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Trying to make 5e more oldish and want some people's opinions
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<blockquote data-quote="Ovinomancer" data-source="post: 7535849" data-attributes="member: 16814"><p>GAH! I get that probability is tricky and it's easy to fool yourself into thinking you've made something uncommon, but the above system isn't doing what you think it is. I'm assuming that you're using a DC10 DEX check? If you're not, then this is really, really not doing what you think it is.</p><p></p><p>Okay, I'm going to introduce you to a probability concept using a binomial distribution called 'as least x times.' Binomial distributions are good for known probability events to determine what the individual odds for a given number of event to take place over a number of trials. Like, say the odds of rolling 1 and only 1 fumble if you make 20 rolls (37.7%). If you take the odds of rolling 1 one and add it to the odds for rolling 2 ones... up to 20 ones in 20 rolls, you get the cumulative distribution for what the odds of rolling at least one 1 on 20 rolls (64.2%).</p><p></p><p>So, if we have a fighter who makes 20 attacks, there's a 64.2% chance they'll roll at least one fumble. When they do this, and there's a 20% chance they fail a DC 10 DEX check (+2 DEX, +3 proficiency, fail on 4 or less), then the chance they'll drop their weapon in 20 attacks is 12.8%. The chance they'll fall prone is 2.6%. That may sound good, but let's say this is a dual weilding figher, making twice as many attacks -- in 40 attacks the at least one numbers are: fumble: 67.1%; drop weapon: 17.4%; fall down 3.5%. This holds at low level, but what about higher?</p><p></p><p>A level 11 fighter is +4 prof with 3 attacks a round. Over the same time, that's 60 attacks. We're assuming they're not adding to DEX with ASI as STR and CON are important still, so that's a +6 on the DEX check. At DC 10, that's fail on 3 or less or 15%. The numbers now are: fumble: 95.4%; drop weapon: 14.3%; fall down: 2.1%. Things don't get much better. If this a that dual wielder making 80 attacks the numbers go to 98.3%, 14.7%, and 2.2% respectively. </p><p></p><p>So, a funny thing to note about 'at least' probabilities is that as the number of trials grows, the peak of the distribution moves up. For the level 11 fighter, the at least twice numbers in 60 attacks are 12.1% to drop their weapon <em>at least twice</em> and 1.8% to fall down <em>at least twice</em>. The 80 attacks is worse, with 13.7% to drop at least twice and 2.1% to fall down at least twice.</p><p></p><p>Now, here's the thing, I really don't expect the DEX check DC to be 10. To be honest, most people who like critical fumble checks think it's because it makes the game harder, and harder is better, so I expect the actual DC is at least 15. Those odds really suck.</p><p></p><p>Level 1, 20 attacks, fail check on 10 or less (+4) -- drop 35.3%, fall down 19.5 %</p><p>Level 1, 40 attacks, fail check on 10 or less (+4) -- drop 47.9%, fall down 26.4%</p><p></p><p>Level 11, 60 attacks, fail check on 8 or less (+6) -- drop 39.2%, fall down 15.2%</p><p>Level 11, 80 attacks, fail check on 8 or less (+6) -- drop 39.3%, fall down 15.7%</p><p></p><p>Level 20, 80 attacks, fail check on 5 or less (+10) -- drop 24.6%, fall down 6.1%</p><p></p><p>These are all <em>at least once</em> chances. With a Fighter with a +4 DEX at 20th level making attacks for 20 rounds (a reasonable fighting day) they'll drop their weapon at least once one in every four fighting days and fall down once every 18 fighting days. That's a best case, because most fighters will not have a +4 DEX, even at 20th level.</p></blockquote><p></p>
[QUOTE="Ovinomancer, post: 7535849, member: 16814"] GAH! I get that probability is tricky and it's easy to fool yourself into thinking you've made something uncommon, but the above system isn't doing what you think it is. I'm assuming that you're using a DC10 DEX check? If you're not, then this is really, really not doing what you think it is. Okay, I'm going to introduce you to a probability concept using a binomial distribution called 'as least x times.' Binomial distributions are good for known probability events to determine what the individual odds for a given number of event to take place over a number of trials. Like, say the odds of rolling 1 and only 1 fumble if you make 20 rolls (37.7%). If you take the odds of rolling 1 one and add it to the odds for rolling 2 ones... up to 20 ones in 20 rolls, you get the cumulative distribution for what the odds of rolling at least one 1 on 20 rolls (64.2%). So, if we have a fighter who makes 20 attacks, there's a 64.2% chance they'll roll at least one fumble. When they do this, and there's a 20% chance they fail a DC 10 DEX check (+2 DEX, +3 proficiency, fail on 4 or less), then the chance they'll drop their weapon in 20 attacks is 12.8%. The chance they'll fall prone is 2.6%. That may sound good, but let's say this is a dual weilding figher, making twice as many attacks -- in 40 attacks the at least one numbers are: fumble: 67.1%; drop weapon: 17.4%; fall down 3.5%. This holds at low level, but what about higher? A level 11 fighter is +4 prof with 3 attacks a round. Over the same time, that's 60 attacks. We're assuming they're not adding to DEX with ASI as STR and CON are important still, so that's a +6 on the DEX check. At DC 10, that's fail on 3 or less or 15%. The numbers now are: fumble: 95.4%; drop weapon: 14.3%; fall down: 2.1%. Things don't get much better. If this a that dual wielder making 80 attacks the numbers go to 98.3%, 14.7%, and 2.2% respectively. So, a funny thing to note about 'at least' probabilities is that as the number of trials grows, the peak of the distribution moves up. For the level 11 fighter, the at least twice numbers in 60 attacks are 12.1% to drop their weapon [I]at least twice[/I] and 1.8% to fall down [I]at least twice[/I]. The 80 attacks is worse, with 13.7% to drop at least twice and 2.1% to fall down at least twice. Now, here's the thing, I really don't expect the DEX check DC to be 10. To be honest, most people who like critical fumble checks think it's because it makes the game harder, and harder is better, so I expect the actual DC is at least 15. Those odds really suck. Level 1, 20 attacks, fail check on 10 or less (+4) -- drop 35.3%, fall down 19.5 % Level 1, 40 attacks, fail check on 10 or less (+4) -- drop 47.9%, fall down 26.4% Level 11, 60 attacks, fail check on 8 or less (+6) -- drop 39.2%, fall down 15.2% Level 11, 80 attacks, fail check on 8 or less (+6) -- drop 39.3%, fall down 15.7% Level 20, 80 attacks, fail check on 5 or less (+10) -- drop 24.6%, fall down 6.1% These are all [I]at least once[/I] chances. With a Fighter with a +4 DEX at 20th level making attacks for 20 rounds (a reasonable fighting day) they'll drop their weapon at least once one in every four fighting days and fall down once every 18 fighting days. That's a best case, because most fighters will not have a +4 DEX, even at 20th level. [/QUOTE]
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