No it isn't.
There's only one random element involved in the final hit: The dice rolled to deal damage.
Events that are not final hits are not relevant to the question.
Let's say your monster is 8 hit points away from death, and you're attacking with a longsword, and have +4 to damage, and you hit. The chance of bringing him to exactly 0 is 1 in 8, because there's only one outcome that can do that. If you have +5 to damage? 1 in 8. If you have +3 to damage? 1 in 8.
If he has 1000 hit points to start? 1 in 8. If you have +34 to attack? 1 in 8.
You don't count attacks that don't hit because they don't deal damage, and therefore are not killing blows. The math is surprisingly simple.
Yes, I wasn't arguing that a monster with 8 hp is going to have a 1 in 8 chance of being dropped to 0 hp... I was proposing that since the variables below are never constant, determining the likelihood that it would happen in a random encounter is hard.
Variables include
Player Weapon
Player Modifiers
Monster HP
Monster Modifiers
The only thing you could do is round up all of the Level 1 monsters and find an average number to determine HP
Say it was 30HP for example
You then would need to find the average weapon dice that a player would have based on all possible options (which would mean finding an average for each available class and then averaging this out across all classes)
Say it was a D8 for example
You would then need to determine what modifiers a typical player would have... this could most possibly be determined by picking the most appropriate build for each class (high str for a fighter etc etc) and then take the average + Damage modifier for each and perform an average
Say it was +6
In this example you could say that the average damage was 1D8+6 (7-14, 11 avg)
With an average monster hp of 30, the first hit would bring it to 19, next to 8, - with 8 as the final hit value, and the damage die performing at 7-14, the chances of dropping the monster are 1 in 7
Now, I havent done the above research and would imagine it would be quite difficult to do it... Not to mention that an average cross section of each level would need to be performed as well as consulting feats and other modifiers that give you bonuses to damage.
You could perform the test on a 1st lvl fighter vs a 1st lvl Kobold if you wanted to, however if someone asks the question
"What is the chance you could drop a monster to exactly 0hp" the circumstances surrounding what may or may not happen in any given encounter are so vast that calculating this with a simple formula is not possible
If you ask
"What is the chance that a monster at 5hp will drop to 0 when I am wielding a D12 + 3 weapon?" - You CAN answer this one since you can take 2 comparable variables and do the sum (which in this case would be 1 in 15)
