Introducing Mathletics: Modeling thru Sports!

Fall 2 is fully underway and one of the electives that I am taking is called Mathletics. Over the next month, I will be working with Professor Ed Kaplan to provide some insight into this unique class. Here we go: Probability modeling and statistics are fundamental tools of management science. Building upon earlier core coursework in probability, statistics, and spreadsheets, Mathletics is designed to provide additional experience using these modeling tools via applications to entertaining problems in sports. Rating NFL football teams is one application tackled (ahem…) in Mathletics. In the model reported below, each team receives offensive and defensive ratings, while in addition the model estimates the average number of points scored per game per team along with the home edge. The model takes the form: Home Score = League Average + Edge/2 + Home Offense + Away Defense Away Score = League Average - Edge/2 + Away Offense + Home Defense The sum of the offensive ratings equals zero, as does the sum of the defensive ratings. A team’s overall rating is the difference between its offensive and defensive ratings. Here are updated NFL rankings following Week 9 of the current NFL season – the Packers lead the pack while the Colts are charging, albeit in the wrong direction: League Avg: 22.2 pts Home Edge: 2.7 pts Rankings: Team Off Rating Def Rating Off-Def Green Bay Packers 11.52 -0.54 12.06 Detroit Lions 8.69 -3.12 11.81 San Francisco 49ers 4.89 -6.58 11.47 Baltimore Ravens 5.06 -3.51 8.57 New Orleans Saints 9.87 2.16 7.71 Chicago Bears 2.73 -4.34 7.08 Houston Texans 3.15 -2.48 5.63 New England Patriots 4.89 0.09 4.80 New York Jets 2.69 -2.07 4.76 Philadelphia Eagles 5.27 0.60 4.67 Buffalo Bills 4.19 -0.33 4.52 Atlanta Falcons 1.17 -2.87 4.05 Cincinnati Bengals 2.06 -1.81 3.87 Pittsburgh Steelers -0.66 -3.12 2.45 Dallas Cowboys 1.41 -0.74 2.15 New York Giants 2.63 2.80 -0.17 Washington Redskins -6.79 -5.14 -1.65 Carolina Panthers 1.40 3.21 -1.81 San Diego Chargers 1.83 4.19 -2.37 Minnesota Vikings -1.33 1.15 -2.48 Tampa Bay Buccaneers -3.76 -1.08 -2.68 Tennessee Titans -2.90 0.35 -3.25 Jacksonville Jaguars -9.00 -4.37 -4.63 Miami Dolphins -5.80 -0.98 -4.82 Arizona Cardinals -1.48 4.30 -5.78 Denver Broncos -2.01 3.99 -6.00 Seattle Seahawks -5.64 0.36 -6.00 Oakland Raiders -0.31 5.85 -6.16 Cleveland Browns -7.87 0.56 -8.42 St. Louis Rams -10.34 0.78 -11.12 Kansas City Chiefs -8.40 2.73 -11.12 Indianapolis Colts -7.17 9.95 -17.12 These ratings can also be used to form predictions for next week’s games. For example, the prediction for Patriots at Jets is: Jets: 22.2 + 2.7/2 + 2.69 + 0.09 = 26.3 or 26 pts Pats: 22.2 - 2.7/2 + 4.89 -2.07 = 23.67 or 24 pts Looks like a close game!