These are mistakes which almost everyone makes, and, while often not a big deal in the spur of the moment, when trying to mathhammer something out they can lead to wrong conclusions.
The first problem is that people miscalculate expectation. In a binomial distribution (which is what one normally uses for die rolls) the expectation is n*p, where n is the number of rolls, and p is the probability of success. This is all well and good in theory, but we quickly run into a problem... The problem is that sometimes you factor impossible events into your distribution. If I have 10 marines shoot at a carnifex, in our model they have the possibility of doing 10 wounds, which is impossible, all wounds after the 4th would be truncated, thus you can't actually use a straight up binomial model and you can't really use n*p (though n*p will usually be close).
This leads us into the second problem, which is that people use expectation even though they really shouldn't and are interpreting it incorrectly. It pains me to count the number of times i've heard, "well, i'm expected to do at least 4 wounds to X, so half the time I'll do 4 or more wounds to X." UNTRUE! You are talking about the median not the mean (aka expectation) of the distribution! The median number of wounds is the number (not necessarily unique) such that half the time you will do better, and half the time you will do worse. This solves our first problem because in the truncation example, unless the median of a distribution is in the truncated, it will not be changed by truncation.
The mean minimizes the square sum of the error terms, while the median minimizes the absolute sum, so Expectation is much less robust to outliers (ie if a gun has a 1/1000 chance of doing 5000000 wounds to the target, it's going to totally screw up the mean but do almost nothing to the median)
Now, even with the median people can still misinterpret in a different way! I also hear people say "If I shoot with 10 guys at the Falcon and my expected number of vehicle destroyed results is exactly 1, then the expected number of guys I need to kill the Falcon in one round of shooting is 10." WRONG AGAIN! In order to determine what the expected number of guys needed to kill the Falcon is you need to look at a geometric distribution. You figure out the probability to kill a carnifex with 1 guy, then plug that in for p, and find its expectation (which you probably dont want anyways...) or find the median (which is more useful).
Anywho, all this said, the median is a huge pain in the ass to calculate and usually must be done by simulation, and outliers are usually not that fair out or that heavily weighted (like 100 bolter shots doing 100 wounds to a carnifex) so on the fly expectation is ok, but when people say "I mathematically proved that X is better than Y" they better have their statistics right... (or i'll melee them with my bolt pistol)
enjoy
The first problem is that people miscalculate expectation. In a binomial distribution (which is what one normally uses for die rolls) the expectation is n*p, where n is the number of rolls, and p is the probability of success. This is all well and good in theory, but we quickly run into a problem... The problem is that sometimes you factor impossible events into your distribution. If I have 10 marines shoot at a carnifex, in our model they have the possibility of doing 10 wounds, which is impossible, all wounds after the 4th would be truncated, thus you can't actually use a straight up binomial model and you can't really use n*p (though n*p will usually be close).
This leads us into the second problem, which is that people use expectation even though they really shouldn't and are interpreting it incorrectly. It pains me to count the number of times i've heard, "well, i'm expected to do at least 4 wounds to X, so half the time I'll do 4 or more wounds to X." UNTRUE! You are talking about the median not the mean (aka expectation) of the distribution! The median number of wounds is the number (not necessarily unique) such that half the time you will do better, and half the time you will do worse. This solves our first problem because in the truncation example, unless the median of a distribution is in the truncated, it will not be changed by truncation.
The mean minimizes the square sum of the error terms, while the median minimizes the absolute sum, so Expectation is much less robust to outliers (ie if a gun has a 1/1000 chance of doing 5000000 wounds to the target, it's going to totally screw up the mean but do almost nothing to the median)
Now, even with the median people can still misinterpret in a different way! I also hear people say "If I shoot with 10 guys at the Falcon and my expected number of vehicle destroyed results is exactly 1, then the expected number of guys I need to kill the Falcon in one round of shooting is 10." WRONG AGAIN! In order to determine what the expected number of guys needed to kill the Falcon is you need to look at a geometric distribution. You figure out the probability to kill a carnifex with 1 guy, then plug that in for p, and find its expectation (which you probably dont want anyways...) or find the median (which is more useful).
Anywho, all this said, the median is a huge pain in the ass to calculate and usually must be done by simulation, and outliers are usually not that fair out or that heavily weighted (like 100 bolter shots doing 100 wounds to a carnifex) so on the fly expectation is ok, but when people say "I mathematically proved that X is better than Y" they better have their statistics right... (or i'll melee them with my bolt pistol)
enjoy