Calculating the seedings formula isn’t easy.

It even takes a computer a couple of hours to crunch the numbers that help determine the seed every team receives every week. But with the first postseason approaching, coaches want to know what are the ingredients in the seedings formula.

On Thursday, Maxpreps’ director of business development, Mike Wilkes, answered a handful of questions that the coaches sent to the Arizona Interscholastic Association. Wilkes works with the programmers who produce the algorithm for aia365.com’s seedings.  

"It's important to let everyone know that the algorithm (for the formula) was published in 2005 and is available online," Wilkes said. "The information we can't directly provide are the results in our database from the hundreds of thousands of games we utilize to power the algorithm."

Wilkes did provide the website (http://homepages.cae.wisc.edu/~dwilson/rsfc/rate/papers/BethelRank.pdf) where the public can view the algorithm Maxpreps used to create the formula, however.

"When approached, we were happy to offer our assistance to the postseason seedings process," Wilkes said. "Across the nation we have found that our ratings, which utilize data from across thousands of game nationwide, are received as a drastic improvement over arbitrary points based systems. We will continue to work tirelessly to serve fans, players, coaches and the AIA to strengthen high school sports."

While understanding the logic supporting the use of the results from all games nationwide to produce an accurate seed is straight forward, the manual processing of the algorithm will require an individual with a strong background in mathematics. 

That’s why the AIA’s executive board picked AIA administrators with a math background to review the formula.

Those administrators also served on the seedings committee that made the recommendation to the executive board to adopt the use of the Maxpreps algorithm in September. The only Arizona team sport that won’t use seedings this year and still is using the power rankings is badminton, which Maxpreps is working to add in the future.

Below are the responses Wilkes gave to the questions coaches and aia365.com asked him.

Answers

A simple answer for how the algorithm works?


The simple answer is that the algorithm is not predictive. It analyzes what’s happened in the past as opposed to projecting an outcome. After analyzing thousands of games nationwide, the algorithm then shuffles teams in order.

What is the formula for the AIA Seedings powered by MaxPreps?


The AIA seedings are based on the algorithm derived utilizing statistical mathematics presented in a research paper titled: “A Solution to the Unequal Strength of Schedule Problem” by Roy Bethel in 2005 and developed by MaxPreps for nationwide high school sports. The link to the paper and algorithm can be found here: http://homepages.cae.wisc.edu/~dwilson/rsfc/rate/papers/BethelRank.pdf. The data, which is not available for direct release, is the hundreds of thousands of game results nationwide processed by the algorithm to produce each team’s rating value.

Are there any improvements made to the algorithm that was published?


Yes. They are minimal and virtually negligible on the final ratings. For example, the algorithm doesn’t deal with something like a tie. However, everyone agrees if a game ends in a tie that we can assert the teams are very similar in strength. So we added an additional loop in the algorithm where a tie tells us that those two teams are very similar in strength. 

What are the basics of the formula?


The formula utilizes results from all games nationwide as opposed to only leveraging results from opponents and the opponents of opponents. This results in a rating that leverages significant more amounts of data than a standard power points or RPI based rating. All teams start on a level playing field. No values are given for division, enrollment, returning starters, previous record, etc. Forfeits are skipped, as they do not provide additional results occurring on the field.

Is the formula similar to that of the RPI?


An RPI chooses an arbitrary percentage value for games against opponents and opponent’s opponents. The value selected is not important, but the point is that an RPI really only goes two layers deep whereas MaxPreps can go infinitely deep.  This allows MaxPreps to better seed high school sports, where talent levels are vastly different from top to bottom, as opposed to an RPI produced by a formula used commonly where talent levels are much closer between all teams (such as collegiate and professional sports).

What is the difference between the rankings seen on MaxPreps.com and the seedings on AIA365.com?


The rankings seen on MaxPreps currently are predictive in nature as opposed to the retrodictive formula powering the AIA seedings, which look at games that occurred in the past.  While both process results from thousands of games nationwide, the retrodictive formula was determined to be more appropriate for post-season seedings.

What is the rating value?


The rating value translates into each team’s rank and eventual seed. This value is computed after all games in MaxPreps have been entered and run process by the algorithm.

Will defeating teams with winning records instead of losing records help improve a team’s rating?


Not necessarily. Defeating a team with a losing record that happens to compete in an extremely strong league or schedule can be more beneficial than defeating a team with a winning record playing an extremely weak schedule.

What is the strength of schedule?


Teams are also assigned a strength number. It is the strength of schedule and is an average of all of the opponents’ ratings.

How does the strength of schedule affect seedings?


The strength of schedule is an average of all of the teams’ ratings. There isn’t a direct mathematical link between the strength of schedule and the rating. But it’s an average of all the teams’ ratings. Typically teams with a strong strength of schedule will earn higher ratings than a team with a similar record but much weaker strength of schedule. However, teams with a weak strength of schedule can still be highly rated if they have key victories over highly rated opponents or by winning consistently over the course of the season. Ultimately, you will see a few teams with a weaker strength of schedule that earn their way amongst the top ranked teams, although they may never actually play on the field.  

Is strength of schedule just based on win-loss records or is it also affected by what divisions the win-loss occurs in?


It is not affected by the division and no attribution is given to divisions.

Why is it that a team with a losing record can be ranked higher than a team with an exceptional record? Is strength of schedule the reason why?


Not necessarily.  It means the algorithm is recognizing that the losses occurred against high quality opponents. 

Why do forfeits not count in the seedings?


Forfeits happen, but there’s no context for that forfeit that tells us what a team would actually do on a field. A misconception brought up is that not counting forfeits incentivizes teams to dodge higher ranked teams. The reality is that if a lower ranked team dodges a higher ranked team, the team that is forfeiting is most likely hurting its rating by losing the opportunity to improve the strength of schedule, regardless of the game result. In the end they are actually hurting their rating over the course of the season.

Do invitational tournaments count in the algorithm?


Invitational tournaments are not a part of the algorithm as recommended by the power rankings committee and approved by the AIA executive board.

Does running up the score help my seeding?


Running up the score is not a part of the algorithm. In no way would the AIA Executive Board or the Power Rankings Committee support unsportsmanlike behavior in terms of running up the score on an opponent for the benefit of a school’s seeding. 

Are the seedings based on the number of matches played or the number scheduled?


There’s a minimum of matches you can play as determined by the AIA. The beauty of this system is that there is no way of cheating the system by playing more games, forfeiting games or playing a weak schedule. Ultimately, because of what the algorithm does, it doesn’t just look at just two layers deep. What the algorithm does is connect all of the teams from A to Z.

Could the number of games played be the difference in the seedings based on the fact that the schedules are uneven where some teams have played more than others in some sports at the time the seedings are run?


Because the formula can connect all teams together, via unlimited layers of common opponents, additional games will not arbitrarily help a team’s ranking.  For example, this is why a team with a 25W-5L record in a lower division will commonly be rated lower than a 17W-5L team from a higher division. Remember, divisions are not included in the algorithm, but only used in this example to help provide context.

Is the same algorithm being used for the same sports, for example, football and volleyball?


Yes. The algorithm is exactly the same. 

Does your seeding improve if you play a team in a higher division?


No. No arbitrary value is automatically awarded for playing higher divisions or deducted for playing lower divisions. 

Does it hinder your seeding if you play a team in a lower division?


No. No arbitrary value is automatically awarded for playing higher divisions or deducted for playing lower divisions.