Eric wrote, "To reduce unfair effects of chance, you want to avoid any system that arbitrarily imposes a systematic pattern."
I suppose that's true as stated but it isn't true that a well chosen, as opposed to arbitrary, systematic pattern increases the 'unfair' effects of chance. I had in mind when I made up those patterns that the difference between a player and the next best player decreases the further you go into a draft. This is because one would expect that the amount of basketball talent in a population would follow something like a normal (bell shaped) distribution.
I put that to a test using simulated data, the upper half of the normal distibution - meaning I generated 512 normally distributed random data points, then used the top half for 16 rounds of drafting by 16 teams. The results are below.
The first line gives sort of a baseline - it shows the advantage the first team picking would have over the last if you set up a draft order then simply repeated that order for 16 rounds. The second line shows the effect of re-randomizing the order for each round - a big improvement over the first case. But notice that well chosen patterns of Reversing the draft order have an stronger effect than randomizing alone and, indeed, mixing in randomization with the pattern makes it less effective in some cases - it's less pronounced an effect than I expected. There is no absolute best pattern as it depends on the underlying distribution of basketball talent. I tried 'top third of Normal' and got about the same result however.
Average of 5000 trials each case,
FRpattern=F Rndm=N Hi-Low range=20.24
FRpattern=F Rndm=Y Hi-Low range= 7.91
FRpattern=FR Rndm=N Hi-Low range= 5.63
FRpattern=FR Rndm=Y Hi-Low range= 5.45
FRpattern=FRRF Rndm=N Hi-Low range= 5.21
FRpattern=FRRF Rndm=Y Hi-Low range= 5.25
FRpattern=FRRRFF Rndm=N Hi-Low range= 4.53 <- best
FRpattern=FRRRFF Rndm=Y Hi-Low range= 5.08
FRpattern=FRRRRFFF Rndm=N Hi-Low range= 4.73
FRpattern=FRRRRFFF Rndm=Y Hi-Low range= 4.83
FR pattern means a pattern of using a set draft order in Forward and Reverse order. So FRRF means use it one round in Forward order then two rounds in Reverse order then once again in Forward order. The whole pattern repeats until the draft is done. Rndm=Y means that you re-randomize the order after the pattern is complete and before it is repeated.