Dip2000    Game Ratings    Home

Last Update: 11/02

Draw Distributions

Of the 189 games finished on the Dip2000 website, 94 have ended up in draws ranging from 2 to 6 victors.  So who ends up drawing with whom?  Below are tables of the number of times each pair of countries shares in the same draw.  Certainly when picking allies a player should take into account more than statistics but hopefully these tables will be able to guide players by showing which alliances are more likely to succeed than others.

2-way Draws

We will start with 2-way draws.  There have only been 18 of them so ultimately the following data will not be too significant.  However, trends have begun to form.

With so few games to analyze, the statistics not lying on the extremes should be disregarded due to possible statistical error.  Therefore we will focus only on the highs and lows.  Germany has shared in the least 2-way draws with 3, and Turkey the most with 7.  The highest on the board is the E/T draw, which has occurred 3 times.  This makes 1/6 of all 2-way draws counted so far, and it is obvious that the E/T alliance is a formidable one despite any statistical uncertainties.  This table is also useful for seeing what alliances don’t work in the long run.  There are a lot of zeros on the board but hopefully with time they will fill up so the really bad alliance pairs will show.  Right now we have A/E, A/T, E/G (surprisingly), E/R, F/I, G/I, G/R, and I/T.  I’ve seen many FtF games with powerful E/G alliances and I think there will be at least some E/G draws down the line.  The Juggernaut, R/T, is also up there with 2 recorded draws.  A/I and I/R both also post 2.

3-way Draws

First I should explain how the rest of these tables will work.  Because in 2-way draws countries had only one partner the total number of draws could be calculated by just adding the columns.  3-way draws have 2 partners and so after summing up the columns you then must divide by two.  For 4-way draws it will be by 3, etc.

So the 7 in the A/E boxes mean that in 7 3-way draws, both A and E have been a part of the draw, while the 17 at the bottom of Austria’s column means that Austria has shared in 17 3-way draws.  Hope that makes sense.

42 3-way draws have been recorded so it will be easier to make definite conclusions on this table.  First look at the total number of draws.  Turkey is again near the top, though France has the most with 24, sharing in more than half of all 3-way draws.  Germany is starting to show a bad trend in drawing potential with the least number of draws again.  This time it is by an even more significant amount.  Of 42, there has only been ONE time when Germany and England have shared a part of a 3-way draw.  In fact the four lowest numbers on the board involve Germany, with A, E, I, and R.

Highs: France and Turkey seem to do very well together, as more than 1 in every 4 3-way draws include both F and T together.  The fact that there has only been one F/T draw (2-way) but so many 3-ways may be because France and Turkey need a common enemy so a full-scale war in the Mediterranean does not erupt.  Second and third place also belong to France, allied with Italy and Russia.

4-way Draws

Though only 23 4-way draws have been completed, skewing of the statistics will be lessened since each four-way draw produces 6 pairs, and larger numbers equates to sounder statistics.  The trend breaker in this table is Germany, who leads the countries in 4-way draws.  Germany is kept out of the 4-way draw less than one of every three times.  This is sharp contrast to the two German last place finishes in the 2/3-way draw categories.

Why??  Here is my view: 4-way draws usually occur when 2 countries from the Western Triple match up with two countries from the Southern Block.  From the table it looks as if England is often the odd-man out in the Western Triple.  The F/G square boasts the highest number in the table with 10, and both France and Germany score well in number of draws.  In the Southern Block the numbers look pretty even among the four countries, and any combination is equally likely to face whatever comes from the west.  In looking at the 6 pairs possible from AIRT (the Southern Block), all the numbers are within the range 4-6.  So it works out well for Germany if two countries of the three in the Western Triple are left alive, but in 2/3-way draws this does not happen and being a central power Germany gets the axe.  That is the best *I* can do, other explanations are welcome.

