Refer to this spreadsheet while reading this article.
Last season, I developed a metric for kickers which I called Points Above Replacement (or PAR). This calculation, similar to WAR and other replacement-level metrics, asks how many more points a kicker scores than the "replacement-level player," a fancy term that essentially just means the league average player. Kicker is an especially easy case study to understand for this type of metric. We can calculate the league average make rate on field goals from each distance and multiply that number by 3 (the amount of points scored for a made field goal). This is the Expected Points (EP) for a field goal from that distance. Then multiply the EP from that distance by the number of kicks attempted by a kicker from that range. That number is the EP from that range for the specific kicker. For example, the average kicker made 9.21 field goals from 40-49 yards, and attempted 11.21, or 82.16%. 3 pts times 82.16% gives us 2.46, the expected number of points for a kick from that range. Sam Sidekick attempted 11 field goals from that range, so we would expect 11 * 2.46 pts = 27.06 pts. Sidekick actually made 10 FGs out of those 11 attempts, scoring 30 points, about 3 points better than expected. Make that same calculation for every kicker, and we get the total Expected Points for the player. Subtract Expected Points from actual Kicking Points, and we get the points above or below expectation, which I call PAR. Notice that Danny King leads all kickers in PAR with 8.00, while Datsum Phastbawls has a league-worst -7.41 PAR.
This season, I began to think how we may evaluate players at every position using some sort of PAR metric. Given that kickers' performances are directly tied to scoring points, calculating PAR is fairly simple. But how does one apply a point value to rushing yards, fumble recoveries, first downs, and other significant football plays that do not actually score points? For these questions, I combined my own intuitions with internet research. Here are some initial ideas:
That's enough hypothesizing for now. Let's move on to evaluating punters:
This is quite a simple task now that we know how much a yard of field position is worth. We calculate the expected punt yards for each player (Punt attempts times league punt average). Actual minus expected punt yards gives us a yards above replacement metric (YAR). Convert YAR into PAR by multiplying YAR by 0.064, and we're left with a metric which shows how valuable a punter is. Do punts within the 20 add any quantifiable value? In my opinion, the net yardage encompassed by punt average already reward a player for a punt inside the 20, so the only additional value a punt inside the 20 might add is setting up the defense for a safety. Given the rarity of safeties and other game scenarios which might lead to them, I am content leaving out Inside20 as a contributing factor to PAR. Matty McDairmid dominates the Punting PAR (PPAR) with 11.64 PAR and Armando Gallaraga has a woeful -12.76 PPAR. Since all ISFL players both kick and punt, we can combine KPAR and PPAR to find that Matty gives San Jose 17 points above the average K/P and nearly 30 points more than the worst K/P in the league.
Moving up one level of complexity, let's look at returners. They also deal mostly in field position yards as their currency, with the added wrinkle of scoring the occasional touchdown. For both kick return yards and punt return yards, we can once again find the Expected Yards and YAR for each player, and convert YAR to points by multiplying by 0.064. However, we also have to add the value of a return touchdown. We could find the EP for every kick and punt return and subtract it by six points (the points scored by a touchdown) but return touchdowns are so rare in this league that the EP is basically zero. Instead, I will just assume that every return touchdown is six points above the expected value of a return. So, add six points per TD to our YAR*0.064 equation, and we get a PAR metric for returners. The returner of the year is clearly Flash Panda. Not only do they have the most PAR (13.00), but if we completely ignored touchdowns, Panda also led the league in Return Yards Above Replacement, with 109 more yards than expected due to excellent kick returning and solid punt returning. On the other hand, Dermot Lavelle Jr cost Baltimore 7.83 points with his returns. Despite being league average at punt returns, his woeful 20.56 yards per kick return were five yards worse than league average.
Let's attempt a more difficult problem: wide receivers. Wide receivers are primarily pass catchers, though theoretically they may have some value as blockers as well. A wide receiver has a broad range of outcomes in a passing play:
1. Not targeted (neutral result)
2. Targeted and dropped the ball (very bad result)
3. Targeted but incomplete without a drop (marginally bad to neutral; perhaps the defender made a great play or it was a bad throw)
4. Caught the ball and tackled short of a first down (might be marginally bad on third down or marginally good on first down, probably essentially neutral on average)
5. Caught the ball for a first down (good result)
6. Caught the ball and scored a touchdown (very good result)
How might each of these results affect PAR? Well, if a player is not targeted, the EP is zero. If a player is targeted, there will be an expected value per target, and each outcome of every target will either meet, exceed, or fall short of the EP per target.
Let's start with EP per target. It seems to me that there are three factors for determining the value of a target: how many yards were gained, was a first down converted, and was a touchdown scored.
