*Wins Above Replacement in the ISFL: An Introduction

[Suggs]

Hey yall. Recently I’ve become very interested in baseball. Not only because it’s a cool game to watch, but also because I’m obsessed with statistics and baseball has tons of it. And one of those stats interested me the most: Wins Above Replacement. I found it amazing how one can attempt to calculate the value of a player based on how many wins he can give to a team. Obviously, it is easier to both understand and calculate WAR in a league with more straightforward game mechanics and functioning than others such as Football. In baseball, the existence of an outfielder and his positioning will not discourage a player to bat the ball in his direction, since things such as errors, HRs, and RBIs exist. In football, however, that’s not the case. A quarterback will be generally discouraged from throwing the ball to his receiver if players from the other team are nearby him (unless your receiver is Randy Moss). And that can be avoided by using different plays and playbooks to counter other playbooks (if team A is playing against team B and the latter uses a lot of zone coverage of defense, the former may be encouraged to run play concepts that attempt to overload these zones, such as Flood. Needless to say this is a major simplification of the complexity of football playcalling and the sport as a whole). In simulated football, however, that is not the case. As you all know, playcalling is somewhat random, as GMs can only adjust things such as the % of run plays, pass plays, coverage plays, and blitz plays in a single game. And the result of plays is a wild combination of RNG and the ratings of the players involved in a certain play. So statistics in the sim can provide a better picture than they do in the real sport. Therefore, the question stands: can you calculate Wins Above Replacement in the ISFL?

Whilst it is easier to determine W.A.R in baseball because of the fewer basic stats involved (HR, RBIs, errors, so on) and their relatively obvious value to a win (a triple is three times as valuable as a single, a double is twice as valuable as a single, so on), it is no so simple in football. For the sim, however, one can calculate the importance of each stat based on how much stats correlate to a team’s success. Since I’ve already done a study with defensive stats in Ultimus winning rosters where I calculated the correlation between each stat and a team’s success, I decided to use that data and other that I gathered to evaluate the WAR of defensive players. For this, I used the statistics of each defensive player in Season 27, mostly because despite the small sample size, the sim changed from S27 onwards and, consequently, results would not be so representative in previous simulations (also because if not it would take me way longer to do it).
In the table below are the data I used for this (difficulty of schedule, whilst represented here, was not used, since I could not find a correlation with this study. I also calculated home advantage, which I will expand upon later in this article. What I found, however, showed that this advantage was negligible and was also not included).




I calculated the deviation of each category (how much success in a certain category represented the team’s overall success, standings-wise) by obtaining the absolute difference of each stat to each team’s position in the standings at the end of the regular season and averaging all 14 results for each category, as is shown in the table below, with the table from my last media post as a comparison.



Looking at both, I decided to rank each stat in this order of importance, from most important to least:

1. Sack
   
2. Tackles for Loss (TFL)
   
3. Forced Fumbles (FF)
   
4. Interceptions (INT)
   
5. Tackles (TKL)
   
6. Pass Deflections (PD)
   

In the scale presented, a smaller number means there is a bigger correlation and is, therefore, more impactful. To add to the WAR formula, I divided every value by 10 (to obtain a value smaller than 1, as to not obtain large results that would eschew the representation of WAR) and subtracted by 1, as to give smaller numbers a higher multiplier. Inspired by the formula used by Baseballreference.com to calculate Wins Above Replacement in baseball, I made up (with PAperW = Points Allowed per Win):



I decided to use as an example Melvin Murder-Moose, LB for the Colorado Yeti and winner of the Defensive Player of the Year award of S27. When putting these stats into the formula, it would spit out the number 5.3. Yet this was a problem. It would imply that he alone won 5.3 games for the Yeti. Whilst Melvin is an amazing player who played a wonderful season, no individual player wins 5.3 games in a 16 game season. Mike Trout, for example, who was W.A.R leader for MLB in 4 separate years, averaged about 11 in these 4 seasons. In 162 game seasons. So whatever I calculated was, it was still not it. I then remembered an article I saw from Eric Eager and George Chahrouri from Pro Football Focus where they went into detail as to how PFF calculates this stat in football. And they explain early on that their formula is, basically,



This inspired me to understand WAR as:



What is AV? AV is Approximate Value, a stat developed by Pro Football Reference to give a number to each player’s importance on the pitch. Whilst it is obtained in a completely different manner from the one I devised, I understood my formula as a representation for the simulated football we watch.

Average Player AV is the average Approximate Value for players in specific positions. And 10.125 is the result of (Games in a baseball regular season)/(Games in an ISFL regular season), as to adapt the stat to the 16 game reality of the league.
I wanted WAR to be a value of low numerical value, since a win in a football season is considerably (to be exact, 10.125 times) higher than a win in a baseball season. As an example, Melvin Murder-Moose’s Wins Above Replacement would be 0.203. It seems like a small number, but to say that a team would have a 20% higher chance of losing a game by not playing a single player, out of 22 starters in defense and offense + special teams players, in a 16 game regular season, seems like a huge statement to his value on the field.



Some final considerations:

• Please notice that this is not a final formula, as this is exclusive to defensive players and may not even reflect their true value based on different positions. I did not calculate their WAR, as it is position dependent, but DPOY finalists Andrew Witten and Ke'Oke'O Kane-Maika'I had AVs of 6.2 and 2.9, respectively. This, especially the latter’s AV, shows that WAR and maybe even AV needs to be further changed in order to take the importance of each position into consideration.

• As I said in the beginning, I calculated home field advantage, in case I somehow needed it in my calculations. Surprisingly, whilst going through 175 games (the 16 weeks of the S27 regular season and 9 weeks of the S28 regular season), I found out that home field advantage was basically nonexistent. Home teams won an incredible 50.3% of their games. Even when considering what teams were expected to win (considering their standings either at the end of the S27 season or until W10 of S28), home teams only won 1 extra game (when considering all 175 games and adding a +1 value to teams who won a game that they were not expected to win because they were playing at home and adding a –1 to teams who lost a game they were expected to win even when at home, home teams had a net advantage of 1. Out of a maximum value of 87).

• It is important to remember that I am nowhere close to being an expert on statistics, most of the time I barely understand the true meaning of them in depth. This is all full of assumptions and approximations that are not really appropriate to make. This is all for fun.