5-way Draws

There have only been 9 5-way draws.  Looking at the table there is not too much of significance anyways.  One thing that caught my attention was that while England was usually the odd-man out in forming alliances for 4-way draws, England does just fine in 5-way draws.  There has only been one 5-way draw in which England was not a part.  However, I should probably wait for more definitive statistics before trying to explain why this is so.  One thing almost for certain is that F/I do bad.

6-way Draws

Well there have only been 2 6-way draws I don't know why I bothered to put this up in the first place.  England has been left out of one, and Italy the other.  Whether this is due to the countries themselves or just chance is impossible to tell.

Totals

Ok so is there anything conclusive when you put them all together?  Here is the compilation table.

Points are calculated based on the system that each game is worth 1 point and each drawer gets an equal share of that point.  

Points / 100 estimates how many points each country would have if 100 games had ended in draws.

Drawers means the average number of countries involved in a draw.  For example, in a perfect world, Austria would constantly be involved in 3.33-way draws.  This statistic was derived simply by dividing # of draws by total points.

For all those visual people then here is a graph showing the percentages in which each country is involved in a certain type of draw.

From looking at the graph the differences among the countries in the Total category is not very striking.  What is significant are the differences when you split up the countries and the types of draws.

Points by pair.  This is the most important table.  From the point system described above this graph tallies up the points each pair of countries has gotten.  It is also adjusted so that 100 games have been played.  This is done so we can track the trends in each pair as more games are played.

It took me a while to figure out how the Total points here were different from the total points in the previous table.  Here it is: For a 3-way draw, a country will get 2/3 points added to their total since they have two partners.  A 5-way draw would add 4/5 points.  This is the opposite of what we want, and so the last line is a statistically misleading line.  I didn’t want to leave it out since if someone added up the numbers themselves they may think Austria is the best drawer, but in fact Austria just has a larger number of group-draws (a bad thing).  Good for you if you figured the difference out by yourself as it certainly took me a while.

So what have I gotten from all these tables?  Some points of interest:

• Germany is indeed a poor drawer, and by a sizeable margin Germany shares in larger draws than the other coutries (3.57-way draws as opposed to second worst Austria - 3.33-way)

• On average Turkey draws with the fewest number of people, though France, Italy and Russia are close by

• Perhaps the E/G alliance is not as good as I thought, or maybe it is just good in FtF games.  In Dip2000 games it is just horrible.  The E/G square posts the lowest number on the board.

• Highest number of draws goes to F/R.  The two have Germany and England as their common enemy, and have an obvious alliance potential.

• Highest score goes to E/T.  The three 2-way draws really helped them out.

• There are 21 pairs and based on the above data I will try to accurately separate the pairs into 3 groups of 7.  Pairs are ranked within categories as well, from best to worst.
      o       Gold: E/T (7.13), F/R, F/T, A/F, I/R, F/G, A/I
      o       Workable: F/I, G/T, I/T, A/E, E/I, R/T, A/G
      o       Stab without Prejudice: E/F, A/R, A/T, G/I, E/R, G/R, E/G (3.46)
      o       The productivity of E/T more than doubles that of E/G

• France and Turkey are both good drawers, both being involved in more than half the draws

• Here is the draw ranking: FTIAREG and the solo ranking: RGFIAET.  Good soloists are rarely good drawers, and the other way around.  England seems to be the biggest loser.

From the points by pair table we can see which countries are most important to which in terms of looking for draws.

France is the most important country to 3 powers - Austria, Germany, and Russia.  Russia is either first or fifth to all other countries.  Turkey and Austria are last on one another's list, as are England and Germany.  France and Russia are on top of one another's list, as are England and Turkey.  Remember that this chart is only based on draws and not on solos.

Finally, something that may be of interest.  These are common draws.

2-way Draw: ET(3)
3-way Draw: FIR(4), AEI(3), EFT(3)
4-way Draw: AEFG(2), AFGT(2), AFIR(2), EGIT(2), FGIT(2)
5-way Draw: AEFGR(2), AEIRT(2)

Not much more to add.  Other revelations will be left to the reader.  Updates to the text will be made as points of interest pop up though numbers will be updated monthly (hopefully).

top
John Nham