In this plot:
We look at the distribution as an histogram (through the stacked bins). But to confirm there is actually a trend, it is better to look at some statistical metric. We could use box plots but it would not be pretty to see the evolution. We can just plot the mean and median
We observe exactly what we expected. At the beginning, the shortest paths length increases because more paths are added without shortcuts and as n increases, we don’t add a lot of path but we add connectivity which reduces the shortest path lengths.
We could do the same plot but seeing how many players paths would be still possible. Even further, we could see if it is related to a player finishing or not. If he has to scroll a lot to finish a lot, he might abandon earlier.