Yards per catch does not serve a useful purpose here. Instead, let's look at yards per target, as it can reflect both average and catch percentage. We can figure out expected yards (targets * league yards per target) and compare that with actual yards to find YAR. We can also do something similar with first downs, and multiply the "first downs above expected" times the 0.55 EP we mentioned before. The last piece is the touchdowns, and we will use the same process. We find that 0.05 touchdowns are scored on every taget, which when multiplied by 6 points, gives us an EP of .3 pts per target. Conveniently, the calculation for total EP per target is (8.17 yds per target * 0.064 EP) + (0.33 first downs per target * 0.55 EP) + (0.05 TD per target * 6 EP) = exactly 1.00 EP per target. In layman's terms, a wide receiver is expected to add 1.00 points of value every time they are targeted. Naturally, we can now calculate the expected yards (also subtracting penalty yards), first downs, and touchdowns for each player with their actual results to find their PAR. We also need to remember to subtract for drops. A drop should be exactly -1.00 EP, since a completion should have happened, and each target has a 1.00 EP. Next, we subtract the fumbles lost and we have our final metric. We see that WR are significantly more valuable than special teamers, with Videl-San and Owen Holloway both eclipsing 50 Points Above Replacement, while Lalo Salamanca has a PAR of -54.5.
Thank you for reading this far if you made it this far. This has been a fun experiment I hope to continue throughout this week. Next, I have the arduous task of trying to put a value on tackles and pancakes (which intuitively might have identical EP, since a pancake is essentially preventing a tackle). If you have any criticisms of my methodology, especially WR since that one was a bit shaky, or if you have suggestions for future work on other positions, please contact me. I'd love to iron out this methodology and make it better.
Last season, I developed a metric for kickers which I called Points Above Replacement (or PAR). This calculation, similar to WAR and other replacement-level metrics, asks how many more points a kicker scores than the "replacement-level player," a fancy term that essentially just means the league average player. Kicker is an especially easy case study to understand for this type of metric. We can calculate the league average make rate on field goals from each distance and multiply that number by 3 (the amount of points scored for a made field goal). This is the Expected Points (EP) for a field goal from that distance. Then multiply the EP from that distance by the number of kicks attempted by a kicker from that range. That number is the EP from that range for the specific kicker. For example, the average kicker made 9.21 field goals from 40-49 yards, and attempted 11.21, or 82.16%. 3 pts times 82.16% gives us 2.46, the expected number of points for a kick from that range. Sam Sidekick attempted 11 field goals from that range, so we would expect 11 * 2.46 pts = 27.06 pts. Sidekick actually made 10 FGs out of those 11 attempts, scoring 30 points, about 3 points better than expected. Make that same calculation for every kicker, and we get the total Expected Points for the player. Subtract Expected Points from actual Kicking Points, and we get the points above or below expectation, which I call PAR. Notice that Danny King leads all kickers in PAR with 8.00, while Datsum Phastbawls has a league-worst -7.41 PAR.
This season, I began to think how we may evaluate players at every position using some sort of PAR metric. Given that kickers' performances are directly tied to scoring points, calculating PAR is fairly simple. But how does one apply a point value to rushing yards, fumble recoveries, first downs, and other significant football plays that do not actually score points? For these questions, I combined my own intuitions with internet research. Here are some initial ideas:
- The average field goal attempt scores 2.61 pts, so a blocked FG should be worth 2.61.
- Offensive TDs could be assigned point values by the following: (points scored per passing attempt/average points per passing attempt)
- According to Chase Stuart of Football Perspectives one yard of field position is worth approximately 0.064 EP and one first down is worth approximately 0.55 EP.
- A yard of field position being worth 0.064 points seems reasonable to me, as that would mean 100 yards of field position are worth 6.4 points.
- Analysts typically agree a turnover is worth about four points.
- We might divide that into two points per fumble/forced fumble and fumble recovery.
- For example, if a running back fumbles, he loses two points, but if he recovers the fumble, he gains the two points back.
- On the defensive side, the points would be evenly divided if one player punches it out and another recovers.
- A safety scores two points and forces a turnover (worth four points) so it should count as 6 EP.
- Brian Burke of Advanced Football Analytics suggests that a a sack is worth about 1.7 EP.
