That's a very close approximation though. IIRC in the "real" performance rating there is another quadratic term that almost always gets rounded off anyway.

Based on the available information about CF’s rating system, this actually turns out not to be especially unreasonable.

Recall that the performance corresponding to a rank is the rating at which this rank gives exactly zero delta (thus, above this value, achieving the given rank would decrease rating). The Codeforces rating system essentially computes each participant’s expected rank by summing the probabilities that they lose to each other competitor (and adding one), increasing their rating if the participant’s rank is better than their seed and decreasing their rating otherwise. There is, of course, no finite rating at which a participant’s seed is better than or equal to first place, and thus, no rating at which a participant should receive zero delta for winning.

In practice, there are two reasons it might be possible for someone achieving rank 1 to see no change in their delta. First, CF requires rating changes to be integers, so competitors with extremely high ratings could receive a rating increase less than one upon winning, which would be rounded to zero. Second, CF’s anti-inflation metric could make it impossible to avoid a negative delta, given a sufficiently high initial rating. However, both of these scenarios require an extremely high initial rating vastly beyond what anyone has achieved in practice. Beyond being somewhat hard to calculate accurately, it’s unclear that this performance level would be especially meaningful, given that nobody has or ever will reach this hypothetical rating. As a result, reporting first place’s performance as infinity seems like a fairly reasonable decision to make, as it’s unclear that showing a performance level over, say, five or six thousand would be much better.