Kinematics
Hero
Not correct. There is a correlation between hits and crit (though I wouldn't say a dependency), but the individual attacks are completely unrelated to each other. There is no dependency between attacks.Your math is a nice simple approximation, but it is simply not correct for calculating the actual expected value. That's why I got a different result compared to doing the simple calculation you did above--because the number of crits you can potentially get depends on how many hits you already got (since you cannot crit if you missed!)
If you make one attack each turn, then after four turns you have exactly the same damage distribution as if you made four separate attacks on one turn. The probability of any individual attack does not influence the probability of any other attack, nor does the chance of hitting have any bearing on the crit totals (though it will influence what percentage of your total damage comes from crits). So all you need to do is examine the damage results of a single attack and multiply that by 4.
You can, of course, examine how the number of crits are distributed if you want.
0 crits: 95% * 95% * 95% * 95% * 1 combination = 81.450625%
1 crit: 5% * 95% * 95% * 95% * 4 combinations = 17.1475%
2 crits: 5% * 5% * 95% * 95% * 6 combinations = 1.35375%
3 crits: 5% * 5% * 5% * 95% * 4 combinations = 0.0475%
4 crits: 5% * 5% * 5% * 5% * 1 combination = 0.000625%
And then use that to calculate what the average amount of crit damage you'll see over 4 attacks would be:
Average crit damage = 5.5
81.450625% * 5.5 * 0 + 17.1475% * 5.5 * 1 + 1.35375% * 5.5 * 2 + 0.0475% * 5.5 * 3 + 0.000625% * 5.5 * 4
= 0 + 0.9431125 + 0.1489125 + 0.0078375 + 0.0001375
= 1.1
Alternatively: 4 attacks * 5% crit chance * 5.5 damage per crit = 1.1