*NSFL Season 20 Approximate Value

[iStegosauruz]

[div align=\\\"center\\\"]Tl;dr - I calculated the Approximate Value for each player and looked at how that compared to TPE and Contracts. There are headings for each part that you might be interested in and the graphs and pictures are pretty obvious. If you're looking for something specific - value of a position group, value of a player, etc - it shouldn't be hard to find.[/div]

[div align=\\\"center\\\"]Introduction [/div]

Football is a hard game to apply traditional advanced metrics that determine individual player value to. The most popular and well-known value metric in sports is arguably “Wins Above Replacement (WAR).” WAR is a sabermetric that dates back to Bill James’ postulation of a method that would determine a baseball player’s value as it relates to a variety of actions in the game including batting, baserunning, fielding, and pitching.

This same value structure is hard to apply to football, however, because football often lacks the same individual aspects that baseball does that can be distilled down into variable. The closest metric football has is the “Approximate Value (AV)” calculation created by former Pro Football Reference founder that “is an attempt to put a single number on the seasonal value of a player at any position.”

[div align=\\\"center\\\"]Offensive Line Overview
[/div]
AV starts by formulating the idea that if football is based around cohesive units working together than there should be a calculation for the effectiveness and value that unit has in comparison to the rest of the league. That metric is dubbed “team_offense_points.” Each team starts with a base of 100 points that is then adjusted based off of their respective performance when compared to the rest of the league.

[div align=\\\"center\\\"]team_offense_points = 100 * (team offensive points per drive) / (league average offensive points per drive) [/div]

To calculate the offensive points per drive for each team you break down the amount of points each team scored with their offense that year and compare it to the amount of drives each team had.

[div align=\\\"center\\\"]offensive points per drive = (7*(rushTD + passTD) +3FG) / (rushTD + passTD + turnovers + punts + FGA)
[/div]

Of note - the fumbles given up metric in the NSFL database for stats isn't completely accurate to the number of times each player fumbled so I manually counted those and used that number as the figure for fumbles which is included in the turnovers metric.

With those overarching numbers in mind the team_offense_points are broken down into team_points chunks for respective position groups. There is a complex breakdown of how the proportions are allocated that I’ll link to at the end of this, however it breaks down to offensive lineman being valued with approximately 45.5% of the team_offense_points based off of historical averages.

Thus to determine the team_points_for_o_line:

[div align=\\\"center\\\"]team_points_for_o_line = 5/11 * team_offense_points[/div]

The points allocated to the offensive line are broken down further into individual points for offensive lineman based primarily off how many games they played, started, and any recognition they may have garnered throughout the season.

[div align=\\\"center\\\"]individual_points = [(games played) + 5*(games started)*(pos_multiplier)] * (all_pro_multiplier)[/div]

The position multiplier (pos_multiplier) serves to put more values on tackles because of their contribution to stopping edge rushers. They receive a 1.2 multiplier. Centers and guards are held constant with a multiplier of 1.0, while fullbacks are given a 0.3 multiplier and tight ends are given a 0.2 multiplier.

The all_pro_multiplier serves to put value on the individual recognition each lineman earned throughout the year. A multiplier of 1.9 is awarded for first-team all-pro, 1.6 for second-team all-pro, and 1.3 for a pro bowler who was not selected to an all-pro team.

With these numbers in mind an individual offensive lineman’s approximate value is determined by:

[div align=\\\"center\\\"]approx_value = (individual_points) / (sum of individual_points for all players on team) * (team_points_for_o_line)
[/div]
[div align=\\\"center\\\"]Skill Positions Overview [/div]

Skill players are broken down using a similar set of formulas. They draw their respective points from the portion of team_offense_points that was not allocated to the offensive line:

[div align=\\\"center\\\"]team_points_for_skill_positions = team_offense_points – team_points_for_o_line[/div]

That is further split into chunks for rushers, receivers, and passers. Rushers are weighted with the aver rushing yards to total yards ratio of all NFL teams from 1970 to present which was 37%. Historically that has broken down to an average team allocating 22% of its skill position points to rushers.

