Predictions of Scores of District Games

Using the scores of the games that have already been played among district teams, it is possible to define mathematically an "offensive strength" and a "defensive strength" for each team, and to do so in a mathematically optimal manner (in the sense that no other choice of strengths will generate a better approximation to the scores of the games that have already been played). 

The higher the strength number, the stronger the team's offense or defense is. Those offensive and defensive strength numbers can then be used to predict the scores of future games among district teams.  That's what the tables on this page do. 

The mathematical predictions are imperfect, of course.  (Were they perfect, someone would have gotten rich using these ideas long ago!)

Each week, as more games are played, these tables will automatically be updated with new strengths and new predictions based on the full set of games actually played so far.  Later predictions will not necessarily be more accurate than earlier predictions.

10/21/2006: Prior to the 10/20/2006 game, Clements was predicted (mathematically) to beat Willowridge 31-28.  Taking into consideration the results of the two 10/20/2006 games, Clements is now "predicted" to beat Willowridge 28-17.  The Clements offensive and defensive mathematical strengths have both improved since Friday night's game, and Clements (mathematically) now has the second-strongest offense and the second-strongest defense in the district, and is (mathematically) the overall strongest team in the district.  But Dulles is still in first place, Hightower second, and Clements third, as of the morning of 10/21/06.  But all of the mathematically-defined strength numbers will change again with this evening's two district games. See the District Standings.




Click on a column header to sort by that column.  The prediction for the game between Team 1 and Team 2 is that Team 1 will score o[1]-d[2] points, and Team 2 will score o[2]-d[1] points, where, for any Team i, o[i] is its offensive strength and d[i] is its defensive strength.





This table shows the predictions for all district games this year---those that have already been played and those that are still in the future.  For the team at the left end of a row, green is a win, pink is a loss, and yellow is a tie, according to the predictions.  Some of the predictions are correct, and some are wrong.  See the next table.

 

This table shows only the district games that have already been played.  It shows the predicted score, not the actual score.  In the orange cells, the predicted winner of the game was incorrect.  In the aqua cells, the predicted winner (but not necessarily the exact score) was correct.







 This table shows the predictions for the games that have not yet been played.  For the team at the left end of a row, green is a win, pink is a loss, and yellow is a tie, according to the predictions.