten active players in career AV. These are probably not the ten most valuable players in the NFL.
I have adapted the AV statistic to develop a model consisting of three components. The first component is a player’s Five Year Value Score (FYVS), a weighted sum of the AV accumulated in a player’s last five seasons. The second component is a Draft Value Score (DVS), an adaptation of Jimmy Johnson’s trade value model contextualized to a player’s present value [6]. The third and final component combines the previous two to create the Present Approximate Value (PAV) statistic. The model gives a possible way to measure the current value of all active players before the start of the 2023 season, determine the draft capital necessary to acquire a player, evaluate past trades, and propose trades in the future. This model is exploratory but can still give an idea of where each player is valued. How much draft capital would it take to trade for Patrick Mahomes? Was the Stefon Diggs/Justin Jefferson trade indeed a win-win? Read more to find out.
Data and Model
Five-Year Value Score (FYVS)
The primary step in creating the FYVS is determining the weight of a player's past seasons. Balancing a player’s most recent season while considering past performances is necessary to accurately assess a player’s true worth. My solution was to use R to weigh the AV accumulated in each season as follows: 100% of the player's most recent season (2022) plus 80% of the player's 2021 season plus 60% of the player's 2020 season plus 40% of the player's 2019 season plus 20% of a player's 2018 season. A player’s performance over five years ago shouldn’t affect their current value. A lot happens in five years, after all. I assumed the value of a player’s season diminishes linearly as the season ages. Since I was evaluating a player’s last five seasons, the weight of their performance should decrease by 20% for each year in the past. In addition, I multiplied a player's AV each season by ten to make the numbers more comprehensible.
Here's an example. Patrick Mahomes's AV per season from 2022 to 2018 reads as follows: 19, 18, 17, 17, 22. His FYVS would be (19*10*1) + (18*10*0.8) + (17*10*0.6) + (17*10*0.4) + (22*10*0.2) or 548.
While FYVS can determine a player's productivity, it does not capture a player's actual worth. For instance, individuals with less than five years of experience are more valuable due to their young age. However, they would naturally have a lower FYVS due to playing fewer seasons. Using solely FYVS, a rookie who accumulated 12 AV in their lone season would be less valuable than a 10-year veteran who averaged five AV per season over their last five seasons. As of now, the data contains the FYVS for over 2100 players and displays the year they were drafted. However, this dataset contains retired players and needs to be further refined, as mentioned above.
Draft-Based Value Score (DVS)
My goal for the Draft-based Value Score was to create a model that would show how much each draft pick is worth, contextualized to FYVS. This way, it would be easy to see how many draft picks a player was worth. To do this, I divided the career AV of players in the last 10 NFL drafts (2013-2022) to find each player's average AV per season. Since it is possible for a player drafted later to outperform a player drafted earlier, I decided to rank the players by AV per season in each draft from highest to lowest. The player with the highest AV per season would be the first overall pick. The player with the second highest would be the second overall pick, and so on. This makes logical sense since a team would expect the first overall pick to hold the most value. Even if the player drafted first overall might not end up as the best in the draft class, that draft slot is still valued the highest. This is why it does not make sense to say that a draft slot’s expected value is the average AV per season of the last 10 players selected with that pick. Doing this could lead to a draft slot in a later position holding more value than a draft slot in an earlier position due to a couple of draft steals or draft busts that happened to be picked at that slot. After averaging the players' AV per season for my given sample size, I could see the value of each draft pick from the first overall pick to Mr. Irrelevant. Now that I had the expected AV per season of each draft pick, I needed to convert my chart to FYVS. I assumed that the draft pick would produce their given AV per season for five seasons. In a similar fashion to calculating the FYVS for players, I assigned a weight to each of the five seasons of the player and added up the five seasons. The result was the DVS of every draft pick [Figure 2].
For example, the first overall pick is projected to average 12.87 AV per season. The DVS would be (12.87*10*1) + (12.87*10*0.8) + (12.87*10*0.6) + (12.87*10*0.4) + (12.87*10*0.2), which equals 386.1.
Figure #2: The draft value score of every draft pick. Note: not all draft picks are included, and the picks do not necessarily correspond with the labeled round.
Age-Adjusted Five-Year Value Score
To correct for players with less than five years of NFL experience, I created a Python code to combine FYVS and DVS. My goal was to use DVS to create a five season sample size for every player including those with less than five years of NFL experience.
Take Trevor Lawrence, for example. Lawrence has two full seasons of experience, producing an AV of 7 and 14 in 2020 and 2021, respectively. Based on the current model, he would have an FYVS of 196. However, this is based on a two-season sample size when, in reality, we want a five-season sample size. How would we create a 5 season sample size for a player who has played only two seasons in the league? That’s where DVS comes in. I assumed Trevor Lawrence would accumulate the same amount of AV as the average first-overall pick in the seasons where he wasn’t in the league. As a result, Lawrence’s age-based FYVS would be 196 plus the sum of the projected AV for the previous three years, weighted appropriately. This would be 196 + (12.87*10*0.6) + (12.87*10*0.4) + (12.87*10*0.2). This equals 350.44.
