Turning Advanced Statistics Into Fantasy Football Analysis What can machine learning and statistics do for fantasy football? It turns out, quite a bit. In this model, I apply a clustering algorithm called the Gaussian mixture model to an aggregation of expert ranking data provided by Fantasypros.com. The algorithm finds natural tiers and clusters within the data. The charts that result visualize the tiers and help you decide your starting lineup each week. The intuition behind both this model and the Fantasypros model is that a panel of a hundred experts can provide more accurate predictions than any one single expert can. Each expert uses his or her own sources and analysis to generate player rankings each week according to matchups. When you combine them, you get the Fantasypros" E.C.R., or Expert Consensus Rankings. But all ranked lists share a flaw. They imply a strict monotonic ordering and do not illustrate the true distance between players. A list implies QB1 > QB2 > QB3, whereas the reality might be QB1 >> QB2 = QB3. The Gaussian mixture model addresses this, and the results are clear in the charts that are generated. The black dot for each player is his position in the two-dimensional space of weighted E.C.R. (by expert accuracy) and average rank. The bars represent a half standard deviation of average rank. The color corresponds to the tier of each player found by the algorithm. I recommend starting players in higher tiers with higher ranks. When two players are very close, this means experts are near 50/50 and the algorithm finds them as equal. In this case, I recommend diversifying your starters across different teams, flipping a coin, or going with your gut. If the experts cannot agree, there is no right or wrong answer. Boris Chen/The New York Times The chart shows the top 4 tiers of the defense/special teams rankings for Week 6. To view the charts for all positions, click here. You can view the full text versions of the charts on my blog. Boris Chen is a data scientist for The New York Times. Read more about his statistical analysis at his blog and follow him on Twitter at @borisachen.