next, i will work on the individual countries and supply a variety of other statistics that may be fun or useful.

im confused regarding the percentages....can you explain the logic behind percents adding to be over 100% total?

e.g. in a two way draw, two players "won" as computed in the first statistic.

This is the solo wins by country, if I understand it correctly.
Russia: 20.3%
Turkey: 18.1%
France: 15.6%
Germany 14.3%
England: 14.3%
Austria: 9.8%
Italy: 7.3%

Nice!!

to explain the stats a little more:

the % of total wins is a calculation of all wins and draws combined by a country over the 1001 games and listed in order from highest pct to lowest, thusfrance came out ahead winning or drawing in 30.0% of all games.

the % of solo wins out of all games / out of all solos are the calculations of a country's solo win percentage first given out of the 1001 games followed by the pct of all solo wins out of all games that ended with solo wins (684). thus in this case, russia solo won 13.9% of all games and solo won 20.3% of all games in which a country took a solo victory.

the next set of percentages are the same as they are for the solos but for draws instead. france drew 19.3% of all games and france participated in 60.9% of all drawn games (amazing!)

the final country statistic series is a calculation of all eliminations a country had (both in drawn games and solo win games) followed by all eliminations a country had in which a country took a solo. austria came out as the biggest loser here by being eliminated 60.8% of the time out of all 1001 games regardless of whether it came through a draw or solo win and they were eliminated in 58.8% of all games in which a player solo won.

the last statistic is the percentage of all n-way draws first as a percentage of all games played followed by a percentage of all drawn games (317). thus, the highest percentage of draws was with 3-way draws in 15.2% of all games played (1001) and 47.9% of all draws ended in a 3-way draw.

the reason some percentages go over 100% is because of draws. for example if we take 3 3-way draw games as follows:

game 1: drawn by austria, france, italy
game 2: drawn by russia, france, turkey
game 3 drawn by england, germany, russia

this means that france and russia drew 66.7% of the time while the other countries drew 33.3% of the time. thus if we look at the stats to it, it will read as follows:

france: 66.7%
russia 66.7%
england 33.3%
italy 33.3%
turkey 33.3%
germany 33.3%
austria 33.3%

clearly this does not add to 100%. instead, it will add to 300% (100% calculated over 3 games).

the only way to get percentages of draws to add to 100% is to grant a partial win instead of a complete win by dividing the 1 win over the n-players thus each player in the games listed above would get 1/3 of a win.

in order to do that for this list, you would have to take the average number of players per draw (its a little over 3) and divide all of the percentages by 3.

if people are interested in seeing this manipulation of the percent, i can calculate it when i get time. it wouldnt take much.

According to convential wisdom of Geography is Destiny (http://www.diplom.org/Zine/F1999R/Windsor/dipmap.html) the stats should of been
Russia
France
England
Turkey
Austria
Germany
Italy

The central powers are hard if you suck, sure.

France is hard to kill. So if there is a draw, shes likely to be in it.

Nice work TruNinja. I would be interested in knowing percentages for games with pot buy-ins over 100 , or something along those lines. Because as Acosmist wisely quips, some countries suck if you suck, while other countries (like France) you can win with basically by accident.

France certainly is a pleasant experience, whereas Germany is a skill-tester. Austria is peculiar because you depend on convincing other people not to destroy you immediately, and few people pass up that chance at an easy early kill, but once you survive the holocaust Austria is a powerhouse. Proximity to the typical stalemate line and to the Balkans = GOOD TIMES

I think Turkey's good numbers can be attributed to proximity to the Balkans as well. Unlike Austria, Turkey is defensively very solid, so it doesn't suffer early crises as much, meaning it typically emerges from the Balkan Blitz (as I'll name the early struggle among Austria, Italy, Russia, and Turkey for regional control) alive. Being alive in the midgame + being near the Balkans = good times. And Turkey's position IS a lot better than Italy's.

I think Austria would be more of a force if she had better fleet capabilities. All armies limit expansion. Next to the early vulnerability this is Austria's biggest weakness.

Armies are very useful going south and east, though; not such a big deal if you can resolve the Italian issue.

