Best ways to evaluate randomness of a shuffled list

I'm trying to qualify the randomness of some shuffled list. Given a list of distinct integers, I want to shuffle it with different random generators or methods and evaluate the quality of the resulting shuffling.

For now, I tried to do some kind of dice experiment. Given a list of input_size, I select some bucket in the list to be the "observed" one and then I shuffle the initial list num_runs * input_size (always starting with a fresh copy). I then look the frequencies of the elements that fell in the observed bucket. I then report the result on some plot. You can observe the results bellow for three different methods (line plots of the frequencies, I tried histogramms but it would look bad).

The dice experiment over three methods

Reporting plots only is not formal enough, I would like to report some numbers. What are the best ways to do it (or used in academic publications).

Thanks in advance.