The vast majority of Fantasy Football leagues use head-to-head (H2H) scoring, where a (random) schedule is determined at the beginning of the season and mirrors how the sport is played in real life. During the Regular Season (typically Weeks 1-13), each team will usually play every other team at least once, with each team’s win-less record determining its Playoff seeding. Therefore, the objective for each team is to simply maximize its points total every week. While this is a straightforward task, the variability of individual player scoring can get frustrating, especially when coupled with the randomness of H2H match-ups. Everyone has had that one week where they score 150 points, only for their opponent to somehow put up 160. Other times, it feels like the Fantasy Gods are conspiring against you as you finish the season top 3 in Points For, but first in Points Against by a long shot.

So how much additional variability does H2H scheduling really introduce, and are there more equitable scoring formats? To explore this, I looked no further than my previous Fantasy season (shameless plug about winning the Championship in my first year here).

To start off, here are the 14 teams from my league last year and their scoring through the Regular Season (first 13 weeks, ESPN PPR scoring):

Here is the corresponding standings table (yes, there was a tie game…our league has since switched to fractional scoring):

The correlation between final ranking (i.e. Playoff seeding) and total points scored over the Regular Season was 87.6% (technically negative 87.6%, since smaller numbers correspond to higher/better rankings). To further complicate things, my league was structured with two divisions (2D) last season (Division A and Division B with 7 teams each). So rather than teams being ranked solely based on win-loss record, the top team (by record) from Division A and the top team from Division B were awarded the #1 and #2 seeds, while the top 3 teams from each division were given the top 6 seeds (and the only spots in the Playoffs). This resulted in Team 10 (9-4) finishing as the #2 team despite having a worse Regular Season record than Team 11 (10-3), which finished #3. As you can see in the table below, switching to a more standard single division (1D) scoring format led to the swap of Teams 10 and 11, which is arguably more “fair.” The correlation between the rankings under the 1D case and total points scored was 86.1%, very similar to that of the 2D case.

The third scoring format I explored was simply total Points For (PF). As you can see in the table above, this led to a fairly decent shakeup in the overall rankings. Under the PF scoring format, Teams 1, 8, and 11 would have ranked 3 places lower than under the 1D scoring format, suggesting that these teams benefited from “lucky” H2H match-ups (under 1D). On the flip side, Teams 4 and 12 would have ranked 4 and 3 places higher, respectively, than under 1D, suggesting that these two teams were hurt by “unlucky” H2H match-ups. Notably, Team 4 finished 10th under 1D scoring (well outside the Playoffs) but would have finished 6th under PF scoring (securing the last Playoff spot).

Lastly, I ran a Monte Carlo simulation consisting of 1,000 trials, randomizing the schedules of every team over the entire Regular Season. Each individual trial was scored under the 1D format, but my goal was to measure the average ranking of each team over a large number of repetitions, and to compare the results with both the 1D (Base Case) and PF formats.

The results of the simulation were similar to those under the PF scoring format. Once again, Teams 1, 8, and 11 would have ranked 3 places lower than under the 1D scoring format, suggesting that these teams benefited from “lucky” H2H match-ups. In contrast, Teams 4 and 5 would have ranked 3 and 4 places higher, respectively, than under 1D, suggesting that these two teams were hurt by “unlucky” H2H match-ups. The correlation between the rankings under the PF and MC cases and total points scored was 97.4% and 96.2%, respectively. This makes intuitive sense because the MC case minimizes the impact of additional variance introduced by H2H scheduling, while the PF case eliminates such variance completely.

In addition to looking at the correlation between Playoff seeding and total points scored, I also explored the impact of team volatility (i.e. the standard deviation of each team’s weekly score over the course of the 13 Regular Season games) on the final rankings of the teams. I came up with a “Sharpe Ratio“, which took each team’s average points scored per week and divided it by the standard deviation of each team’s weekly score. I hypothesized that teams with higher Sharpe Ratios would generally be more successful, although I was curious whether this would be a stronger indicator of success than simply looking at total points scored. As you can see in the table below, the correlation between ranking and Sharpe Ratio was in fact significantly lower than the correlation between ranking and total points scored, coming in at roughly 41% under the 2D, 1D, and PF cases and 52.4% under the MC case.

So what does all of this mean for Fantasy managers? The name of the game has always been points maximization, and the work that we’ve done in this Post confirms that. In the case of my Fantasy league last season, ranking teams based on one particular (i.e. random) H2H schedule reduced the correlation between overall ranking and total points scored by roughly 10%, thus introducing additional “randomness” to the game. While simply awarding Playoff seeding based on total points scored over the Regular Season may be the fairest scoring format, it certainly takes away from the drama of H2H match-ups that makes Fantasy Football so fun in the first place. One potential compromise is to let the Regular Season run its usual course, but then re-seed the Playoffs according to a comprehensive Monte Carlo simulation. This would minimize the variability introduced by H2H scheduling and ensure that teams are not being helped or hurt by “lucky” or “unlucky” schedules. Another alternative would be to reserve the last seed in the Playoffs for the team that made the top 6 in points scored during the Regular Season (assuming a 6 team Playoff format) but did not make the top 6 in win-loss record. Under this format, Team 4 would have made the Playoffs as the #6 seed last season, displacing Team 13. However, it is worth noting that while different scoring formats would have led to different rankings, the variations on average were still relatively minor. Indeed, the top 5 teams in my league last season (Teams 1, 10, 11, 12, and 5) would have finished in the top 5 regardless of the scoring format used.

Before I sign off, I will leave you with one final chart, which is a box-and-whisker plot of the Monte Carlo simulation results. As you can see, the combination of volatility at the team level and variance introduced by H2H scheduling results in a fairly wide range of potential outcomes for every team (with some interesting results, such as Teams 2, 4, and 13 all potentially finishing anywhere between #1 and #14, inclusive). In general, however, the chart still provides an effective visualization of the relative ranking of each team, which I found quite elegant.

As always, you can find my backup data here.