This is an attempt to raise those miniscule odds 100 fold or more. While we can’t actually quantify this, much less guarantee this, and past performance isn’t always an indicator of future performance, the goal is to put a probability on a running back finishing in the Top 2 each week. This is because some daily fantasy leagues requires you to start 2 RBs although there is a flex. This strategy is based on the idea that DFS players want to maximize their chances of coming in first. This is slightly different than maximizing their points.
As an example, you’re playing a friend in a game where you each flip a coin. If yours is heads, you get one point, if it’s tails you get zero points. Your friend gets .9 points for a heads, and .8 points for a tails. After playing this game 100 times, you will on average get 50 points (Expected Value). Your friend’s Expected Value (EV) is 85 points.
Since we’re talking about daily fantasy sports, we instead look at each individual sub-game and see who scored higher in that game. Through this lens, it’s apparent that you win regardless of your opponents flip if you get a heads. And conversely, you lose regardless if you get a tails. Now, imagine you’re playing this game with 99 friends, who all have the same scoring method of .9 and .8, while you have your one and zero scoring.
This time, your friends EV will be 85 points again, but each friend will win (or tie for first) in only 0.505 percent of the sub-games. You, on the other hand, will come in first 50 percent of the time, but also come in dead last 50 percent of the time. This is the beauty of variance or volatility (an explanation of the minute difference can be found here). We sacrifice our mediocre finishes to either do really well or really poorly.
To see how this actually played out last year, let’s look at the top scorer each week among the Top 12 running backs. Since this is a quick example, ignore the fact that it includes when players like Arian Foster or Jamaal Charles were injured, or when C.J. Anderson and Jeremy Hill started the season as backups.
Under this metric, Demarco Murray, who led the league in scoring at 17.625 points a game, is decidedly worse than LeVeon Bell and Marshawn Lynch. Murray led the week in scoring only once while Bell and Lynch each accomplished this four times. Other running backs finishing ahead of Murray were Arian Foster (3), Matt Forte (2), and Jeremy Hill (2), which is astonishing because Murray on average outscored these backs by approximately 0.6, 1.8, 3.7, 3.2, and 6.9 points a game – yet he would be less helpful in winning in daily fantasy.
Now for the methodology of this post. Using depth charts, I looked at the Pro-Football Reference game logs for each starting running back. I scraped the last two seasons of data if it existed (the four rookies weren’t included in this analysis). Next, I applied a “function” which removed games in which a player was either injured or wasn’t starting* to help balance players like Hill or Anderson, who have been backups, but have played phenomenally when given the chance. These remaining games were scored using the DFS scoring system (NOTE: Pro-Football Reference data doesn’t include fumbles, while some daily fantasy leagues have a penalty of one point for each fumble). Finally, using the fit distribution function (fitdistr from the MASS package), I fit each player to a normal distribution.
*Each player started the season as a backup.The first game in which they amassed 10 carries, they became a starter, which they kept that status until the season ended, or they received zero carries (the case of being benched or injured). However, they could regain starter status by once again having a 10 carry game. A design note is that I had to use zero carries (potentially one or two) to reset there status, otherwise we would be biasing the data to only include games in which a backup had good games and had many carries. Furthermore, by penalizing backups slightly accounts for the fact that NFL coaches probably can tell who the better running backs are.
Taking the Frequentist approach, I then simulated 10,000 games for each player from their own distribution and computed how often a player was among the top scorer or among the Top 2 scorers. Thus, the left table sums to 100 percent while the right table sums to 200 percent.
Note the difference between the two tables. For the table on the left, variance is more important because we only care about the top performer. For the table on the right, this is less pronounced because a player who’s consistently good can still be a Top 2 scorer.
This is based 100 percent on historical data. Players like McCoy and Murray have moved to new teams. Players like Stewart are no longer in split backfields. And that brings us to Anderson, who is projected to have a third of a chance of being a Top 2 RB this week. How did he get all the way up there?
Anderson has really only started in eight games, but in those eight games he’s scored over 27.5 points 50 percent of the time. His average score was 25.21 points – more than three points clear of second-place Forte. In an up-tempo Broncos offense, Anderson could easily continue to put up these numbers, especially considering that some DFS leagues give one point per reception.
The potential downside is (besides the fact this will be his ninth game as a starter) that Anderson is a low-variance back. Of the 28 backs (there are four rookies projected to start), Anderson had the 11th lowest standard deviation of 6.4 points.
By comparison, Jamaal Charles was first with a standard deviation of 11.6 and, even though he was only fourth in average points, it allowed him to leap frog the safer Forte and Murray. Below are tables representing the Top 8 in points and standard deviation:
As you can see above, there are five running backs who appear on both charts: Charles, Peterson, Lynch, Forte, and McCoy. Unlike Anderson, they’ve been in the league longer, they’re established players, and they can produce some awesome games. This might, however, also be their weakness. You didn’t need a whole article to know Charles and Peterson are among the best RBs.
Thus, many people are going to pick them and maybe taking a shot on a lesser-known player like Anderson or Rashad Jennings would be more fruitful. Do what you want! Good luck and may the odds ever be in your favor.
Carlos Pena-Lobel is a member of the Harvard Sports Analysis
Collective, a student-run organization at Harvard College dedicated to
the quantitative analysis of sports strategy and management.