Does self-rated performance predict objective performance over and above other-rated performance? Context:
I was at a talk today where data was  presented  where a group of sports people ranked their own performance and everyone else in the group. This enabled self-rated performance to be correlated with the average of other-rated performance. The general observation was that there was a strong relationship between the two variables, but that where self-rated performance deviated from other-rated performance, people tended to rate themselves higher.

This raises the question of what this self-other discrepancy represents.
One answer is that people have a self-serving bias. 
Another answer is that people have unique information about themselves.

Question:
Thus, I'm interested in studies that have looked at what self-rated performance predicts over and above other-rated performance. In particular:

To what extent does self-rated performance predict objective performance over and above other-rated performance?

I imagine these findings would vary as a function of a range of factors including type of task, number of rated used form the other-rating, and so on. But at first instance, I'd be interested in any empirical examples.
I don't know of a study that tries to answer your specific question but you might want to have a look at illusory superiority, "a cognitive bias that causes people to overestimate their positive qualities and abilities and to underestimate their negative qualities, relative to others" (wikipedia).

I can especially recommend the paper by Dunning and Kruger (1999): Unskilled and unaware of it: How difficulties in recognizing one's own incompetence lead to inflated self-assessments (also the winner of the ignoble price for psychology, 2000). In this paper the authors show that people who are competent in a certain domain are pretty accurate in predicting their performance in this domain (compared to objective standards). On the other hand, people who are incompetent typically overestimate their performance (i.e., predict to perform good, whereas they perfom poorly). This overestimation is mainly driven by their lack of knowledge about that domain. If they are taught that they are poor performers, their prediction goes in line wit their actual performance. 

These results could explain your observation of self-other discrepancy, as others might have more knowledge about how to accurately predict performance than the poor perfomers who over-rate their performance.

Reference:

Kruger, J., &amp; Dunning, D. (1999). Unskilled and unaware of it: How difficulties in recognizing one’s own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77(6), 1121–1134. doi:10.1037/0022-3514.77.6.1121