Fantasy Football and Wins Above Replacement

Recently, I’ve started to read up on sabermetrics in baseball.  I wanted to take the same methods for an area almost entirely devoid of sabermetrics – fantasy football – and apply it there.

Despite the abundance of numbers everywhere, many fantasy football managers aren’t thinking optimally. The concept of WAR completely changed the way 30 Major League Baseball team managers looked at their teams.  Wouldn’t it be great to change the thoughts of millions of fantasy football players too?  It’ll definitely make me less money, but it’ll also be twice as fun.

Wins Above Replacement in a Fantasy Football League

Wins Above Replacement shows us how valuable a given player is in his respective league when he is compared to an ‘average’ player in that league. With WAR, we can see which players are the most valuable, not necessarily the most skilled (although they are often related).

Instead of searching for a WAR number for the National Football League, I decided to take a shot at finding how valuable certain players are to my fantasy football league. Touchdowns are worth different points for each respective position on the field, and interceptions count for zero. The players in this particular league rarely interact with each other on any real field. We’re creating an entirely new league in which the players rarely interact with each other in real life.

Everything else about the league remains equal to the real thing – players are assigned values and drafted, players are traded for each other, and players are traded for unquantifiable draft picks in future seasons. With a WAR statistic exclusive to this league, I could find more insight into those three situations.

We Found WAR

For this league, I took the basic concept of WAR and simplified it. Actually, the league simplified it for me.  In NFL Football, a Kicker can kick a field goal worth three points and a Quarterback can pass for a touchdown worth six.  In this league, all possible actions that affect the score of our games are translated into a single point system. If we take the total points over a season for a given player, we could compare that to the “average” player for that position that one might find easily available in the waiver system. Those points above replacement for each player translate to wins, and here’s how:

For example, in the entire 2010-11 season Aaron Rodgers scored 191 Fantasy Points more than the 13th highest scoring QB, Josh Freeman. This translates to 12.73 points per game, the highest in this particular league. Mike Vick, the 12th overall highest point-scoring QB, scored 23.4 points more than the most average QB over the season. This comes out to about 1.80 points per game.

Let’s take a look at the team who started Aaron Rodgers the entire season. We’ll call him Dan. Dan gained an additional 191 points above replacement from his QB over the course of the season from starting Mr. Rodgers every game. Additionally, his team won a total of 8 games, or .75 games above the league average. Had the rest of Dan’s team been made entirely of replacement players, we could find Aaron Rodgers’ value through this formula:

Rodgers’ Points Above Replacement Level Total / Fantasy owner’s team games won above the average team = Aaron Rodgers’ points that contributed to those wins

But the rest of Dan’s team isn’t made up of replacement level players. Each of them also contributed to the win or loss record every week. We take those players, add up their PAR total, and divide by games won above what a team of replacement level players would win. In this way, we can find the PAR/win of a certain team.

If we average the PAR/win number for each team, we find that a certain pattern emerges. In this  league, the average team gains an extra win for every 126.03 PAR they can get from players over the entire season.

Now, we’ve found our magic number.

Let’s try another formula to convert these players’ points into wins.

Individual player season PAR / 126.03 = Season wins contributed per player

If you remember, Aaron Rodgers scored 191 points in this league that year. If we divide his points above replacement by our magic number, we can get the exact amount of wins he contributed last season – 1.52. In this league, any team that started Aaron Rodgers in all their games would gain an additional 1.52 wins over a team that started a replacement-level QB.

Does it reflect reality?

Let’s add the league total of WAR for all the teams and divide it by the amount of teams in this league. On the average in this league, teams gained 3.67 WAR over the season. But, the average team had 7.25 wins. We can subtract the two numbers and see that a team full of completely average players would win 3.58 games in this league.

With our WAR number, we can double check to see if a team’s total WAR on the season adds up to their actual number of wins above the average team. Dan’s team total ended up adding up to 3.62 WAR over the season. Since we found out that a team of replacement level players would win 3.58 games, we can add that number to his actual team WAR.

The result is around 7.28 wins. But, Dan’s team won 8 games in reality. It’s close, but not exact. What happened?

