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Message: <blockquote data-quote="Asisreo" data-source="post: 8220285" data-attributes="member: 7019027">I also want to touch up on the effects that using exclusively average damage does to the difficulty of the game. Surely, I also use average damage at times, but its important to know that the more you use average damage, the easier the game becomes because of predictability. If a wizard has 6HP and a goblin does an average of 5 damage per turn. It wouldn't take much to know that the goblin must hit twice before the wizard goes down. There is a 0% chance the wizard goes down on first hit. However, if you take the probability of the goblin doing 6 damage on round 1, you'll find that the wizard could easily go down with a 50% chance on round 1. If you assume their AC is 15, that's a 25% chance they go down round 1. You might as well roll a d4 and knock unconscious on a 1. No, actually! Surprisingly, as the number of dice increases, the variance of the dice also increases. It actually increases significantly too. For reference, Variance is an actual statistical term that measures how much the values of the data set differ from the mean. Its telling you how spread out the data set it. For example, a set {1,2,3} has a smaller variance than the data set {0,1,2,3,4} despite them having the same mean. In other words, the higher the dice, the less likely you can be certain it will reliably hit your average and the less precise your rolls will be from the average. Rolling 2d6 means you have an average of 7 and you're likely to hit that average 16.66% of the time. The standard deviation is 2.42 and therefore the variance is 5.85. Rolling 8d6 means you have an average of 28, but you only have a 8.09% chance of hitting the average. Its standard deviation is 4.83 and its variance grew to a whopping 23.32. What does this mean, exactly? Does it mean that rolling an infinite amount of dice actually won't get you closer to the average of those dice? Well, its more complicated than that. The Law of Large Numbers would agree with you, but there's also the distinction between Relative Frequency and Cumulative Relative Frequency. That difference being that Relative Frequency (RF) is what you actually rolled in the individual trials while Cumulative Relative Frequency (CRF). True: The CRF will converge towards the average, expected value of the dice. Meaning each die will cumulatively average out to 3.5 across all trials. However, this is irrelevant to play, completely. The reason is because it doesn't matter at all that your dice will converge to an average because damage isn't a cumulative value. Damage is based on the specific trial that you're facing, independent on any previous trials. TL;DR The damage that you did to the goblin at 1st level is completely unrelated to the damage you're doing to the dragon at 20th level. This means that having alot of dice doesn't make you more likely to obtain the average, it makes you less likely and the further in play you get, the less reliable your dice alone become (in terms of damage).</blockquote>

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