quote="peterrjohnston"]There are certainly less armies in the smaller and larger BG series. I would say this is for obvious reasons. First, at 800AP, the intention of a lot lists seems to be that armies should be around 11-14 BGs (Nik?). And there are many popular lists for which it is hard to get above 12/13 BGs, especially in the medieval time period. 100YW English is one, Dailami another, although see Dave's Santa Hermandad Nueva Skythian on madaxeman.com for an example of how to get to a lot of BGs in late medieval...

The second is that now players realise <=11 BGs is a bad idea at 800AP.
However, there are some good armies which can easily make 16+ BGs and function well. Dominate is obviously one, Christian Nubian another, and many of the skirmish steppe armies.[/quote]
I was thinking about this too as the choice of BG is conditional on the choice of army (or is it the other way around?

) which complicates things as we now have to separate the influence of army from BG size from the data. I suppose if someone paid you money to do it one could set up controlled experiments with a sampling of armies , same set of players with armies designed with large / small BG's but that'd be no fun unless it was a lot of money.
peterrjohnston wrote:When I did the original analysis on the Italian results, I was expecting something like a normal distribution of scores, but with the added complication of a rise in the 20-25 scores because of the +5.
I wouldn't expect normal distributions in general since a number of things are conditional (e.g., game designed to suit a particular range of BG, influence of army type on numbers of BG, prior success with a particular army, etc.) and not independent.
peterrjohnston wrote:I normalised the data for the obvious reason of being able to compare the ranges on the same graph.
That’s understandable, but, as I’m sure you know, that means there’d be less confidence in the results for the bins with lower numbers….add to that the possibility of fewer army choices in those bins.
peterrjohnston wrote:For this reason I didn't start doing anything more sophisticated in the analysis (as well as the fact I don't have a great deal of time to devote to this!

).
That’s understandable – see “lots of money” statement above. One of things I’d consider doing is a principle component analysis using a variety of factors (e.g., like the suggested fields above). However, I think the bigger issue is player perception and enjoyment. If people are really concerned about this as an issue feedback surveys are an idea…at least in Spain.
peterrjohnston wrote:What do you mean by "slope per series"? If it was a linear regression, that would be wrong, the relationship is not linear, the +5 complicates the relationship. Without this I would probably expect a normal distribution of scores, not a linear one.
Yes, I did use linear regression but I did not mean to imply the relationship was linear. I only had the graph above to work with and just wanted to get an idea of the trend. Estimating a trend and de-trending data is, for example, a common practice with something like Fourier analyses – but that certainly doesn’t imply linear relationships. And, yes, the +5 should be removed first. I’m not sure if a normal distribution is right. There could be “fat tails” as a result of the factors you mention that skew results or because of changes in time with changing experience, preferences, etc. of the community.
I think it’s a real challenge this case (i.e., disproving a null hypothesis such as “numbers of BG has a significant influence on game scores) as it is complex, which BTW is what makes the game enjoyable – for me anyway.
Still I think it was interesting and useful to see the graphs. However, all I can see that’s reasonably substantiated by the data is that “11 or fewer BGs” is a bad idea.
Cheers
Paul