This solution is beneficial because it considers the untapped potential of younger players. Just because a player does not initially accumulate a ton of AV does not mean they should lose all of their value.
Present Approximate Value
The final part of the model is accounting for older players. As a player gets older, their value decreases. A player’s performance begins to regress after their rookie contract and into their second contract. Due to this, I chose their value to decrease after six years in the NFL. This would put them right in the middle of their second contract. While there isn’t any consensus surrounding when a player actually starts to decrease, and it definitely isn’t a one-size-fits-all standard, six years seemed appropriate. Given the dataset, an NFL player with six years of experience would have been drafted in 2017. For all players drafted after the year 2017, I set up an exponential decay function in form 0.9^(2017-x), where x is the player's draft year, and 0.9 is the rate at which a player’s value diminishes. While the actual rate of decay isn’t grounded in any literature, I analyzed recent trades involving older players in the hopes of getting a league-wide consensus. After experimenting with the decay rate, I decided that 0.9 would still preserve a player’s value while favoring younger players, which generally follows what the league thinks. This resulting value is then multiplied by the player’s age-adjusted FYVS, yielding a final value: Present Approximate Value [Figure 3].
Figure #3: The top 100 most valuable players in terms of Present Approximate Value (PAV)
Practical Applications
Evaluating Past Trades
Besides showing a player’s value, this model has several other practical applications. PAV can help evaluate recent trades. The model can compare the value that each team gave up, determining who won and lost the trade. I have evaluated some of the significant blockbuster trades in the past few years. It is worth noting that it is very difficult to determine how to value draft picks for future drafts. If the draft selection is for next year’s draft, I decided that it would hold half the projected value. If the draft selection is for a draft two years in the future, its value would hold even less weight. The players resulting from the draft selection are not considered in these evaluations, although they will be mentioned if someone notable is selected.
Matthew Stafford to the Rams - 2021
Trade details:
Rams receive:
- QB Matthew Stafford
Lions receive:
- QB Jared Goff
- 2021 third-round pick
- 2022 first-round pick
- 2023 first-round pick
For the sake of this simulation, these first-round picks will be evaluated as the same value as the 20th overall pick, weighted by their respective year, as that was where the Rams were projected to draft directly after the Stafford trade.
On the surface, the Lions won the trade. However, this model does not factor in Goff’s contract. Stafford did win a Super Bowl for the Rams and, in his minimal sample size, has brought value to the Rams. His PAV remains the same, which is impressive considering his age. Goff has been a pleasant surprise for the Lions, bringing more value to the team than Stafford himself. While his PAV has stayed roughly the same, this is impressive, considering his age and downward trajectory on the Rams. Although the Lions got much more value, the Rams got that elusive Super Bowl ring. For that reason, I call this trade a win-win.
Stefon Diggs to the Bills - 2020
Trade details:
Bills receive:
- WR Stefon Diggs
- 2020 seventh-round pick
Vikings receive:
- 2020 first-round pick
- 2020 fifth-round pick
- 2020 sixth-round pick
- 2021 fourth-round pick
While this became the famous Stefon Diggs for Justin Jefferson trade, it initially seemed like the Bills got the better end of the deal. Having seen Diggs in Buffalo for three full seasons, I can confidently say this was an excellent trade for the Bills. Stefon Diggs produced more AV/season, and his PAV also increased. As we know, the Vikings got Justin Jefferson in return. He has a PAV of 370, vastly outproducing his DVS. While Justin Jefferson has a greater PAV than Stefon Diggs, this trade goes down as a win/win based on the unlikelihood of hitting such a home run at pick 22. The seventh-round pick the Bills received turned into Dane Jackson, who currently has a PAV of 90. Icing on the cake for the Bills. Bravo Rick Spielman and Brandon Beane.
Odell Beckham Jr. to the Browns - 2019
Trade Details:
Browns Receive:
- WR Odell Beckham Jr
- OLB Oliver Vernon
Giants Receive:
- S Jabrill Peppers
- OG Kevin Zeitler
- 2019 first-round pick
- 2019 third-round pick
This seems like a very clear win for the Giants. Odell and Olivier Vernon only played a couple of years with the Browns, with the former getting released and the latter not re-signing with the team. While Jabrill Peppers and Kevin Zeitler did not record eye-popping AV numbers for the Giants, the first-round pick that the Browns sent allowed the Giants to select Dexter Lawrence. Lawrence is now one of the best defensive tackles in the game and the most valuable player in this trade.
Evaluating Recent Trades
Some trades are too recent to assign a winner to either side. I decided to go through some blockbuster deals over the past two years and analyze the value that each team received.
AJ Brown to the Eagles - 2022
Trade details:
Eagles receive:
- WR AJ Brown
Titans receive:
- 2022 first-round pick
- 2022 third-round pick
This looks like a pretty even trade overall. The Eagles got more value and, as of now, the better end of the stick.
