ADLG: Size Matters

In my last post I looked at army performance under version 4 (V4) of Art de la Guerre (ADLG).   I made the point that, as far as the data analysis goes, size matters:

• For V3, with 40,545 records, It's easy to see the long term trend: namely that the more an army is used, the more its performance (efficacy in ADLG-speak) tends towards 50%.
• For V4, with 8,675 records, the situation is less clear and probably will be until the number of records has increased significantly.

The penny drops
Whilst writing the previous post I had cause to revisit the data sets for V3 from 2018 & 2020 and check a few things.  It then occurred to me that I might be able to provide specific examples of the "50% trend" by comparing 2018 with 2020.

If you're not a fan of chart and data posts, even if they are about wargaming, look away now.  Otherwise read on!

2018 (V3) & 2020 (V3)
After a little extra analysis I was able to produce some charts that illustrate the "50% trend" for ADLG V3.  The following are for the Late Medieval period:

This shows most armies clustered either side of 50% with a few outliers.  Two years later with 58% more data the chart looks quite different:

All of the low frequency outliers have gone.  For the low scoring armies either their luck changed or they were used by better players.  Either would improve their average efficacy.  For the high scoring armies the opposite has happened.

If you like your date in tables:

Late Middle Ages
Year	2018	2020
Played	4,792	7,574
Avg Efficacy	51.0%	51.0%
Std deviation	8.9%	6.4%
Armies played	44	46
Games / army	109	165

The above neatly illustrates the "50% trend" and also raises a couple of interesting points.  As the number of records increased 58% from 4,792 to 7,574:

• The average efficacy didn't change.  So with this data, the average doesn't differentiate between the distributions at all well.
• The standard deviation is far more descriptive as it did change (reducing from 8.9% to 6.4%), reflecting the tightened distribution of the later data set.

As an aside, it's interesting to note that nearly all 48 Late Medieval V3 armies had been used by 2020.

In case you were wondering about the other periods, I have checked the Classical, Roman, Dark Age & Feudal periods and the changes between 2108 and 2020 follow the same pattern (if a little less stark).

2020 (V3) & 2022 (V4)
It's really far too early to say much about V4.  Nonetheless, here's a quick look at the corresponding Late Medieval data for V4:

As expected the V4 distribution is broad, much broader that the 2020 (V3) data, and the standard deviation reflects this.  Even so the average efficacy is essentially the same:

Late Middle Ages
Year	2020	2022
Played	7,574	1,498
Avg Efficacy	51.0%	50.5%
Std deviation	6.4%	14.0%
Armies played	46	42
Games / army	165	36

Note: so far only 79% of the 53 Late Medieval V4 armies have been used compared to 96% of the 48 in V3.

Closing remarks
I hope this analysis helps you visualise the "50% trend" under V3 and the state of the data for V4 armies.

The question of super armies, and whether the "50% trend" applies, in ADLG V4 is as yet unanswered and will remain so until the size of the results database increases significantly.  Given the popularity of ADLG, I am sure this won't take long.