I have data on runners who run marathons; for each runner I have their final times on a number of races. I would like to predict how fast they are running considering outliers i.e.
- he's running faster than x hours with probability:
x | P(x)
1:30 | 0%
2:00 | 1%
2:30 | 30%
3:00 | 66%
4:00 | 3%
So, I have a curve for each athlete for the probability he's running the marathon in x hours.
How can I evaluate the curve?
Background: Currently I'm doing my evaluation using RMSE i.e. I guess that he will run in 2:45h and evaluate the error.
This doesn't make much sense for me, since in reality he's running usually in 2:30 hours but he has some outliers which influences the mean downwards to 2:45 hours.
I would like to evaluate my curve, which encodes that I have downwards outlier with certain probabilities.