Tyreek Hill to the Dolphins - 2022
Trade details:
Dolphins receive:
- Tyreek Hill
Chiefs receive:
- 2022 first-round pick
- 2022 second-round pick
- 2022 fourth-round pick
- 2023 fourth-round pick
- 2023 sixth-round pick
Another fairly even trade. Tyreek Hill is blossoming in Miami. While it is too early to tell if this is a win-win, the Chiefs did win a Super Bowl without Hill.
Deshaun Watson to the Browns - 2022
Trade details:
Browns receive:
- Deshaun Watson
Texans receive:
- 2022 first-round pick
- 2022 fourth-round pick
- 2023 first-round pick
- 2023 third-round pick
- 2023 fourth-round pick
- 2024 first-round pick
Sure enough, the Texans fleeced the Browns. The Browns might be regretting this one just a little bit.
Limitations
PAV, while valuable in assessing a player's worth, does have its limitations. First, the DVS assumes that the selection will be relatively successful. The 1st overall pick will be the best player in the draft, the 2nd overall pick will be the 2nd best player in the draft, etc. However, this is not how the draft works. While a player could outperform their selection, the player could also bust. That is why trading for players is safer than acquiring draft picks, and teams might need to pay more than the model predicts to acquire a player. Second, this model calculates a player's value solely based on their on-field performance, neglecting financial considerations. This was especially problematic when evaluating the Matthew Stafford trade, as the model overlooked Goff’s expensive contract. The Rams essentially paid the Lions extra draft capital to take on Goff’s contract. Third, the PAV projection is based on the upcoming draft, not future ones. A 2025 first-round pick holds less value than a 2024 first-round pick. The question is, by how much? There is no easy mathematical way to determine this.
With all that in mind, I seek to answer the question that motivated me to create this model in the first place. How much draft capital would it take to trade for Patrick Mahomes? Let's take a look. Mahomes's value is around the draft capital sent for Deshaun Watson, adding on a fourth-round pick from this year's draft. However, I can't simply take the trade package for Deshaun Watson and apply it to Mahomes. Mahomes is in a much better situation than Watson was at the time. He has no legal issues and has played more consistently (he didn't sit out the season before getting traded). It is also worth noting that Patrick Mahomes is under contract till 2031 on a relatively team-friendly deal and is more valuable than Watson ever was. Given Mahomes's situation, it is reasonable to add this year’s #1 overall pick to the trade package.
To summarize, a trade package that takes into account all aspects of Mahomes's value would consist of the 2024 first overall pick, a 2024 mid-first round pick, a 2025 mid-first round pick, a 2026 mid-first round pick, a 2024 third-round pick, a 2024 fourth-round pick, a 2025 third-round pick, and a 2026 fourth-round pick.
This may still be a significant underestimate, as a team that acquired Mahomes would instantly become a Super Bowl contender and have lower-valued draft picks.
Future Research
I would like to create my own AV statistic if given an opportunity. Since AV may not be completely current with positional trends in the NFL, I would like to determine a proper way to assign positional weight and then evaluate players. Secondly, I don’t think my model perfectly accounts for younger players. It seems to punish players drafted in later rounds while inflating the value of players drafted in earlier rounds. I would like to explore ways to assign value to players with less than five years of experience. Lastly, it would be valuable to add a financial aspect to the model. If the team trading the player pays off most of the player’s contract, that player would be more valuable. If a player is going into their contract year, that player is probably less valuable because of their impending free agency. This would enhance the practical application of the model.
Glossary
Approximate Value (AV) - Player value metric developed by Doug Drinen of Pro Football Reference
Five-Year Value Score (FYVS) - Weighted sum of the AV accumulated in a player’s last five seasons
Draft-based Value Score (DVS) - Expected FYVS for every draft pick based on the last ten drafts
Present Approximate Value (PAV) - Metric that gives a player’s current value. Based on FYVS and DVS
References
[1] Sports Reference. Approximate Value. Sports Reference. https://www.sports-reference.com/blog/approximate-value/
[2] Drinen, D. Approximate Value: Methodology. Sports Reference. https://www.sports-reference.com/blog/approximate-value-methodology/
[3] Elsner, B. (2021, April 4). Using Approximate Value To Evaluate First-Round Draft Success. The Thirty Third Team. https://www.the33rdteam.com/using-approximate-value-to-evaluate-first-round-draft-success/
[4] Lopez, M. (2016, May 4). Approximate value and the NFL draft. StatsbyLopez. https://statsbylopez.com/2016/05/04/approximate-value-and-the-nfl-draft/
[5] Hart, G. (2021, March 20). An NFL draft AV data set. Medium. https://greg-hart.medium.com/analyzing-nfl-draft-positions-by-av-663a2633fc04
[6] Drafttek. (2023, November 28). Trade Value Chart - NFL Trade Value Chart - 2024 Version. Drafttek. https://www.drafttek.com/NFL-Trade-Value-Chart.asp