That's enough hypothesizing for now. Let's move on to evaluating punters:
This is quite a simple task now that we know how much a yard of field position is worth. We calculate the expected punt yards for each player (Punt attempts times league punt average). Actual minus expected punt yards gives us a yards above replacement metric (YAR). Convert YAR into PAR by multiplying YAR by 0.064, and we're left with a metric which shows how valuable a punter is. Do punts within the 20 add any quantifiable value? In my opinion, the net yardage encompassed by punt average already reward a player for a punt inside the 20, so the only additional value a punt inside the 20 might add is setting up the defense for a safety. Given the rarity of safeties and other game scenarios which might lead to them, I am content leaving out Inside20 as a contributing factor to PAR. Matty McDairmid dominates the Punting PAR (PPAR) with 11.64 PAR and Armando Gallaraga has a woeful -12.76 PPAR. Since all ISFL players both kick and punt, we can combine KPAR and PPAR to find that Matty gives San Jose 17 points above the average K/P and nearly 30 points more than the worst K/P in the league.
Moving up one level of complexity, let's look at returners. They also deal mostly in field position yards as their currency, with the added wrinkle of scoring the occasional touchdown. For both kick return yards and punt return yards, we can once again find the Expected Yards and YAR for each player, and convert YAR to points by multiplying by 0.064. However, we also have to add the value of a return touchdown. We could find the EP for every kick and punt return and subtract it by six points (the points scored by a touchdown) but return touchdowns are so rare in this league that the EP is basically zero. Instead, I will just assume that every return touchdown is six points above the expected value of a return. So, add six points per TD to our YAR*0.064 equation, and we get a PAR metric for returners. The returner of the year is clearly Flash Panda. Not only do they have the most PAR (13.00), but if we completely ignored touchdowns, Panda also led the league in Return Yards Above Replacement, with 109 more yards than expected due to excellent kick returning and solid punt returning. On the other hand, Dermot Lavelle Jr cost Baltimore 7.83 points with his returns. Despite being league average at punt returns, his woeful 20.56 yards per kick return were five yards worse than league average.
Let's attempt a more difficult problem: wide receivers. Wide receivers are primarily pass catchers, though theoretically they may have some value as blockers as well. A wide receiver has a broad range of outcomes in a passing play:
1. Not targeted (neutral result)
2. Targeted and dropped the ball (very bad result)
3. Targeted but incomplete without a drop (marginally bad to neutral; perhaps the defender made a great play or it was a bad throw)
4. Caught the ball and tackled short of a first down (might be marginally bad on third down or marginally good on first down, probably essentially neutral on average)
5. Caught the ball for a first down (good result)
6. Caught the ball and scored a touchdown (very good result)
How might each of these results affect PAR? Well, if a player is not targeted, the EP is zero. If a player is targeted, there will be an expected value per target, and each outcome of every target will either meet, exceed, or fall short of the EP per target.
Let's start with EP per target. It seems to me that there are three factors for determining the value of a target: how many yards were gained, was a first down converted, and was a touchdown scored.
Yards per catch does not serve a useful purpose here. Instead, let's look at yards per target, as it can reflect both average and catch percentage. We can figure out expected yards (targets * league yards per target) and compare that with actual yards to find YAR. We can also do something similar with first downs, and multiply the "first downs above expected" times the 0.55 EP we mentioned before. The last piece is the touchdowns, and we will use the same process. We find that 0.05 touchdowns are scored on every taget, which when multiplied by 6 points, gives us an EP of .3 pts per target. Conveniently, the calculation for total EP per target is (8.17 yds per target * 0.064 EP) + (0.33 first downs per target * 0.55 EP) + (0.05 TD per target * 6 EP) = exactly 1.00 EP per target. In layman's terms, a wide receiver is expected to add 1.00 points of value every time they are targeted. Naturally, we can now calculate the expected yards (also subtracting penalty yards), first downs, and touchdowns for each player with their actual results to find their PAR. We also need to remember to subtract for drops. A drop should be exactly -1.00 EP, since a completion should have happened, and each target has a 1.00 EP. Next, we subtract the fumbles lost and we have our final metric. We see that WR are significantly more valuable than special teamers, with Videl-San and Owen Holloway both eclipsing 50 Points Above Replacement, while Lalo Salamanca has a PAR of -54.5.
Thank you for reading this far if you made it this far. This has been a fun experiment I hope to continue throughout this week. Next, I have the arduous task of trying to put a value on tackles and pancakes (which intuitively might have identical EP, since a pancake is essentially preventing a tackle). If you have any criticisms of my methodology, especially WR since that one was a bit shaky, or if you have suggestions for future work on other positions, please contact me. I'd love to iron out this methodology and make it better.
![[Image: Mith.png]](https://media.discordapp.net/attachments/754506686688919573/1049975202924199986/Mith.png)
![[Image: Witten_HOF_3.png]](https://cdn.discordapp.com/attachments/760203360971784263/1014156341608202280/Witten_HOF_3.png)