France is the best country to play in high end WTA games.

@Tru Ninja, while your numbers ring true on draws, your explanation of the higher percentage is flawed.

Let's take your same three sample games and remove france from game 1, making it a 2-way draw.

game 1: drawn by austria, italy
game 2: drawn by russia, france, turkey
game 3 drawn by england, germany, russia

You logic of three games = 300% should still apply, but we'll show why it doesn't:

Austria draws 1/3 of the time
Italy draws 1/3 of the time
France, who used to draw 2/3 of the time now draws 1/3 of the time
Turkey, England, and Germany still draw 1/3 of the time each and Russia still draws 2/3 of the time.

That adds up to 8/3 or 266.7%. Where did the other 33.3% go?

I'll explain.

The real logic is that the total percent is based on the total number of a given type of draw/total number of drawn games then multiplied by the number of players in that type of draw (2 for 2-ways, 3 for 3-ways). So, in this example 1/3 of the games are 2-way draws and 2/3rds are three way draws. The total percentage is then 2*33.3333 (the 2 times the percent of 2-way draws) + 3*66.6667 (3 * the percent of 3-way draws) which equals 266.7%.

Apparently among drawn games there is an average of 2.9 players. I'd have thought it would be between 3 and 4 myself.

So using this table of numbers:
out of all games / out of all draws
3-way: 15.2% / 47.9%
4-way: 7.2% / 22.7%
2-way: 4.9% / 15.5%
5-way: 2.0% / 6.3%
6-way: 1.5% / 4.7%
7-way: 0.9% / 2.8%

Solos: 68.3% / N/A

So, your "out of all games" draw percentages should add up to:
(.9*7) + (1.5*6) + (2*5) + (4.9*2) + (7.2*4) + (15.2*3) = 109.5
(another 68.3% of the games are solo victories)

And your out of draw percentages add up to 344.8%

A check of this confirms:

% of drawn games out of all games / out of all drawn games
France: 19.3 / 60.9%
England: 17.2% / 54.3%
Turkey: 16.8% / 53.0%
Germany: 16.6% / 52.4%
Russia: 14.8% / 46.7%
Italy: 13.2% / 41.6%
Austria: 11.1% / 35.0%
----------------------------------
Total 109% / 343.9%

This is roughly correct when you figure in rounding errors.

I compute the average size to be 3.4 players in a draw? There is no way it is below three when the top 2 types of draws or 3-way and 4-way and together they hold more than 2/3 of all drawn games.

@ draugnar: thats what i was explaining is that you have to total all of the draws in a way that 2-ways are 1/2, 3-way draws are 1/3, etc. in my example, all of the draws were 3-way since its easier to show. if you look at the total number of the 317 drawn games, the average is somewhere between 3 and 4. (hence 344.8% total)

yes, TGM, the average is between 3 and 4. you can find this by looking at the actual numbers.

@draugnar, the reason your math is flawed is because you tabulated the example game 1 as a 2-way draw. you forgot a country :)

@ centurian, good point. i can certainly tabulate that given some time.

right now, im working on some austrian percentages on thru to the other 7 countries

Draugnar, Tru Ninja: Must have missed a country out or something.

No, Tru Ninja, That was to show that it isn't then number of games * 100% as you said. I intentionally took France out. Reread my post. My numbers are 100% accurate. I write statistical software for a living.

@Tru Ninja - read this sentence form my post. It shows why I removed France to show where you explanation was wrong.

"Let's take your same three sample games and remove france from game 1, making it a 2-way draw."

Oh, and your numbers are fine, it was just you explanation of the tabulation being over 100% that was slightly flawed. You "number of games * 100%) should produce a percentage in the 10s of thousands (assuming more than 100 draws which I'm sure there are).

ah, ic. its either cuz its been late or lack of sleep from baby. i see what youre saying.

Probably a combination of both. Congrats on being a dad (assuming you are dad, not mom or <gasp> sibling).

yes, a two-time dad. i couldnt handle being a mom. something about another human being syphoning liquid from my nipples does things to my mind.

I'm just making sure this is in my replies.