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More fun with Excel spreadsheets!
I created my own computer ranking last night, called the GRaNT Computer Rankings -- (Stands for "Grant's Reasonable and Not Terrible Computer Rankings"). Pretty exciting stuff. here is the link to the ranking..
Here's the jist of the rankings:
-All teams are assigned an arbitrary rating. It doesn't matter what you use because the rankings will come out the same regardless of what you start with. Since it doesn't matter, the calculator literally starts each team out with a RAND() value.
-Each team's rating is recalculated based on their winning percentage and their opponent's rating as follows:
---A win adds the opponent's rating
---A loss adds zero
---A tie adds 1/2 the opponent's rating
------The sum is divided by the number of games played, and then adjusted to equal the percent of the average of the new ratings.
The GRaNT Rankings are constructed somewhat similarly to KRACH in that it uses each team's ranking to calculate everyone else's ranking. I'll explain.
Example: Teams A, B, and C each play each other once each.
Team A's starting rating: 0.666
Team B's starting rating: 0.444
Team C's starting rating: 0.222
Team A beats Team B and ties Team C. Team A's new unadjusted rating is (0.444+0.111)/2=0.278.
Team B beats Team C and loses to Team A. Team B's new unadjusted rating is (0.222+0)/2=0.111
Team C ties Team A and loses to Team B. Team C's new unadjusted rating is (0.333+0)/2=0.167
The average of the new ratings is (0.278+0.111+0.167)/3=0.185
So, each team's new rating is:
Team A: 0.278/0.185=1.503
Team B: 0.111/0.185=0.600
Team C: 0.167/0.185=0.902
Then the process repeats itself, recalculating based on the new ratings instead of the starting rating. Each team's rating will converge to a different number such that when you recalculate, you get the same number:
Team A: 0.6190/0.4491=1.3784 (percent of average)
Team B: 0.3837/0.4491=0.8544
Team C: 0.3446/0.4491=0.7673
Team A: (0.8544+0.38365)/2=0.6190
Team B: (0+0.7673)/2=0.3837
Team C: (0.6892+0)/2=0.3446
-- and those convergent values are each team's final rating.
That final rating is scaled to make zero equal average, and ranked, naturally, from best to worst. The result is the GRaNT Rankings.
You'll notice that teams are awarded 0 points for a loss, no matter who they play -- that means that teams are not penalized for losing to good teams, since all losses count the same. The end result is that teams are rewarded for playing and beating good teams, not penalized for playing but losing to good teams.
It also means that teams are not overly penalized for bad losses. In this way, the ranking is more focused on how good your team can be, not how bad your team can be.
I feel that come tournament time, when teams are focused and playing at their highest level, this will be a better indicator for success than overly penalizing them for a couple of bad mid-season losses when not playing at their full potential.
Anyway, let me know what you think!
I created my own computer ranking last night, called the GRaNT Computer Rankings -- (Stands for "Grant's Reasonable and Not Terrible Computer Rankings"). Pretty exciting stuff. here is the link to the ranking..
Here's the jist of the rankings:
-All teams are assigned an arbitrary rating. It doesn't matter what you use because the rankings will come out the same regardless of what you start with. Since it doesn't matter, the calculator literally starts each team out with a RAND() value.
-Each team's rating is recalculated based on their winning percentage and their opponent's rating as follows:
---A win adds the opponent's rating
---A loss adds zero
---A tie adds 1/2 the opponent's rating
------The sum is divided by the number of games played, and then adjusted to equal the percent of the average of the new ratings.
The GRaNT Rankings are constructed somewhat similarly to KRACH in that it uses each team's ranking to calculate everyone else's ranking. I'll explain.
Example: Teams A, B, and C each play each other once each.
Team A's starting rating: 0.666
Team B's starting rating: 0.444
Team C's starting rating: 0.222
Team A beats Team B and ties Team C. Team A's new unadjusted rating is (0.444+0.111)/2=0.278.
Team B beats Team C and loses to Team A. Team B's new unadjusted rating is (0.222+0)/2=0.111
Team C ties Team A and loses to Team B. Team C's new unadjusted rating is (0.333+0)/2=0.167
The average of the new ratings is (0.278+0.111+0.167)/3=0.185
So, each team's new rating is:
Team A: 0.278/0.185=1.503
Team B: 0.111/0.185=0.600
Team C: 0.167/0.185=0.902
Then the process repeats itself, recalculating based on the new ratings instead of the starting rating. Each team's rating will converge to a different number such that when you recalculate, you get the same number:
Team A: 0.6190/0.4491=1.3784 (percent of average)
Team B: 0.3837/0.4491=0.8544
Team C: 0.3446/0.4491=0.7673
Team A: (0.8544+0.38365)/2=0.6190
Team B: (0+0.7673)/2=0.3837
Team C: (0.6892+0)/2=0.3446
-- and those convergent values are each team's final rating.
That final rating is scaled to make zero equal average, and ranked, naturally, from best to worst. The result is the GRaNT Rankings.
You'll notice that teams are awarded 0 points for a loss, no matter who they play -- that means that teams are not penalized for losing to good teams, since all losses count the same. The end result is that teams are rewarded for playing and beating good teams, not penalized for playing but losing to good teams.
It also means that teams are not overly penalized for bad losses. In this way, the ranking is more focused on how good your team can be, not how bad your team can be.
I feel that come tournament time, when teams are focused and playing at their highest level, this will be a better indicator for success than overly penalizing them for a couple of bad mid-season losses when not playing at their full potential.
Anyway, let me know what you think!
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