[div align=\\\"center\\\"]team_points_for_rushers = team_points_for_skill_positions * (.22) * [(team_rush_yards / team_total_yards) / .37][/div]

Using the points allocated to rushers, the approximate value of a rusher is determined by:

[div align=\\\"center\\\"]approx_value = [(rushing yards) / (team rushing yards)] * team_points_for_rushers[/div]

Rushers are also given a bonus based off their yards per carry. If their average was better than the league average yards per carry:

[div align=\\\"center\\\"]Bonus= .75 * [(yards per rush) – (league yards per rush)][/div]

If their average was worse than league average:

[div align=\\\"center\\\"]Penalty = 2 * [(yards per rush) – (league yards per rush)][/div]

Passers break down similarly. There is some advanced reasoning behind the calculation but they are allocated 26% of the points for skill positions that were not awarded to rushers:

[div align=\\\"center\\\"]team_points_for_passers = (team_points_for_skill_positions – team_points_for_rushers) * .26[/div]

The other 74% is allocated to receivers:

[div align=\\\"center\\\"]team_points_for_receivers = (team_points_for_skill_positions – team_points_for_rushers) * .74[/div]

Approximate value for the respective groups is determined in a similar manner to that of rushers. Receivers break down with a ratio of their receiving yards to the team’s receiving yards:

[div align=\\\"center\\\"]approx_value = (receiving yards) / (team receiving yards) * team_points_for_receivers[/div]

Quarterbacks break down with a ratio of their passing yards to a team’s passing yards.

[div align=\\\"center\\\"]approx_value = (passing yards) / (team passing yards) * team_points_for_passers[/div]

Quarterbacks are also given a bonus based off their adjusted yards per attempt when compared to the league average adjusted yards per attempt. Adjusted yards per attempt:

[div align=\\\"center\\\"]AY/A = (pass yards + 20*(passTD) – 45*(interceptions))/(passing attempts)[/div]

Quarterbacks are then given a bonus if their average was higher:

[div align=\\\"center\\\"]Bonus = .5 * [(adjusted yards per attempt) – (league average adjusted yards per attempt)][/div]

Or a penalty if their average was lower:

[div align=\\\"center\\\"]Penalty = 2 * [(adjusted yards per attempt) – (league average adjusted yards per attempt)][/div]

[div align=\\\"center\\\"]NSFL Offense Line Approximate Value[/div]

Offensive line approximate value is hard to calculate for the NSFL. Recall that offensive lineman are given a bonus based off their individual accomplishments. In Season 20, however, the NSFL did not award any all-pro or pro-bowl honors to offensive lineman, meaning that their approximate value is often determined by how many games they each played, how many games they each started, and how many people their teams had factoring in to the pool. The more players in the pool, the higher the amount that is available to be split amongst players.

I also made the judgment call in calculations to give FBs, TEs, and RBs who had blocking stats all the multiplier of 0.3 instead of giving some 0.2 as the formula dictates because I figured they were all serving in a similar function in simulation.

The top 10 offensive lineman – with ties included, which expanded the list to 12 – are:

[div align=\\\"center\\\"][/div]

[div align=\\\"center\\\"]NSFL Rushers Approximate Value [/div]

Rushers were a lot more interesting because each had individual stats – rushing yards – that factor into an approximate value calculation for them. When sorting by only value added on the ground, two of the top ten most valuable rushers in the league last year were quarterbacks.

[div align=\\\"center\\\"][/div]

When limiting it to only running backs:

[div align=\\\"center\\\"][/div]

There were several running backs who also had substantial shares of their value gained throughout the air. The top 10 running backs when factoring in their share of the receiving yards:

[div align=\\\"center\\\"][/div]

[div align=\\\"center\\\"]NSFL Receivers Approximate Value[/div]

Receivers were similar to wide receivers in that it was fairly simple to curate a list of the top values at the position.

[div align=\\\"center\\\"][/div]

[div align=\\\"center\\\"]NSFL Quarterbacks Approximate Value
[/div]
Quarterbacks are split into two camps. There are some who made their value through the air and some who made their value on the ground. When ranked by value with only passing included the top 10 was:

[div align=\\\"center\\\"][/div]

When factoring in rushing the top 10 changed drastically:

[div align=\\\"center\\\"][/div]

[div align=\\\"center\\\"]NSFL Skill Positions Approximate Value[/div]

The top 25 NSFL skill positions players during season 20, ranked by approximate value:

[div align=\\\"center\\\"][/div]



[div align=\\\"center\\\"]But then…[/div]

Calculating approximate value for players was interesting but I was curious about the practical application of the values. How much did it matter towards wins that Orange County had the single most valuable individual player? How much were they paying him to produce that value in comparison to the value produced by other players? I expanded my calculations to include the amount of TPE a player had and their contract values and then looked at how those added variables impacted their perceived values.

