[FVC]: Analysis Shows Improvement Possible in Ranking System

[billw]

Blake, Thanks for filling the void once again.

Sean is correct in that I actually did say:

For those who are not looking at the results, keep in mind that simply switching to a “Total Points” system far surpasses the ability of the current algorithm as well as that of the grouping algorithm. Furthermore, it does away with the inconvenient requirement imposed by the grouping algorithm that a specific multiple of robots be used.

If I were to lobby for a new system, it would probably be in the direction of a random assignment of partners, playing in the grouped method, using a total points method of scoring. I haven't actually tried to simulate the above, so I can only speculate that it would produce the most accurate and flexible system.

Sean, your comments made me curious as to the probability of repeat partners (offensive or defensive) that a team would typically encounter when assigned on a random basis. Obviously the probability goes up as more matches are played and fewer unseen partners remain.

If I have done the calculations correctly, a random selection will produce fewer repeats than the grouped method in most cases, but the number is not as dramatic as you might expect. In fact, when using 32 teams, the number of repeats is about equal over 6 matches and actually less for the grouped method when playing 9 matches.

Note that in the grouped method, you will never have the same offensive partner, and you will always have the same defensive opponent twice.

I have attached the spreadsheet used to calculate this. In genial, it supposes that if you are on the third match, your team has played with/against 6 robots in the prior two matches. This means that the probability of a repeat partner in the third match would be the following for 32 robots:

6/31 + 6/30 + 6/29

The above really needs to be adjusted to account for the fact that one of the prior 6 partners may have already been a repeat. If, for example, this prior probability was 0.3, then the corrected calculation would be:

(6 - 0.3)/31 + (6 - 0.3)/30 + (6 - 0.3)/29

As always, I am open to any corrections/improvements.