What method to use for comparing rankings?

[Qvickis]

I'm into gambling on trotting (harness horse racing) and have a set of indicators I use to create my own rankings for each race on the race days I want to bet. There are quite a few services around (this is in Sweden) that gives you their ranking. I have found that usually when the ranknings are much alike the favorite wins and when they differ more an outsider is more likely to win. I guess no rocket science is needed to understand that correlation, but I would very much like to see if there are any metrics to this where the results are more or less likely.

I have searched around on the Internet a bit and tried to find a way to do this, but still haven't found one I very much like because most of them seem to use some kind of "distance" variable and that's not what I'm after. The prerequisites are that there is a finite number of items (in my case horses) that can be ranked in different orders (n^x I guess). But then I would like to see how similar they are, and also the top is much more important then the bottom. So if for example it's a 12 horse race and two ranks have 6 of the horses ranked exactly the same way, but then it differs slightly on the other 6 [say 1,2,3,4,5,6,9,10,7,8,11,12 vs 1,2,3,4,5,6,10,9,7,8,12,11] would I want "more" alike then if only the first 2 are the same...

Does anyone have any ideas?

 

[obh]

If understand you, you want to check the level of difference between any 2 ranking? (rank1 and rank2) ??

horse rank1 rank2 abs(difference)
1 1 1 0
2 2 2 0
3 3 3 0
4 4 4 0
5 5 5 0
6 6 6 0
7 9 9 0
8 10 10 0
9 7 8 1
10 8 7 1
11 11 11 0
12 12 12 0
-------------
total: 2

 

[Qvickis]

Well... Not really like that. I would like to have an "indexed"/comparable number to see how much alike or different they are. And an indication as I said the more number of horses at the top would preferably yield a greater similarity then if the same ranking is done from say ranked number 3 and downwards and the two top ranked are different from each other.

If understand you, you want to check the level of difference between any 2 ranking? (rank1 and rank2) ??

horse rank1 rank2 abs(difference)
1 1 1 0
2 2 2 0
3 3 3 0
4 4 4 0
5 5 5 0
6 6 6 0
7 9 9 0
8 10 10 0
9 7 8 1
10 8 7 1
11 11 11 0
12 12 12 0
-------------
total: 2

 

[obh]

In the example above horse #9 appears as rank 7 in one list and rank 8 in another list
the difference in rank for horse #9 = abs(7-8)=1

Is this what you are looking for?

You can decide that you want to give more weight the bigger the difference between the rank: abs(7-8)^2
measurement = sqrt(Σ(RanK1 - Rank2)^2/n)

You can decide to give more weight to the horse with the better rank:
measurement = sqrt(ΣW(RanK1 - Rank2)^2/n)