- last post: 01.01.0001 12:00 AM PDT
Okay, I just thought I would throw in my two cents after reading the original explanation and tons of these posts.
First off, I would like to say that I dislike this ranking system in practice. Second, I would like to double-check the master formula you provided, because I don't believe it makes any sense mathematically. Also, you fail to clearly define K.
Mu - (K*sigma) = rank. This is the master formula you provided. In statistics, mu = mean, and sigma = standard deviation, or in some cases volatility.
You say, "Mu increases after a win. Always. The increase is proportional to the winner's Sigma and the Mu difference between the winner and the loser. So, if your Sigma is high, you will proceed faster through the ranking system (in BOTH directions). If your Sigma is low, you will both gain and lose rank more slowly." I will assume that the "Mu difference between the winner and loser" becomes a factor for determining K, the unknown constant.
For your rank to increase slowly, you would have to have a HIGH sigma, according to the formula, because you are subtracting a greater amount from Mu (which just increased because you won). If you had a LOW sigma, you would be subtracting a lesser amount from your Mu (which just increased because you won), which would result in a greater net increase in your rank. You claim that by winning, all you are doing is increasing your Mu value. If that is the case, then this would make much more sense:
Rank = Mu
Rank after a win = Mu + (K*sigma)
Rank after a loss = Mu - (K*sigma)
I believe this is a correct formula that you meant to provide. Your formula doesn't make any sense, and this one does. Also, you mentioned that Mu = rank in one part of your explanation, but then you are also using it in your formula to calculate rank. Wtf?
Please, somebody respond to this post and verify that this revised formula is actually correct. I don't see why you are subtracting anything from Mu unless you are losing (unless K can be negative), and I think it should be clarified that Mu is actually your rank, not some arbitrary number.
[Edited on 12.05.2007 2:38 AM PST]