I will explain this with a simple example as I don't quite know how to word this. I was taking a look at the statistics on the success rate of SpaceX landing their first stages. If you look at the complete statistics they have landed 136 of 147 attempts, giving a success rate of around 0.925.
however, this number does not reflect the current success rate, as one would expect the success probability to be increasing over time. In fact, if one assumes the rate of 0.925, their current streak of 62 consecutive landings seems incredibly unlikely to have happened.
My question is whether or not there exists a technique for analysing situations like this which would give an estimate of the current success rate. As of now I can think of just removing the first sqrt of the trials; however, this is just a guess of mine.