Introduction
I am honored to be able to blog about the interface between math and sports on the Huffington Post's new sports section. In my day job I teach spreadsheet modeling at Indiana University's nationally ranked Kelley School of Business. I also teach spreadsheet modeling at organizations such as Microsoft, Diamond Consulting, Cisco and the US Army. Math and sports has been a passion of mine since 7th grade and my new book Mathletics provides an introduction to the use of math by baseball, football, and basketball teams. The goal of my posts will be to show you how simple mathematical concepts can often lead to important insights about the burning sports questions of the day. Don't be scared of the math; it isn't that hard!
It's the Schedule Strength, Stupid
Upsets in sports matchups can be exciting or frustrating, depending on how your team does. But if you understand the concept of schedule strength, some-so called upsets become much less surprising. Schedule strength can enlighten us on the following important sports questions:
* The Saints were only favored by 3 points when they played the unbeaten Giants during week 6 of the NFL season. Most people were surprised that the Saints routed the Giants. They should have not been surprised!
* Sports Illustrated recently ran a cover story claiming the SEC is college football's best conference. Is this really true?
* The odds makers in Vegas favored the Cardinals over the Dodgers in the recent Divisional Playoff Series. They shouldn't have!
* We are around two weeks into the NBA season. How can the idea of schedule strength help us sort out the surprising and disappointing teams?
A team's schedule strength is simply the average ability of a team's opponents. For example, through week 9 of the NFL season the Dolphins have played the league's most difficult schedule (8 points more difficult than average) while the Redskins have played the league's easiest schedule (6 points worse than average). Chapter 40 of Mathletics tells you how to compute a team's schedule strength. Good estimates of schedule strengths can be found on Jeff Sagarin's USA Today sports rating site. Now let's use the idea of schedule strength to analyze the four questions posed earlier in our blog.
Giants and Saints
Before the Giants-Saints game, each team had outscored their opponents by around 15 points a game. The Saints, however, had played a schedule that was 14 points more difficult than the Giants. Since home-field advantage is worth 3 points in the NFL, the fact that the Saints were favored by 3 indicates that the odds makers (and the public) perceived the two teams as even. A rational analysis of the numbers would indicate that on a neutral field the Saints were 14 points better. The Saints won by 21 points!
Is the SEC Number 1?
If we look at the power ratings for the SEC and Pac-10 teams this season we find that, after adjusting for the difficulty of the schedule played by the teams in these conferences, the Pac-10 is actually one point better than the SEC. We also find that six of the nation's top 30 teams are in the Pac-10 and only 4 of the top 30 are in the SEC! By the way, five of the nation's top 30 teams are in the ACC. While in past years the SEC was slightly better than the Pac-10, this year it is not clear that the SEC is #1.
Should the Cardinals Have Been Favored over the Dodgers?
During the regular season the Cardinals won four fewer games than the Dodgers. The Dodgers had the extra home game in the series. When you also factor in the fact that the Cardinals played the easiest schedule in baseball (by the way, the Toronto Blue Jays played baseball's most difficult schedule), it is hard to understand why the Cardinals were favored over the Dodgers. More specifically, the Cardinals' schedule was around three games easier than the Dodger's schedule. Of course, the Dodgers defeated the Cardinals in four games.
Schedule Strength and the 2009-2010 NBA Season
As of this writing (November 8) we can look at each team's schedule strength to date and draw some interesting insights.
* The Wizards have played the league's most difficult schedule, so they are probably better than their 2-4 record indicates.
* The Nets (0-7) are the NBA's only winless team. The Nets, however, have played the league's most difficult schedule and are probably playing better than the 1-6 Knicks who have played a schedule that is three points easier than the Nets schedule.
* Of the four one-loss teams (Suns, Celtics, Magic and Heat) the Suns have played a schedule that is the toughest by more than two points, so it looks like their apparent improvement is probably not a mirage.
Attention, Stats Geeks
For the more technically inclined, I will close with a more detailed explanation of power rankings and schedule strength.
Power rankings simply assign numbers to each team in a way that best "fit" the scores of the games to date. For example, if you assigned the Saints a poor power ranking, this would not predict the Saints game scores very well, so any sensible ranking system (we like the Sagarin ratings) would assign a very good rating to the Saints. Once power rankings have been computed, the schedule strength of a team (assuming half their games are home games) is simply the average of the power rankings of the team's opponents. To see the importance of schedule strength, suppose our team is 0-4 but lost to the four best teams in the league by one point. If the four best teams were all 10 points better than average, then despite our 0-4 record we are actually 9 points better than average!