  1. Noise (luck). Since game results are completely binary, there are going to be rounding problems. A team can’t finish a season with 7.28 wins, but certain teams are ‘luckier’ and will win more than their indicated WAR. Some of the ‘unluckier’ teams will win less.
  1. Not all players compete every single week like Aaron Rodgers. The rosters I’ve used reflect the last games of the season.  Most fantasy owners switch players in and out every week. Some of those replacements are still above replacement level – those teams will have a little more success since they can sustain their WAR levels that week. Others use players below replacement level – this could cause a huge swing in a given week and contribute to a loss.
  1. Certain positions aren’t consistent week-to-week. Certain players are much more inconsistent than others, especially those at the WR position. Either way, it’s difficult for the average fantasy football manager to accurately predict which games these players will far exceed the average WAR and which they will fall below. However, there are few players who deviate so high on their points scored weekly average that WAR becomes meaningless.

Wrap Up

Overall, the number isn’t perfect and could use some refinement. But the average expected win total of all teams combined in my league(WAR + Replacement Level Wins) is 87.38 wins. The actual total of games won combined by all teams that season: 87.

Further research:

  1. Including position swaps each week – Unfortunately, I can’t search every single week over the past season. If we could, we would have a more accurate team WAR total and better see how each player contributed to a team over the course of the season.
  1. Finding out if sitting/playing players for their matchups works. If so, we could find players who will exceed their usual WAR on weeks when our starter’s WAR is scheduled to go down. This would maximize the use of WAR and is good practice for fantasy managers in general.
  1. Looking into previous seasons. The sample size for this league is relatively small. Previous seasons’ statistics could help us get a more accurate WAR.

What does it mean?

Earlier on, we set out to discover how players are assigned values and drafted, how players are traded for each other, and how players are traded for unquantifiable draft picks in future seasons.

Now that individual player value can be quantified using the WAR stat, we can look towards the past for an idea on what happened. However, a new draft will begin this season and all the players will be available for picking. We can’t assume that these players will exactly repeat their performance, so we’ll have to depend on projections for these players to see what their value might be in the future. I haven’t yet seen a good football projection system like ZiPS or PECOTA in baseball, but I’ll keep searching.

Once the teams are drafted and some data has come in on their current season, I’ll have a better idea of their WAR. This will be incredibly valuable in trades, since exact numbers will quantify each players’ worth. Trading players will become much less of an art and much more of a science.

Future analyses will have to go into the worth of a draft pick in this league. First, we’ll need the WAR for draft slot over a period of years. From there will we see the average value in draft picks and be able to add them into the science of the trade. Unfortunately, I’m just one person with a job and a college course load so this may take me some time.

And?

So we only solved one of our three problems in this analysis. We’re dependent on outside sources for another, and we’re a few months of work away from the third. The good news is that all of them are within reach with a little effort. I’m optimistic!

But Really

Unless you’re one of the other 11 members of my league reading this, these exact WAR statistics don’t apply directly to you since point systems differ.  But the concept remains valid.  The formulas I’ve used in this analysis are generic enough for anyone with an archived fantasy football league to check out on their own.

Even if you don’t want to do the work, re-consider how you run your fantasy football team.

Certain players are more valuable than most people think.  They’re not always superstars, and they probably won’t be your first round picks.  But a little preparation before your season can pay huge dividends the rest of the year.  Those of you in for-money leagues could greatly increase your odds of a payout by simply looking a the value of each player over how his actual skill.  If you work to get the most valuable players, you’ll find yourself at the top.

Want more? Read Fantasy Football and Wins Above Replacement Pt. 2 and the series finale, Fantasy Football and Wins Above Replacement Pt. 3.

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4 thoughts on “Fantasy Football and Wins Above Replacement

  1. Football Outsiders and their KUBIAK projections are the most comparable football projections to ZIPS and PECOTA.

  2. If you are in a league that does not have a head-to-head format, would it be simpler to calculate points above replacement?

    1. I think it would be – since there really isn’t the concept of a Win in a roto league, maybe you would focus on the 12th best QB, 24th best RB, etc. (depending on your system). I don’t think you can turn that into WAR, but you could definitely use Points Above Replacement to give you some idea of a player’s value!

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