Of note – I did not compile contract data or TPE totals for Season 20. All figures are based off Season 21 and what was in the database as of Monday, March 9, 2020. This will result in some margin of error for these calculations, but it should not be a substantial difference. I also had to cut any players from the sample who I couldn't get TPE or Contract data for. So anyone who is still currently a free agent or who retired is not included in this sample. I still have AV calculations for them, however, which are in the google spreedsheet linked at the end.

[div align=\\\"center\\\"]Quarterbacks [/div]

The first thing I was interested in understanding was the base level numbers for how much TPE a player had per AV unit they produced and how much they were paid for each unit of TPE and AV.

[div align=\\\"center\\\"][/div]

Then I graphed the ratio of wins to AV produced:

[div align=\\\"center\\\"][/div]

What this shows is that there is a not a linear relationship between the AV a player produces and the amount of wins a team gets. There is a strong clumping around 15 AV for the playoff teams, leading to the postulation that if a team gets approximately 15 AV from their quarterback they have a strong chance of winning 7 games and making the playoffs.

I also looked at how much the amount of TPE a quarterback has impacts the wins they produced:

[div align=\\\"center\\\"][/div]

There is less of a strong correlation there. I then looked at the amount of TPE a quarterback has compared to the AV they produced. If more TPE correlates to more AV than there would be a way to mathematically approximate how much TPE a quarterback needed on average to produce the 15 AV and a playoff spot.

[div align=\\\"center\\\"][/div]

What this shows is a slight linear correlation between the amount of TPE a player has and the amount of AV they produce for a team. I don’t think the correlation is strong enough to approximate how much TPE an ideal playoff quarterback has, however. Nor do I think there is enough data to try to calculate that yet.

With all of that in mind I looked at how much a team would have to pay their quarterback with 15 AV.

[div align=\\\"center\\\"][/div]

The sweet spot in value for a quarterback looks to be about $4,000,000. A team can get more AV from a quarterback for more money, however that doesn’t appear necessary to make the playoffs, albeit based on a small sample size.

[div align=\\\"center\\\"]Running Backs[/div]

[div align=\\\"center\\\"][/div]

I produced the same graphs for running backs as I did quarterbacks. I first looked at AV as compared to wins:

[div align=\\\"center\\\"][/div]

Similarly to quarterbacks it appears if your starting running back produces around 7 AV on a season you’re a safe bet for around 7 wins and a playoff spot.

I then looked at TPE compared to wins:

[div align=\\\"center\\\"][/div]

There does not appear to be a strong correlation between wins and the amount of TPE a RB has.

If you do need 7 AV on average from your running back to produce 7 wins, how much TPE do you need to produce that AV?

[div align=\\\"center\\\"][/div]

It does not appear there is any correlation between the amount of TPE a running back has the AV they produce for a team. The consistently high TPE players do produce more AV on average, however the same production can be found in lower TPE players as well.

When looking at running back contracts, there is a fairly weak correlation between contract value and AV produced. For teams looking to get the 7 AV necessary for the average playoff spot, however, they can find values at all spectrums of contracts – ranging from $2,000,000 to $5,000,000.

[div align=\\\"center\\\"][/div]

There is also a strong correlation between the TPE a running back has and the value of their contract. Recalling that there is not a strong correlation between TPE and AV, however, it isn’t fully necessary to max the running back with the highest TPE. Values can be found along the spectrum.

[div align=\\\"center\\\"][/div]

[div align=\\\"center\\\"]Receivers [/div]

[div align=\\\"center\\\"][/div]

First, looking at AV compared to wins:

[div align=\\\"center\\\"][/div]

Unlike running backs and quarterbacks there does not appear to be a specific amount of AV required to produce the wins necessary for a playoff spot. This is the most jumbled position group in regard to that metric because there are underperformers at each AV slot.

