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Hypothetical Statistics Question
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<blockquote data-quote="nhl_1997" data-source="post: 1897310" data-attributes="member: 22380"><p>One thing to consider:</p><p>Greater chances in major fluctuations tend to increase PC mortality rate.</p><p></p><p>Suppose everyone and everything exclusively uses this 3-11 weapon (spell, ability, whatever.) For any specific distribution, there is an equal chance for the dice to favor the PCs or their opponents. Obviously, if the dice favor the opponents, then that tends towards PC death. The PCs go through many encounters, so eventually, the dice will favor the opponents.</p><p></p><p>For a flat distribution (1d9+2), when the dice favor the opponents, they'll be dealing out well above average damage. For a non-flat distribution (4d3-1 or any other distribution you proposed), the above average dice rolls will correspond to only "slightly above average" damage.</p><p></p><p>Distributions ranked from most flat to least flat:</p><p>1d9+2 (100% flat)</p><p>1d7+1d3+1 (flat from 5-9, triangular at tails)</p><p>1d4+1d6+1 (flat from 6-8, triangular at tails)</p><p>2d5+1 (triangular, same distribution as a greatsword)</p><p>2d4+1d3 (peak sharper than triangular)</p><p>4d3-1 (sharpest peak)</p><p></p><p>Over the long-haul, 4d3-1 favors the PCs the most and 1d9+2 favors their opponents the most.</p></blockquote><p></p>
[QUOTE="nhl_1997, post: 1897310, member: 22380"] One thing to consider: Greater chances in major fluctuations tend to increase PC mortality rate. Suppose everyone and everything exclusively uses this 3-11 weapon (spell, ability, whatever.) For any specific distribution, there is an equal chance for the dice to favor the PCs or their opponents. Obviously, if the dice favor the opponents, then that tends towards PC death. The PCs go through many encounters, so eventually, the dice will favor the opponents. For a flat distribution (1d9+2), when the dice favor the opponents, they'll be dealing out well above average damage. For a non-flat distribution (4d3-1 or any other distribution you proposed), the above average dice rolls will correspond to only "slightly above average" damage. Distributions ranked from most flat to least flat: 1d9+2 (100% flat) 1d7+1d3+1 (flat from 5-9, triangular at tails) 1d4+1d6+1 (flat from 6-8, triangular at tails) 2d5+1 (triangular, same distribution as a greatsword) 2d4+1d3 (peak sharper than triangular) 4d3-1 (sharpest peak) Over the long-haul, 4d3-1 favors the PCs the most and 1d9+2 favors their opponents the most. [/QUOTE]
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