Answer
nominal level;
ordinal level.
Yes. It changes.
Work Step by Step
In the first case, the number works like a name. So, it does not allow for the values of the variable to be arranged in a ranked or specific order. The number 1 is not better than number 2.
But in the second case, the number 1 means the best, and so on. The players are ranked by the number. But the difference between the numbers has no meaning. So, now, the variable is measured at the ordinal level.
