Why is the average shot damage global statistic so high?
Solution 1:
Lets look at the nice weapons table on the XCOM:EU Wiki. The average damage for any weapon is nowhere near 16.xx. Even with the 100% bonus of HEAT ammo and similar abilities, it would be difficult to get a single weapon to consistently generate a damage of 16+. Let alone, average ~16+ across all weapons.
If we assert that damage above 16 is rare in vanilla XCOM:EU, that can suggest that modding maybe responsible for biasing the World's average damage.
Solution 2:
The World Statistics are a little bit borked because there is little validation done of the records submitted (just look at the tens of thousands of "average" scientists).
While it's impossible to determine how this statistic is calculated without delving into the code (do Rockets count as shots? Is Rapid Fire one "shot" or "two"), it is possible to do More than this in a single shot:
A heavy with HEAT ammo shooting at a Shredded target, for instance, can easily do upwards of 30 damage. Plasma Snipers and Crit-Specced Assaults can also break into the 20s, if properly set up.
So while my bet is on mods for many of the "outlier" statistics, it is certainly plausible for average damage to be that high, especially if Rockets count as a single shot.
Solution 3:
It is possible that people could just avoid ending the game for a long time and keep running more and more missions with maxed out troops.
Taking numbers from: http://www.ufopaedia.org/index.php?title=Damage_(EU2012)&oldid=45621
An Assault Colonel with Killer instinct and Bring 'em On and an Alloy Cannon will do 16-30 damage (crit presumed) depending on the number of targets and the order these modifiers are applied.
(15 + 5) * 1.5 = 30
(15 * 1.5) + 5 = 27
(10 * 1.5) + 1 = 16
An Assault Colonel with Killer instinct and an Alloy Cannon does 15-20 damage (crit presumed).
A Sniper with Headshot and a Plasma Sniper rifle does 19-21 damage on a crit.