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Unread 04-10-2011, 13:11
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Re: Match Scheduling Algorithm Competition

Quote:
Originally Posted by IKE View Post
For an event like MSC, the average score was about 79 pts. The equal strength of opposition would then try to balance out your opponents so that on average, you would play opponents whose average contributions would be 79 pts. This would give an average contribution of around 26.3 points. If you were a team with an OPR of 60, the pool of rremaining candidates would now have an average lower than the 26.3, and thus in order to get to the average 79 pts/match of opposition, you would on average have to play a tougher than "random" schedule. If your team had a OPR significantly below 26.3 (some would), then you would have a softer than random schedule as it would require balancing in the other direction. Unfortunately, algorithms must do the groupings at the same time (opponents and partners), and invariably work out the way I discussed (at least on average). While the differences are not huge, there is a shifting that occurrs.
This is going to be difficult to explain but I will try. I understand what you are saying. I knew that and I thought through it already. By trying to achieve an average opponent strength of 79 pts/match (using your example), there will be an effect on your alliance as well. Afterall, the total strength of all the teams is a constant. However the key is that the algorithm do not force your alliance to be 79 pts also even though you are somebody else's opponent. Those 3 opponents that have to play your alliance will most probably be playing an opposing alliance that is higher than 79 for that match, but it is still possible for each of them that with all their other matches, their average opponent strength is still 79.
In this optimization, even though everything is related, we are only trying to control average opponent strength and not your alliance strength. Yes, your alliance strength is affected as you said. So let's do the numbers as in your example.
Let's say your team has strength of 60. Your opposing 3 teams have a total strength of 79. In a 64 team tournament, the remaining teams will have an average of ((79/3)*64-60-79)/60=25.77
Explanation of the formula: 79/3 is the average strength of each team. There are 64 teams. Hence the total strength is (79/3)*64. However we have to subtract out your team with strength of 60 and the combined strength of opposing alliance which is 79. Since we took out these 4 teams, we should divide by 60 which is 64-4. So the average is 25.77.
The original average was 79/3 or 26.33. As you can see, the change is very small. The irony is that the perceived assignment of weaker partners is due to your team's strength of 60. So what is the bottom line, your alliance's strength is 60+25.77+25.77=111.54 and is still way higher than 79. Your "penalty" of having a high strength is only (26.33-25.77)*2=1.12. Your alliance is still at an advantage of 111.54 versus 79 due to your high strength.
Before I continue, I need to address other people's concern that by controlling average strength of opponents that it will guarantee a team with strength of 60 will be at an advantage to win every match. That is not the case. We are only talking about average here. This strong team is not going to face opposing alliance with strength of 79 in every match. Sometimes they will face opposing alliance with strength of 110 and sometimes they will face opposing alliance with strength of 48. But the average is 79. As far as their partners are concern, they will not have partners with 25.77 in every match either. This is especially true since we are not controlling what the total alliance strength is. Sometimes they will get strong partners and sometimes not so strong. However when all is said and done, with their strength of 60, they will probably win a lot of matches, and there is nothing wrong with that. They deserve to.
Remember that this algorithm still allows quite a bit of randomness in it since we don't look at the predicted outcome of each match.
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