ADLG: Yuan Chinese Super Army?

In 2018 and 2020 I used the Art de la Guerre (ADLG) results database to probe the perennial question of super armies.  My starting definition of a super army was an army that, in the hands of almost anyone, will deliver an above average number of victories.

In ADLG games the number of variables involved in determining the outcome is huge; player skill, list choices, terrain deployment etc etc.  So to get to the influence of the army list alone I looked at a very large number of games to avoid the perils associated with small data sets.

Then last week I received an email from Mike Guth politely disagreeing with my conclusion and he sited the success of Yuan Chinese armies at the World Championships from 2016 to 2019.  

This piqued my interest.  Is there something special about the Yuan Chinese in a two list competition like the World Championship?  I began to dig.

In my research I came across the Madaxeman Podcast from 2019 which tackled the same issue.  After listening to the show I began to wonder if I had missed something?  In the end I had another look at the data.

Qualitative Approach
If you were to describe the World Championship headline results for 2016-19 qualitatively you might say Mike had a point: 

• The Yuan Chinese have won this competition three times in four years in the hands of three different players; with one of the winners coming second in the year when the Yuan Chinese didn't win the competition.

In all four years there were at least two players using Yuan Chinese armies and five players using Yuan Chinese in 2017.  So drawing conclusions about the Yuan Chinese list based on the number of winners & runners up alone is only part of the story.  Looking at all the results shows:

• Other than the competition winners and one runner up, the next best placed players came 10th and 12th.  
• Another seven players came in the bottom third of the table including one placed last (2018).

From these points one is tempted to draw the conclusion that the Yuan Chinese list is an "all or nothing list".  However, the format of the competition and the skill of the players' has clearly played a large part:

• The three winners are all exceptional ADLG players: they are currently 1st (2018), 4th (2019) and 11th (2016) in the 2020 rankings.
• The players who came 10th (2016) & 12th (2019) are also exceptional ADLG players and are currently ranked in the top ten.  

Looking at all of the above it is perfectly reasonable to draw the conclusion that the Yuan Chinese list isn't inherently stronger than any other and that it is at its best in the hands of a skilled and experienced players.  This is the exact opposite of a "super army".

So far I have used only qualitative points to suggest that the Yuan Chinese list is not the killer army it first appears.  This is deliberate as I wanted to illustrate the weakness of using headline or qualitative data alone to "analyse" such a complex issue. 

Now I'd like to use a little quantitative data to look at the same issue.

Quantitative Approach
In ADLG the performance of a list is measured by its efficacy (or efficacity as the French style it).  This is calculated by a simple formula.  The number of wins is added to half the number of draws and expressed as  a percentage of the total number of games played.  To compare results:

Data set	Efficacy	Sample size
Yuan Chinese, Worlds (2016-19)	54.8%	73
Yuan Chinese, All time (2020)	57.6%	400
Late Medieval, All time (2020)	51.0 +/- 6.5%	7,574
All lists, All time (2020)	49.0 +/- 9.1%	40,545

This table suggests: 

• Using the all time data, the efficacy of the Yuan Chinese list is higher than the average for all late medieval lists and higher than the average of all the lists in the 2020 ADLG database. Even so it is still within one standard deviation of the latter.
• The efficacy of the Yuan Chinese list at the World Championships (2016-19) is lower than its all time rating but still above the all lists, all time average. It too is within one standard deviation of the latter.
• As discussed above the quality of players using the Yuan in the World Championship may well account for the small differences in efficacy not least because the small sample size means it is easily skewed by one or two "extreme" results.

The quantitative performance of the Yuan list is a long way from making it a super army.  Numerically, it is above average, and so is in the running for being classed a super army by my starting definition sited above, but that's not the whole story.

An ADLG efficacy between 51-60% is not uncommon and the difference from the average is not really that large given the variation seen in the data.  Specifically, the Yuan Chinese list is:

• One of 18 (of 46) late medieval armies, and one of 97 across all periods, with efficacy between 51-60%.  There are 5 late medieval armies with efficacy in the range 61-70% and none below 40%.
• One of 97 (of 271) armies across all periods with efficacy between 51-60%.  There are 19 with efficacy above 61%.

Overall, the Yuan Chinese list fits readily into the efficacy distribution of ADLG armies where the vast majority have an efficacy between 41-60% as shown below:

Closing Remarks
I hope the qualitative discussion of data has illustrated the pitfalls of focussing on headlines alone and highlighted that there are many more factors at play other than the choice of army; not least a player's ability.

When dealing with small sample sizes quantitative analysis can be tricky.  I'm aware that the quantitative data could be marshalled in support of the opposite conclusion I have drawn depending on how strictly you define "above average" but quantitatively the efficacy of the Yuan Chinese list is unexceptional and similar to a large number of other army lists.

Clearly, the Yuan Chinese list is a strong one and offers genuine advantages to skilled and experienced players but not to all players as the data from the World Championships shows.

On balance I think it would be wrong to class the Yuan as a super army. However as the Madaxeman's podcast points out that doesn't stop players learning from how others play the game.

Resources

• Yuan Chinese - The Worlds best 2-list ADLG list?
• Yuan Chinese at the Madaxeman's wiki pages (includes lists).
• ADLG Competition Statistics