I am writing a software to help me train my speedcubing skills (specifically I want to execute 800 different sequences of moves fast) and there is one subproblem I am struggling with:
What kind of probability distribution can I use to model my times to execute a given fixed sequence of moves? It doesn't have to be perfect, but I want at least some probability distribution that seems reasonable. Here are my observations:
- There is kind of a lower bound. Even if it goes well and I make no mistakes, there is just a limit on how fast my fingers can turn.
- Most of the times are kind of close together, but sometimes I screw up and I am much worse than most of my "normal" times.
- Sometimes (rarely) I screw up very badly and really takes 5 times as long as usually.
- Sometimes it goes really well, but then it is only slightly better than most of my "normal" times.
Does any reasonable distribution come into your minds that I could use to model this?
Clarification: The fact that it is a sequence of moves is irrelevant. I consider each sequence as one individual unit and don't care which moves it consists of. (The reason is that there are so many ways to execute a move with your fingers and it really depends which moves come before and after and it's too complicated to model that. So one sequence of moves is just one unit)
There are 800 such sequences and I assume that they should have the same distribution, but with different parameters.
Note: I posted this on MathOverflow recently, but people told me it was the wrong place, so I came here.