FiveThirtyEight publishes its sports forecasting formulae

Nate Silver’s predictive analytics journalism website FiveThirtyEight has published some of the maths behind its sports forecasting.

Using the Elo rating system (named after its creator Hungarian-American physicist Arpad Elo) as a basis for rating teams, FiveThirtyEight has incorporated Monte Carlo simulation, logistic regression and Poisson distribution to compare team rates, account for variables and predict winners.

Earlier this year, FiveThirtyEight added hockey to its system, using results from every game in America’s National Hockey League history from the 1917-18 season to the present day to compile data and assign each team a ‘power rating’. These ratings were then used to determine the probable winner of the league’s Stanley Cup.

To establish the team ratings, FiveThirtyEight took into account factors including: whether or not a team was on ‘home ice’, which increased their likelihood of performing well; whether the game was a playoff, in which underdogs tended to do worse than ‘normal’; and how impressive the margin of victory was.

“Our NHL Elo system not only cares if you win, but how you win — a blowout is worth more than eking out a close win,” said the model’s creators Ryan Best and Neil Paine of FiveThirtyEight. “We adjust for this with the margin-of-victory multiplier, which accounts for diminishing returns.”

Best and Paine also had to adjust for Elo’s “pesky side effect” of autocorrelation, which is a tendency to inflate the ratings of “already good teams” and suppress the ratings of “not-so-great teams”. Once this and other sophisticated adjustments were achieved, the system could be used for predictive modelling.

They ran thousands of iterations of the remaining games using Monte Carlo simulation, running each one “hot” – meaning that a team’s rating wasn’t static but changed within each simulated season based on the results of every simulated game, including bonuses for playoff wins and blowouts.

Logistic regression was then used to determine the probability that simulated games went into overtime, and a Poisson distribution formula was used to predict goal totals.

FiveThirtyEight gave the Tampa Bay Lightning team the highest Elo rating of 1569 and a win probability of 58% against another highly-rated team, Colorado Avalanche. The 2021 season concluded in July, with defending champions Tampa Bay Lightning beating Montreal Canadiens to claim victory.

Best and Paine’s maths are fully explained on the FiveThirtyEight website. You can also download a CSV file of their model and run your own simulations.