The computer power rating for college lacrosse is based on margin of victory calculations, including a 10-goal limit constraint. In addition, predictions are made for the selection of teams to the men and women's NCAA championship tournament for Divisions I, II, and III, which is predicated on strength of schedule, ratings percentage index, quality wins, win-loss records, and polls.

Criteria

The following six criteria are displayed on the LaxPower pages:

(1) Margin of Victory
(2) Strength of Schedule (NCAA tournament prediction)
(3) Ratings Percentage Index (NCAA tournament prediction)
(4) Quality Wins (NCAA tournament prediction)
(5) Win-Loss Records (NCAA tournament prediction)
(6) Polls (for comparison to computer ratings only)


Explanation of Criteria

Which criteria make sense?

Margin of Victory and Home Field Advantage

The first criterion is margin of victory, which is based on the strength of an opponent (i.e., its power rating), the home-field advantage in points or goals, and the game score. Most computer rating program are based on goal margins because that provides the most important data relating the strength of two opponents based on each team's outcome in previously played games.

The computer program solves a set of equations, one each for every game played, such that:

(1) P(i) - P(j) = Score(i) - Score(j) + HFA

where P(i) and P(j) are the power ratings for team(i) and team(j), score(i) and score(j) are their scores, and HFA is the home field advantage, which is "+" if i is the home team and "-" if i is the away team. Equation 1 states that the difference in power ratings between two teams is equal to the goal difference of these two teams if they were to play on a neutral site (HFA = 0). Now this equation is never solved exactly, and there is an error produced for every game:

(2) Error = {P(i) - P(j)} - {Score(i)-Score(j)} - HFA

The objective of the algorithm is that for every team, the sum of these errors for all games played = 0.0. This means that Equation 1 is valid when averaged over all games a team plays.

The calculation of P(i) is an iteration procedure where if the sum of errors for all teams is > 0, then P(i) is reduced a small amount and all calculations are repeated. The P(i) values are adjusted over thousands of iterations until the sum of errors for all teams = 0.0. When this happens, the ratings program has converged. This is nothing more than a trial-and-error procedure that stops when convergence is reached. The method is also referred to as a predictor-corrector procedure, because as new data become available, all results are updated.

Ten-Goal Limit

Head-to-head contests represent only one game, and the results of all games collectively are more important. So it is possible that one team can beat another team and yet still have a lower power rating. The accuracy of this method is, on average, 3 goals for lacrosse. That means, if you subtract the power rating for two teams and add in the home field advantage, the result will be within three goals of the actual game score difference. The criticism of margin of victory is that it promotes unsportsmanship by encouraging running-up-the-score and penalizing teams if they hold the score down.

The LaxPower system is such that, if the goal margin exceeds a threshold value, neither team benefits or loses rating points. In lacrosse, this threshold is 10 goals and is referred to as the 10-Goal Limit or TGL. In football, 30-point limit is used.

Strength of Schedule

A second criterion is strength of schedule (SOS), which determines the relative difficulty of the opposition a team plays. There are three ways to compute SOS. The first is to take the average strength of all opponents based on margin of victory computer power ratings (PR). The second is to use a weighted average (exponent) of the margin of victory PR. The third is to sum the last two components of the RPI formula described below. The results will vary, sometimes significantly between the RPI method and the first two methods.

Win-Loss Percentage

A third criterion is win-loss percentage. Four methods are employed. Teams that win, regardless of schedule, receive consideration even if the schedule is weak. The percentage can be based on (1) total games, (2) conference or division games, (3) weighing games played later in the season more heavily than games played earlier in the season, and (4) weighing games depending on where the game was played: where road wins and home losses count more than home victories and away losses.

Ratings Percentage Index (RPI)

A fourth criterion is the ratings percentage index (RPI), which is used by the NCAA for most college sports. The RPI is based strictly on wins and losses by all teams and does not include margin of victory. This means a 1-goal or 1-point victory counts the same as a 10-goal or 50-point victory. While eliminating margin of victory promotes sportsmanship, it does not consider what many believe is compelling information in determining the relative strength of teams.

The RPI in most cases does not distinguish between home games and away games. The RPI is made up of three components: (1) a team's record (winning percentage), (2) the average of all opponents' records, and (3) for those opponents, the average of their opponents' records. The total RPI value is the sum of 25% of (1) + 50% of (2) + 25% of (3). Two derivative quantities – significant wins and significant losses – are based on defeating teams with a higher RPI rating or losing to teams with a lower RPI rating.

Quality Wins

A fifth criterion is quality wins. A team will receive additional consideration for defeating a highly ranked team. The points awareded are based on the rank of the opponent such that the higher the rank, the more points received. The calculation can be based on poll ranking, RPI ranking, or margin of victory rankings.

Polls

Finally, the sixth criterion is poll results. Polls are based on expert input, and pollsters can consider factors not taken into account by computer ratings. Polls are often criticized, however, for being subjective and biased.

A more comprehensive formula with additional criteria can be found here. The current formula may be expanded in the future to contain additional criteria found in this more comprehensive algorithm.

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