Fantasy football may not have all the blood and sweat and violence and trauma of the game as it's played on the field, but there's at least one way in which it's just like the real thing: as John Madden put it, "usually the team that scores the most points wins." How you get those points may be very different—as we'll get to, it often involves prizing running backs over quarterbacks, the opposite of what a sane general manager does in real life—but the points are the thing.

That means that when you draft, you're looking for players who have value, which is to say are worth more points than the ones your opponents have. How to judge that, though, is a tricky thing. A player who's worth 150 points isn't worth much at all if he plays a position at which everyone else in your league has a player who scores at least 200; at a different position, though, he could win the league for you. To value a player, you need to compare him to everyone else at his position, and the positions to each other.

To do this, I look at how well a player compares to a replacement player at the same position, similar to how WAR is calculated in baseball. A simple way to define a replacement player for a given year is the first player that would not start. I play in a 12-person league with 1QB/2RB/3WR/1TE (we're ignoring kickers and defense), so the replacement player would be the 13th-highest scoring QB, the 24th RB, 37th WR, and 13th TE. Subtracting the replacement players' score gives a position independent measure of value.


Below, I plot the results from the 2012 season. The players are ranked such that the highest scoring player for each position is plotted on the left. The x-axis is scaled such that "1" is a full roster for each of 12 teams in the league, so there are 12 QBs between zero and one, 24 RBs, 36 WRs, and 12TE. For each player, I plot their average points per game above a replacement level player for that position.

For reference, in 2012 the replacement players were Josh Gordon (154 points), Josh Freeman (267 points), Danny Woodhead (116 points), and Scott Chandler (93 points). Here's how this metric stacks against Yahoo's average draft rank for this season 2012 fantasy ranking:


2012 Ranking Points Above ReplacementYahoo
1Adrian PetersonAdrian Peterson
2Arian FosterDrew Brees
3Doug MartinAaron Rodgers
4Marshawn LynchTom Brady
5Alfred MorrisCam Newton
6Calvin JohnsonDoug Martin
7Brandon MarshallArian Foster
8Ray RiceRGIII
9C.J. SpillerPeyton Manning
10Dez BryantMatt Ryan
11Drew BreesMarshawn Lynch
12A.J. GreenAlfred Morris
13Jamaal CharlesTony Romo
14Demaryius ThomasAndrew Luck
15Aaron RodgersMatthew Stafford

Looking at the data, a couple things become clear. First, while Yahoo's user-base seems to favor QBs, the premier running backs scored more points above replacement running backs than any other position. Even the first couple of wide receivers score better than the top quarterbacks. Looking further down the list, quarterbacks slightly outvalue wide receivers in the rest of the early rounds, and tight ends bring up the rear by a wide margin. For example, last year the 4th-highest scoring TE, Heath Miller, only scored 1.6 points per game more than the 11th, Kyle Rudolph.

I performed the same analysis for every season since 2000 (see bottom). Running backs do not always lead the pack in points above replacement. In some seasons, most notably 2004, 2007, and 2011, the top quarterbacks have merited top ranking based on points above replacement. In 2011, Calvin Johnson even edged all running backs for the lead. Nevertheless, the most common trend is the primacy of running backs.

So what does all this mean as far as draft strategy? Looking at the graph, the highest value comes from selecting players where the graph is steepest. When it is steep, that means the next best available player scores significantly fewer points. When the graph is flat, the next best player scores nearly the same number of points.* In the first couple of rounds, I want players that score high points above replacement, and in a typical season these players are almost always running backs. The truly top wide receivers are second, followed by the premier quarterbacks.

In later rounds, I want to avoid established players with little upside and take my chances on high-risk, high-reward players. While good fantasy football teams will win on the strength of their top draft picks, the great teams—the teams that win championships—find a late-round player that produces at a top level. Searching for these players will leave you with a lot of busts, but the lack of marginal value of mid-level players, as seen in the flatness of the graph, suggests that it is worth waiting a round or two to fill out the bottom of your roster. This amounts to sacrificing two to three points per game on the chance of obtaining a true steal.

There are several types of players that can significantly outplay their draft position. Obviously, highly touted rookies have upside. Players coming back from significant injuries also have the potential for high rewards, as do talented backups for injury-prone starters. Players moving to a new team or wide receivers with a new quarterback are also high-risk, high-reward players. Using this draft strategy with your mid-round picks can blow up in your face, but if your goal is to win a championship, and you don't care if you come in second or last, then it's worth it to take the risks.

*Note that there is some subtlety to the notion of flatness when looking at the graphs. This is because I have scaled the data to fit more wide receivers and running backs in the same space than quarterbacks and tight ends. The wide receiver graph is actually three times flatter than it appears and the running back graph twice as flat.

Dillon Gardner is a physics PhD candidate at MIT.