Help me understand "average rolls"

[Viktyr Gehrig]

At least one thing that'd need a complete overhaul if you changed from a d20 to 2d10 would be the critical hit system. All of a sudden, weapons that crit on a 20 only crit 1/3 as often as weapons that crit on a 19-20, and, what, 1/6 as often as 18-20 weapons? Things like Keen Edge and Improved Critical couldn't simply double the threat range anymore, either.

That seems like an argument in favor of the change, from my point of view. It makes the Keen enchantment and the Improved Critical feat more useful, when I've found them to be a little lame, as well as generally improving weapon skill for use with critical hits.

The only game-breaker I can think of there is Vorpal weapons, and the various permutations of them (bladed gauntlets, anyone?)-- but I already consider Vorpals nerfworthy.

 

[dcollins]

Re: Re: The Sage weighs in

Also just FYI, the correct statistical way of saying this is that the long run average roll will be a 10.5...

Not so. Any random variable does have a statistical mean, or average, regardless of whether the variable will be tested once or many times.

Consider the following from a college lecture on statistics: "The mean of a random variable X is also an average of the possible values of X by taking into account the fact that the values can occur with different probabilities (similar to weighted average)."
( http://engineering.uow.edu.au/Courses/Stats/File34.html )

So it is entirely proper to say that a random variable (like 1d20) itself has an average value (or mean).

It is, however, true that a minority of thinkers only recognize probability measurements in terms of long-run results: "The other approach to probability is if we think of probability as a longrun relative frequency. The relative frequency approach to probability states that if an experiment is conducted a large number of times, the probability of that event will become stable and equal to the relative frequency."
( http://engineering.uow.edu.au/Courses/Stats/File245.html )

 

[shadowlight]

Re: Re: Re: The Sage weighs in

...
So it is entirely proper to say that a random variable (like 1d20) itself has an average value (or mean).
...

Agreed. My point is that you can refer to an average result for a die (rather than having to say 50% chance of being higher or lower).

I still am bewildered that "On average, Devis will roll 10 or 11 on the d20,..." could be construed to imply frequency. As you say a random variable has a mean... but that's an arguement for James Beach.