NFL Losers Pool - 2022

R
Sports Analytics
Data Visualization
Optimizing fantasy picks in an annual NFL losers pool.
Published

September 7, 2022

Coming out of of Labour Day weekend only means one thing, it is time again for the annual NFL Losers Pool competition. This is the second time I am writing about this type of competition. You can see my blog post about trying to draft an optimal lineup here: 2021 NFL Losers Pool.

Below are the rules for our 2022 contest.

Losers Pool Rules

  1. You must pick exactly one team per week to lose their game.
  2. You cannot pick the same team more than once per season.
  3. If your team wins their game, you are eliminated.
  4. Rebuys back into the competition are allowed for Weeks 1 and 2.
  5. You may enter up to three sets of picks.

Pick Optimization

The objective of this competition is to outlast the other competitors in the pool. Specifically, this means avoiding elimination and being the remaining player in the pool. The second point is worth noting because we will shift our strategy from simply minimizing the risk of our picks losing, to maximizing the likelihood that our picks move on relative to the picks of others in the pool. A quick foreshadowing - this will involve using team ownership to trade-off probability of making it to the next week for increasing our expected value in the competition.

There are a total of 32 teams to choose from, and we can expect the pool to run for roughly 10 weeks - going off of last years competition. This is a large number of potential combinations of teams to select in each week. In fact for 10 weeks, it is \(32 \times 31 \times ... \times 22\) which is roughly 234 trillion combinations (I’m not including teams with bye weeks but you get the idea, the space of possible picks is very large).

Fortunately, we can be smart about our optimization, and conditional on game forecasts, reach the global optimum without much computation work. I use two different algorithms to compare pick schedules; what I call the Opportunity Cost Model and Greedy Model. The Greedy Model will out preform the Opportunity Cost model in the short run, but eventually the Opportunity Cost model will pass the Greedy Model in future weeks.

  1. Opportunity Cost Model - picking the lowest win probability team in a given week conditional on it having the largest distance to the second lowest win probability that same week.

  2. Greedy Model - Picking the team with the lowest win probability in the first week, then the second, and so on…

Opportunity Cost Model Algorithm

  1. Step 1: Compute the difference between the least and second least likely teams to win in each week for each team and week in the pool.
  2. Step 2: Pick the team & week combination with the largest difference between the least and second least likely teams.
  3. Step 3: Remove the week and team combination from the pool and repeat Steps 1 & 2 until all weeks are filled.

Greedy Model Algorithm

  1. Step 1: Start at the earliest week we wish to optimize over.
  2. Step 2: Pick the team with the lowest probability of winning, and remove this team from the candidate pool.
  3. Step 3: Move on to the next week, and repeat Steps 2 and 3 until we reach the terminal week.

Making Picks

Lets put the above algorithms to action. Like last year, I am using the FiveThirtyEight NFL Projections to estimate each teams likelihood of winning their game. These ratings are based off of each teams computed ELO score, with some additional adjustments - read about their methodology here.

We can see that there are some clear weeks below with drastic underdogs, and each week after Week 1 contains at least one game with a win probability less than 25%.

I choose to run the above two algorithms starting in Week 3. Since we can rebuy back into the competition in Weeks 1 and 2, we do not want to take a valuable pick from our elimination weeks. Therefore, I make my set of picks on weeks 3 through 10, then pick Week 1 and 2 after removing the Weeks 3 - 10 picks, this ended up being the Pittsburgh Steelers and Chicago Bears.

The pick schedules using both algorithms are shown below. Notice the trade off of early week win probabilities for later risk savings.

We can compare the performance of both algorithms by comparing the likelihoods of reaching a given week for both models. The likelihood we move on from a given week \(w\) is equal to the probability \(P(W\leq w)\) where,

\[\begin{align*} P(W\leq w) &= \Pi_{w=3}^{12} p_{i, w}\cdot x_{i, w} \\ \text{Subject to } & \sum_i x_{i, w} = 1 \\ & \sum_w x_{i, w} \leq 1 \end{align*}\]

Which is the likelihood a given schedule of picks reaches week 10 subject to being able to pick only one team per week, and picking any given team at most once.

Optimal Decisions under Multiple Entries

One interesting aspect of the Losers Pool is that we are able to submit multiple submissions into the competition. The above analysis works for the Single-Entry case, however things become more complex in the Multiple-Entry case. When dealing with multiple entries, I move from minimizing the cost of being eliminated in any given week, to minimizing the likelihood all of the entries are eliminated in a given week. We can represent each combination of an N-team tuple as a possible pick in a given week, and calculate the probability of at least one team moving onto the next week from a tuple of N picks. Given we have two entries in the competition, this is equal to \(1 - (p_{i, w} \cdot x_{i, w})(p_{j, w} \cdot x_{j, w})\).

By computing the above likelihoods of each tuple moving onto the following week, we can then run the Opportunity Cost model on the set of picks, taking the pick with the largest difference between the best and second best pick across all weeks we are considering.

The above plot has its axis removed, however is interactive. By hovering each cell you can see the pick tuple as well as the likelihood one of the two teams moves on. The darker the cell, the greater the likelihood of at least one team losing their game that week.

Some observations:

  • It is almost always best to diversify your picks. Despite Atlanta having a low win rate in Week 5, combinations of picking Atlanta and another team still dominate picking Atlanta.
  • The matrix is symmetric, however ordering of picks matters as picking a team in the first spot can still allow for the same team to be picked in the second spot. i.e. (DET, JAX) and (JAX, DET) are valid in consecutive weeks.

As above, we can compare the performance of the OC model with the Greedy Model in the Multi-Entry case. The below plot is in terms of the likelihood of moving onto the following week, and so a higher is better. As with the Single-Entry case, we can see the OC model trading off some early likelihood for greater future likelihoods of having at least one team move onto the next week.

Results

Below are picks per entry, where picks which won their game are shown with red text. Once a player is removed, they no longer show up on the plot, and players are sorted in ascending order in terms of their average win probability - players higher in the plot have had lower win probabilities up to the shown week.

I followed the Opportunity Cost model recommendations for most of my picks. I swapped out the recommended New England in Week 4 for the New York Jets as none of the remaining players in the pool had yet to choose NE, and it is beneficial to separate yourself from the group given how often we see upsets. Unfortunately for me, it was the NYJ and not NE game that resulted in an upset.

And just like that, that is a wrap for the 2022 Losers Pool! Big congrats to Drew2, Billy and DM who chose to split the pot following Week 7. Hopefully we can improve on our algorithms and selection process come the 2023 season. I think there is some value to be found in optimizing across multiple entries, as well as being able to shift from minimizing the risk of being eliminated to maximizing the expected value of a set of picks conditional on who the remaining players have left in the pool.