2021-22 MN Girls HS Computerized Rankings
Posted: Tue Nov 16, 2021 2:55 pm
Hi all,
I'll be attempting to keep a steady stream of computerized rankings flowing for both the Boys & Girls side of things this season. As in past years, the overall ranking/rating profiles will include North Dakota & Wisconsin Teams because of their interlocking schedules, which is fine because these additional games create a stronger mathematical network. There are two distinct algorithms that I will use in the Sportsoft package to compute the ratings profiles: (1) Least-Squares (LSQRank) and, (2) KRACH is based upon Bradley-Terry rankings, which is a probabilistic model for pairwise comparison. There are pros and cons to both methods. The pros when using a least-squares method is that (a) the results of the rating profile is easier to interpret for the average fan, (b) a numerical value for the uncertainty (standard error/deviation) is easily generated and reported, (c) individual and groups of games can be weighted differently, and (d) a reasonable estimate of a score differential can be predicted for future (unplayed) games based upon an earlier rating profile. The cons when using a least-squares method is that one does need actual game scores to process, which sometimes could introduce misleading data when the raw scores are not adjusted for game-time attributes such as power-play goals, empty-net goals, reduction in game length due to running time rules, etc. The pros when using the KRACH method are that one doe not need precise game scores, but only which team won, lost, or tied. The cons are that the KRACH rating profile is much harder to interpret since the rating profile numbers indicate a ratio with respect to expected outcomes (ie. if Team A were to play Team B a certain number of times, then Team A would win X games out of N). Also, there is not any good way to generate a numerical estimate of the uncertainty value in the KRACH profile. Both methods have a connectivity requirement, that is to say, that each team must be interconnected (indirectly) into the greater network by means of games played outside of their local conference or micro-network. This property allows us to generate a meaningful profile that includes all three states (MN, ND & WI) in the same rating profile.
As with all computerized numerical methods, the rating profiles become more precise as the hockey season advances toward the February playoffs and state tournaments. The first rating profile will not be able to be produced until state-wide connectivity is achieved, which is usually met by the time each team has played a minimum of 4 or 5 games each. The initial rating profiles will change incrementally week by week until each team has played 13 or so games. Towards the end of the season, game score differentials become much more predictable.
-enjoy the season, Doc
I'll be attempting to keep a steady stream of computerized rankings flowing for both the Boys & Girls side of things this season. As in past years, the overall ranking/rating profiles will include North Dakota & Wisconsin Teams because of their interlocking schedules, which is fine because these additional games create a stronger mathematical network. There are two distinct algorithms that I will use in the Sportsoft package to compute the ratings profiles: (1) Least-Squares (LSQRank) and, (2) KRACH is based upon Bradley-Terry rankings, which is a probabilistic model for pairwise comparison. There are pros and cons to both methods. The pros when using a least-squares method is that (a) the results of the rating profile is easier to interpret for the average fan, (b) a numerical value for the uncertainty (standard error/deviation) is easily generated and reported, (c) individual and groups of games can be weighted differently, and (d) a reasonable estimate of a score differential can be predicted for future (unplayed) games based upon an earlier rating profile. The cons when using a least-squares method is that one does need actual game scores to process, which sometimes could introduce misleading data when the raw scores are not adjusted for game-time attributes such as power-play goals, empty-net goals, reduction in game length due to running time rules, etc. The pros when using the KRACH method are that one doe not need precise game scores, but only which team won, lost, or tied. The cons are that the KRACH rating profile is much harder to interpret since the rating profile numbers indicate a ratio with respect to expected outcomes (ie. if Team A were to play Team B a certain number of times, then Team A would win X games out of N). Also, there is not any good way to generate a numerical estimate of the uncertainty value in the KRACH profile. Both methods have a connectivity requirement, that is to say, that each team must be interconnected (indirectly) into the greater network by means of games played outside of their local conference or micro-network. This property allows us to generate a meaningful profile that includes all three states (MN, ND & WI) in the same rating profile.
As with all computerized numerical methods, the rating profiles become more precise as the hockey season advances toward the February playoffs and state tournaments. The first rating profile will not be able to be produced until state-wide connectivity is achieved, which is usually met by the time each team has played a minimum of 4 or 5 games each. The initial rating profiles will change incrementally week by week until each team has played 13 or so games. Towards the end of the season, game score differentials become much more predictable.
-enjoy the season, Doc