ECDSA signatures are not deterministic. That is, random information is used in calculating the signature for a piece of data. Approximately how many unique signatures exist for a piece of data?
Another way this question might be phrased is: if I continually sign the same piece of data using random multiples of the generator point then how many signatures (on average) will I have to generate before finding a duplicate signature?
And finally, if instead I start with a random multiple of the generator kG and then sign using (k+1)G, then (k+2)G, ... then will I ever produce the same signature?