从残缺排名表计算分数 [英] Calculating scores from incomplete league tables

问题描述

当我在高中和学习矩阵，我们看到了一种技术，将在这样的情况下帮助：

When I was in high school and learning about matrices, we were shown a technique that would help in a situation like this:

有一些棋手中甲联赛，他们需要确定所有这些排名，但没有足够的时间让每个球员发挥每一名其他人。如果它结束了玩家A击败玩家B和玩家B击败玩家C，你可以肯定某种程度说，玩家A是比玩家C更好，所以奖励一些点，玩家A代替他们居然打对方

There are a number of chess players in a league, and they need to determine a ranking for all of them, but don't have enough time for every player to play every other person. If it ends up that Player A beats Player B, and Player B beats Player C, you can say with some level of certainty that Player A is better than Player C and therefore award some points to player A in lieu of them actually playing each other.

正如我所说的，这是前一阵，我不记得如何实际执行的算法，但我认为这是所谓的东西像统治矩阵。在网上搜索已经无果而终，并可怕次，所以我不认为这是正确的。

As I said, this was a little while ago and I can't remember how to actually perform the algorithm, but I think it was called something like a "domination matrix". Searching the web for that has been fruitless and scary at times, so I don't think that's right.

任何人都可以给我一些帮助吗？理想情况下的算法，我可以使用这个程序我工作，但即使只是一个指针有关程序的更多信息。

Can anyone give me some help? Ideally an algorithm I can use for this program I'm working on, but even just a pointer to some more information about the procedure.

推荐答案

这听起来像你想起了门阶 - 弗罗贝纽斯定理的presentation - 这至少是一个更安全的搜索项:-)。其中一个是 http://www.math.utah.edu/~keener/lectures/rankings .PDF 国际象棋玩家使用的Elo系统，在 http://en.wikipedia.org/wiki/Elo_rating_system和 http://www.chesselo.com/ ，这将是更容易实现。这可能是没有好的排名，即使你知道的一切 - 看 http://en.wikipedia.org /维基/ Nontransitive_dice 。人们模拟足球比赛通常跟踪的防守和进攻的优势分别。

It sounds like you are remembering a presentation of the Perron-Frobenius theorem - which is at least a safer search term :-). One such is at http://www.math.utah.edu/~keener/lectures/rankings.pdf Chess players use the Elo system, described at http://en.wikipedia.org/wiki/Elo_rating_system and http://www.chesselo.com/, which would be easier to implement. It is possible that there is no good ranking even if you know everything - see http://en.wikipedia.org/wiki/Nontransitive_dice. People modelling soccer games usually keep track of defensive and offensive strengths separately.

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