Quote:
Originally Posted by IKE
Ed,
In order to balance the competitive levels, the good teams will invariably have the lowest scoring partners way more often.
An important thing to keep in mind is that this is 3 vs. 3. This can be demonstrated with some dice pretty well (actually the dice are even more "fair" in distribution and probability). If your team is a 3, and your partners are random draw, then on average, you will have a 6 on your alliance about 1/3 of the time (2 of 3 dice are rolled with 6 outcomes thus 2*1/6=1/3 in having at least one 6). On the other hand, the opposing alliance will on average have at least one 6 1/2 of the time (3*1/6=1/2). This would lead you to believe you were given an unfair schedule, even though it doesn't get much more fair than 3 dice vs. 3 dice. The "6" knows that 100% of the time, they will have a 6 on their alliance (its them), and 1/3 of the time (2*1/6), they might even get another 6. This would appear that they have a "stacked" schedule. The average combination for the "3" team would be 10 (3+2*(6+5+4+3+2+1)/6=10), where as the actual average would be a 10.5 (3*(6+5+4+3+2+1)/6=10.5), and the average for a "6" team would be 13 (6+2*(6+5+4+3+2+1)/6=13). The numbers only get worse if you are a 2 or a 1.
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Isaac, based on what you said, I think you misunderstood the criteria that I have in mind. First of all, the algorithm is not to select alliance partners for a team. It is also not to make matches even in score. Let me try to explain again.
It is based on strength of opposing alliance, the other 3 teams. Using your "dice" example, regardless of who your alliance partners are, you will get some opponents that are "6" and you will get some that are "1" and anything in between. On average, every team should face the same total strength of opponents out of all their matches. I don't see how it can be more fair than this. Even if the distribution is not "normal" in terms of strength. Let's say there are very few "6"s and a lot of "2"s and "3" so the average is still 3.5. What I said can still happen. The algorithm will work such that if you face a "6" in one match, then on other matches you will face more "2"s and "3"s to balance it out.
The algorithm I am proposing does not care who your alliance partners are. It also is not trying to prevent blowout matches. There is still a lot of randomness to it, which is what I like also. But nobody can say their schedule is harder than others in terms of the opponents that they have to face. So if you are a better team, the destiny is still in your own hands. And if you are an average team, you may still do well if luck is on your side and you got some good partners. Your assertion that good teams will get weaker partners is not an outcome with what I have in mind. It will only happen if you try to balance your alliance's strength which is a bad criteria.
If anyone out there understand what I am trying to say, please help.