how to compare prediction accuracy?

How can I measure the accuracy of predictions of the finish order of 9 horses in a race - where accuracy of predicting the winner is more important than accuracy of predicting the second place horse, and second is more important for accuracy purposes than picking the third place horse?

I want to take the predictions of ranked finishing order for a group of horseplayers for a specific race and determine who was the most accurate.

It does not seem to me that a simple Rank-order correlation coefficient will capture the relative greater importance of the early positions.

Are there any established techniques that I can use for comparing such data?