(not D points...)
that averages at 6.85 per player, but considering 12, 6 and 4 are the most likely scores, below par would be anyone with 4 or less, par about 6, above par 8-12 . But i wonder if any players have managed (something like) 3x4-point draws and a solo in their last game, scoring (an achievable) 24 ...

http://phpdiplomacy.tournaments.googlepages.com/leaguesautumn2008

Flashman got 2 wins out of 4 games in one of the divisions, which is pretty amazing.

Even more impressive, BartDog42 got 3 wins out of 4 games.

http://phpdiplomacy.tournaments.googlepages.com/leaguesspring2009

i'll work out the distribution in a minute...

http://www.maths.tcd.ie/~orathaic/files/distrib.jpg

i like the magic numbers (like in chemistry where you get lower energy levels for certain number of electrons, or nuclear physics where full nucleon levels give you specific stable atoms which aren't radioactive) You get peaks at 0, 3, 12, and 15...

Of course i've done some messing with the data, where 5 games have been played i have reduced the points by 4/5ths. the intervals are 0-1, 1-2... so the peak at 3 is actually a lot of results of 2.4 (i've also merged results from players who played less than 4 or 5 games with their replacements, so all scores are out of 4 or 5 games...)

still as i suspected the there is a peak at 12 with (as it happens) 12 players getting exactly that score. doing a cumlative distribution, and given 3 of 7 players are promoted(~42%), that is passed 7 .
first place is 1/7 (14%) requires on average 15 . (not including ties, i'll look at supply centres later)

quit drooling.

drooling? i think you'll find i just did a fairly simple analysis of a leauge i'm playing in. I'm not sure where drooling comes into it. Enjoy my results.

"given 3 of 7 players are promoted"

That isn't totally true.

In Premier: 0
A:3
B1/B2: 3 total = 1 per league and the better second placer.
C1/C2/C3: 6 total = 2 per league.
D1/D2/D3/D4/D5:9 total = 2 per league less the worst second placer.

Of course that all goes out the window with withdrawals.

I have the dubious honour of having the league win with fewest points scored (11).

This isn't particularly useful, I don't think, but the mean and standard deviations for the number of points owned by each place:
Place: Mean, Standard Deviation
1st: 18.82, 6.39
2nd: 11.82, 1.96
3rd: 8.27, 3.76
4th: 4.42, 2.31
5th: 3.29, 1.45
6th: 1.20, 1.33
7th: 0.18, 0.57

(Based on last season, I don't think using the season before is that valid)

tbh, because the spread reduces as you go higher up the leagues, the above isn't very useful either. It would be better to wait for about 3 more seasons so you start getting enough data to work out what's going on at different levels (Premier and A; B; C; D).

yeah, sorry, 9 total in the D leagues is right, don't know what i was reading...

in A it is 3/7 ~ 7 pts
in B it is 3/14 ~ 12 pts
C it is 6/21 ~ 11pts
and D is 9/35 ~ 12 pts

not counting withdrawals of course.

ok, i did another analysis

http://www.maths.tcd.ie/~orathaic/files/pics/dip_dist.jpg

This is based on the assumption that all results are equally likely. randomly picking 30002 games. (because i think the total number of combinations of results is too high)

I note in this case i have randomly gotten one 36 point result, but i did three random samples and didn't get any 36 point results from those.

The other thing to note is that a completely random result set there are considerably lower 0 point scoring players (I think some real players give up, or if they are outmatched they will score badly in all 4 games) Also the random case has lower percentages for 12 and 15 point scores with much higher chances of 5-9 point scores - 5-8 point scores were in the original anlysis less likely that 1-3 this being another case of bad player doing badly throughout their league.

sorry, that is 30,002 random four game leagues. (which is 210,014 players playing 840,056 games)