hammy wrote:As you wish
So if you want to win lots of games take armies with 16-17 or 12-13 BGs but not 14-15 or 18+

Thanks for posting, hammy, and producing the fascinating discussion which allows me, cut-off in no-gamer's land, to enjoy wargaming life vicariously.
I'll beg your indulgence to play devil's advocate with your data / statistics since I think I know a thing or two about this kind of stuff.
First, I'm sure I don't need to caution anyone that correlation does not necessarily mean causation. True we have the anecdotal experience of tournament players, but it seems that positions have been staked out (even if no vampire are in sight) and data viewed with an eye to confirming these positions (aka - confirmation bias). Fortunately, we have the rules / tournament scoring to provide reason for causation - e.g., higher breakpoint for larger armies, maneouvreabiltiy of armies of small size BG, etc. My own view on this regard are that, in the hands of a competent player, 2 BG have the upper hand over one double size BG since one of the small BG can fix the large BG frontally while the other attacks the flank.
There are also other factors to consider. Are these results "static" (i.e., would we find the similar results a year ago or a year hence). Perhaps there is a question of fashion - one player has success with a "swarm type" army which means there's a spate of "swarm" armies followed by a demise in "swarm" armies.
All of which says that game results are due to a complex set of factors. However, it's useful to generate the discussion as the most important issues are the perceptions and enjoyment of the players.
I did some playing with your numbers – as posted vice the raw numbers. I noted that your percentages are percentages within each BG size series. It would be useful to know how many data points there are in each series as the graphs actually look quite variable making it questionable whether or not there are statistically significant differences between the series – with the exception of the 11 minus BG series.
Anyway, using the midpoints of the scoring categories and 22.5 for the top category I computed averages and slopes per series. What is shows is that overall the dominant trend is that fewer players win with higher scores – not surprising. The expected / average score for each series (using the percentages as the distribution probabilities) is:
11 minus BG = 9.7 pts
12-13 BG = 11.0 pts
14-15 BG = 10.9 pts
16-17 BG = 12.6 pts
18+ BG = 11.2 pts
Not much to choose amongst the 12 plus group. Maybe 11 minus BG suffers but its difference from the average across all groups, which, weighting each group equally, is 11.1, is less than the difference for the 16-17 BG group (i.e., 1.4 pts versus 1.5 pts). Either there is no significant difference or 11 minus BG are not game winners and there’s something unique about 16-17 BG which might be due dominant troops types in those armies.
Looking at the slope (i.e., the decrease in the percentage of players per increase in points scored) we get…
11 minus BG = -1.1% per pt
12-13 BG = -0.6% per pt
14-15 BG = -0.7% per pt
16-17 BG = 0.0% per pt
18+ BG = -0.5% per pt
Again, except for the two BG groups mentioned, not much to choose amongst the rest.
All of which shows that if you torture the data long enough it will say what you want.
Thanks for the vicarious fun.