#### 2022 Change Log:

Microsoft Research Lab recommends that Leaderboard rankings be calculated based on the formula:

LB = Mu – 3*Sigma.

This calculation results in a very conservative value of the players ability for Leaderboard ranking.  However, this is more practical for situations where there is enough match play to result in lower Sigma values corresponding to less uncertainly in players’skill levels (Mu).

For the high school tennis season, there is a wide variation in the number of matches that teams/individuals play, sometimes on the order of 3x.  Hence, players who play more matches can be ranked higher on the Leaderboard because they will have lower Sigmas.  After looking through the mid-season results, we felt it would be better to adjust the leaderboard formula to;

LB = Mu – 2*Sigma.

Note that this does not change Mu or Sigma for any player, just their Leaderboard calculation and ranking.  And this is applied equally to all players.  You can still sort on player Mus to show the player rankings by absolute skill level (Mu).  Just be cognizant that there is greater uncertainty in a player’s skill level (Mu) with larger Sigma values.

#### New for 2022:

Accuracy charts are created by comparing the actual season outcomes with the predicted outcomes based on the rankings generated by our site.  Violations are those outcomes for which the predicted outcome does not agree with the actual outcome.  Violations are mostly due to upsets, but may also be due to the fact that no one ranking algorithm is able to correctly predict all matchups throughout the season.  Concordant matches are those where the ranking system correctly predicts what actually happened during the season.

For Team Accuracy, the outcomes of each dual team matchup are compared to the team ranks.  For example, if Team A beats Team B by a score of 5 – 2 (matches), and Team A is ranked #10 and Team B is ranked #20, this would be “Concordant” result, meaning the actual result agrees with the predicted result.  If Team A lost to Team B by a result of 5-2, this would be a “Violation”, or in more common sports terms, an “Upset”.

For Singles Player Accuracy, the actual and predicted outcomes are compared to the players’ LB (leaderboard) ratings.  For Doubles Player Accuracy, the sum of each doubles teams LB ratings are compared against each other.  Remember that the LB ratings are calculated as follows:

LB = Mu – 2*Sigma

The width of the tables for Team Rankings, Player Rankings and Player History have been increased to use the entire width of the window.  This will make viewing the entire chart much easier on desktop computers.

The player history now includes only the top 100 players.  We previously included the top 200 players, but found that this significantly increased the load time of the chart.  The smaller data file will now load much quicker.

One of the hallmarks of bayesian inference is the use of “prior” information:  prior information is modified by new data to create a new set of results.  For our Stan rankings, if we did not use prior information, the algorithm would simply assume all teams are the same strength from the beginning of the season and calculate the earned rankings, much like the Massey algorithm does.  At first, we tried using the prior end-of-season season team rankings as our “prior” for the Stan model, but found that we had better accuracy using the current team rankings derived from the Massey model instead (which is run just before the Stan model).  This is also easier to us to implement, since we are using the same list of teams from the current season for both our prior and the result.  Using a previous season team ranking is laborious to implement as the list of teams (and team name spellings) can vary from season to season, creating an accounting headache.

Last year, we introduced player ratings using the TrueSkill algorithm developed by Microsoft Research for use with gaming on their X-Box platform.  The algorithm initially assigned all players, both advanced, intermediate and beginner, an initial skill level (Mu) of 0.0.  This required waiting until the end of the state tournament to see the true player skill levels, as the more advanced players were unlikely to have played enough advanced players during the regular season to obtain a reliable estimate of their true skill level earlier on.

This season, we have gone back and recalculated all player ratings beginning with the 2019 seasons.  The player ratings at the end of each season were then used as the initial rankings for the players at the beginning of the next season.  The only exception is the 2021 boys season:  since the 2020 boys season was cancelled, we felt the 2019 boys rankings were probably too different to carry them forward to the 2021 boys season.  And probably half of those players had already graduated in that 2 year stretch, resulting in at least half of the 2021 players starting with a Mu level of 0.0 anyways.  It doesn’t matter at this point, because the 2021 season is over and the ratings adjusted to where they should be after the completion of the state tournament.  The inclusion of the previous season ratings makes the most difference at the beginning of the new season when there have been relatively few matches played.

As a review, each player’s skill level is described by the parameter “Mu”.  The “uncertainty” of the player’s skill level is represented by the variable “Sigma”.  Think of these two parameters as a mean and standard deviation of a probability distribution.  Since we have waited 9 months since the end of the previous season, we are now more uncertain as to whether or not a player has improved or declined in the recent past.  To model this uncertainty, we initialize each player with their Mu value from the end of previous season, but set their initial Sigma value to twice his/her Sigma value from the end of the previous season. This results in greater mathematical uncertainty in their current skill levels at the start of the season.   This results in the top players being ranked at the top of the rankings, although each players Mu and Sigma will continue to adjust with every match played throughout the entire season.  Just because a player may start out with a high rating from a previous season, does not mean that he/she can’t lose it if they do not continue to play at that same high evel.

These changes will also directly affect the Power 10 values that are listed under the Team Rankings chart.  The Power 10 metric is the sum of the top 10 Player LB (leaderboard) values, similar to the Power 6 value that UTR calculates for each college team.  Remember that players are ranked by comparing their Leaderboard values (Mu – 2*Sigma) per Microsoft’s recommendations.  The leaderboard values listed in the Player Rankings table have also been rescaled so that they range from 0 – 100 for ease of interpretation and comparison.  Normally the Mu values are bound between 20 and -20, whereas the Sigma values are always positive, which results in negative LB values for approximately half of the players prior to rescaling.