I tested on the shooting range dummy with no BAR bonus and no relics. The chance of triggering a DoT with a Maliwan shock sniper is close to the info on the weapon card modified by tree skills.
I fired 312 rounds that only did splash damage. Of those, 216 electrocuted the target. My skill, More Pep, “added 20%” (really a multiplier of 1.2) to the weapon’s elemental chance of 52.7%. Thus 52.7% * 1.2 = 63% expected chance.
216 / 312 = 69% experimental chance.
If I shot 1000 rounds, this might return 630 positives.
I then tested a Maliwan fire SMG. It has an elemental chance of 18.8%. More Pep increases that to 20.6%.
I fired 330 rounds that only did splash damage. Of those, 18 burned the target.
18 / 330 = 5.5%
This is abnormally low for a good random number generator! I suspect the splash on fire weapons (or SMGs) has a fraction of the bullet’s chance to trigger a burn DoT. This might be intentional because burn DoTs can apparently stack, while electrocution DoTs don’t appear to stack.
I also tested a shock pistol, firing 100 times. The splash triggered electrocution 23 times, exactly the weapon card’s rate adjusted for More Pep (23%).
My last test was with the Snider again. The chance of a DoT for a direct hit is extremely high with a Maliwan shock sniper. I fired 216 rounds, and 214 of those electrocuted the dummy! This is a greater rate than expected. Failing with both DoT opportunities should be 0.37 * 0.37 = 0.14 or 14%. If this assumption were true, I’d expect to see 20 to 30 failures, not just 2! Maybe there is an unknown bonus added to the splash’s DoT chance when the bullet hits the target.