There is also not a correlation between the amount of TPE a receiver has and the wins they produce:

[div align=\\\"center\\\"][/div]

There is a fairly strong correlation between the amount of TPE a player has and the AV they produce:

[div align=\\\"center\\\"][/div]

There does not appear to be a correlation between a player’s contract and the AV they produce. Some of the highest AV producers do earn the most but there are also high AV producers making the same amount as low AV producers. Teams can find strong values at cheap prices:

[div align=\\\"center\\\"][/div]

There is a strong correlation between the amount of TPE a receiver has and their contract:

[div align=\\\"center\\\"][/div]

What this all sums at for receivers is that teams can find values in all manners of places regardless of TPE or expected AV they would produce.

[div align=\\\"center\\\"]Conclusions[/div]

All of this data is based off a small sample size – one season in the NSFL – however what it appears is that in Season 20 a team could make the playoffs with a quarterback with an AV of 15 and a running back with an AV of 7. For a quarterback to have that AV he needs approximately 1,000 TPE. There is no correlation between that amount of AV and an amount of TPE for running backs, however. There is not a similar correlation for receivers.

It also shows that the sweet spot amount to pay the average 1,000 TPE quarterback is around $4,000,000 and that running backs can be found at immense values.

Note - its been pointed out to me that the minimum contract for a 1,000 TPE player is $5 million. Based off my rough thinking that would imply you'd want your 1,000 TPE QB at the cheapest rate you could get - paying more doesn't drastically impact team performance.

Finally, I looked at whether or not there was a correlation between a team allocating more of their team_offense_points to rushers and wins and receivers and wins.

[div align=\\\"center\\\"][/div]

[div align=\\\"center\\\"]
[/div]
There does not appear to be any correlation between a team allocating more of their offense towards a passing game and more wins. There is an insignificant but slight correlation between a team allocating more of their offense towards a rushing game and more wins.

What all this means right now is probably not very much besides that teams can find values in players at all contract values and only need average quarterback play to secure a playoff spot. I’ll continue to do these breakdowns every season and compare the results as I get more data points. If you’re interested in checking out all of the data or want to use it for your own calculations or decision making it is all available here:

https://docs.google.com/spreadsheets/d/1-rI...dit?usp=sharing

Approximate Value Methodology

It is a slight mess that I’ll clean up more as I figure out what exactly I want to do with all of the data. Don't hesitate to ask any questions - this whole thing took way too long. The write up alone took about four hours. The data collection and analysis about three or four times that.

[.Laser]

Holy shit.

[Opera_Phantom]

Holy crap, i have an headache now.


This is great work, congrats

[iStegosauruz]

Holy crap, i have an headache now.


This is great work, congrats

Thanks! I only ever expected to calculate approximate value but I ended up going down a rabbit hole.

[IsaStarcrossed]

This is a fascinating article that took a ton of work! The only thing that you didn't really factor in is minimums and how they work. The reason 1000 TPE quarterbacks have a sweet spot of 4m a season is because the minimum at 1000 is 5m a season. Which means that those 1000 TPE QBs who are making 4m signed an extension before hitting 1000 TPE. So they're actually making 1m below minimum value!

[Bigred1580]

This is amazing

[iStegosauruz]

This is a fascinating article that took a ton of work! The only thing that you didn't really factor in is minimums and how they work. The reason 1000 TPE quarterbacks have a sweet spot of 4m a season is because the minimum at 1000 is 5m a season. Which means that those 1000 TPE QBs who are making 4m signed an extension before hitting 1000 TPE. So they're actually making 1m below minimum value!

Makes sense - I'm still getting a handle on how contracts work and such. Only been around a few weeks. The pay some players were getting felt wonky.

I guess that would make the sweetspot the value you could get the QB at closest to $4 million then - so if the minimum is $5 million then thats still better than paying any more because the steps in pay don't necessarily correlate equivalently with more production/the production you do get doesn't always equal wins.

[gucci]

Graders. Can I request a bonus for my man Steg here?

[infinitempg]

First of all - this is amazing work!!!

With that being said, imagine being the #2 AV player in the league and not getting nominated for anything. Discrimination against dogs I swear

[IsaStarcrossed]

Makes sense - I'm still getting a handle on how contracts work and such. Only been around a few weeks. The pay some players were getting felt wonky.

I guess that would make the sweetspot the value you could get the QB at closest to $4 million then - so if the minimum is $5 million then thats still better than paying any more because the steps in pay don't necessarily correlate equivalently with more production/the production you do get doesn't always equal wins.

Precisely this! It really is a beautiful article and it is mind boggling how much research you put into this! I hope you enjoy that research bonus for your efforts.