D&D 5E Rolled character stats higher than point buy?

[Arial Black]

Gamblers fallacy. Given that the first coin flip was heads the next is very likely tobe tails.

Not gamblers fallacy: given that I can reflip a coin that lands on heads one time the probability of the final outcome being tails is 75%

Yet the re-flip is 50-50.

 

[Arial Black]

Which isn't the point at all. So what if they are independent. If you are only keeping the sets that are well above average, the set you end up with will always be much higher than the average set. The average is meaningless.

Since the average set of six 4d6k3 is around 16/14/13/12/10/9, discarding sets whose modifiers add up to less than +1, and sets that don't have any stat of 14+, we are not 'only keeping sets that are well above average'.

If we think of rolled sets as either 'low', 'medium' or 'high', where 'low' is what gets discarded, then the only thing discarding does is prevent low sets from being played. This does indeed increase the observed average of played sets (without affecting stat generation), it does not do this by increasing the likelihood of high numbers being generated, or even by increasing average scores and making them any higher. It only removes low sets from play, not make any played set any higher than it would be without the discarding rule; the discarding rule does not get used at all for any set that is played.

Each rolled set is a separate event. No previous discarded set influences the next rolled set in any way. The possibilities of the second (third, fourth,...) set each include the low rolls that will also be discarded, using the exact same bell-curve as the first, and as it would be without any discard rule in place. 4d6k3 remains 4d6k3, regardless of how many sets you throw away.

And this is the point. The set you roll that isn't discarded had the exact same probabilities as any about-to-be-rolled set, whether there is a discard rule or not. There is no need to fear that high rolls are more likely to be generated, because the only practical effect of discarding low sets is that low sets don't get played, not that the remaining sets are improved in any way.

Since point-buy doesn't allow low sets either, a discard rule when rolling stats should not make you fear especially high results if the same method without a discard rule wouldn't either.

 

[EzekielRaiden]

Since the average set of six 4d6k3 is around 16/14/13/12/10/9, discarding sets whose modifiers add up to less than +1, and sets that don't have any stat of 14+, we are not 'only keeping sets that are well above average'.

If we think of rolled sets as either 'low', 'medium' or 'high', where 'low' is what gets discarded, then the only thing discarding does is prevent low sets from being played. This does indeed increase the observed average of played sets (without affecting stat generation), it does not do this by increasing the likelihood of high numbers being generated, or even by increasing average scores and making them any higher. It only removes low sets from play, not make any played set any higher than it would be without the discarding rule; the discarding rule does not get used at all for any set that is played.

But Bayes' theorem still says the probability is different (and, as any analysis of the altered distributions would show, greater).

Again, P(x|C) = P(C|x)*P(x)/P(C). This is actually true, for any conditional probability you'd want to evaluate.

 

[Maxperson]

Since the average set of six 4d6k3 is around 16/14/13/12/10/9, discarding sets whose modifiers add up to less than +1, and sets that don't have any stat of 14+, we are not 'only keeping sets that are well above average'.

Which is fine, but it's not what people here were talking about. You've shifted the discussion away from what people were talking about to something they weren't talking about, but supports your position.

People here are discussing re-rolling until you get stats of X quality or higher.

If we think of rolled sets as either 'low', 'medium' or 'high', where 'low' is what gets discarded, then the only thing discarding does is prevent low sets from being played. This does indeed increase the observed average of played sets (without affecting stat generation), it does not do this by increasing the likelihood of high numbers being generated, or even by increasing average scores and making them any higher. It only removes low sets from play, not make any played set any higher than it would be without the discarding rule; the discarding rule does not get used at all for any set that is played.

It doesn't increase the likelihood of high numbers being generated in any individual set, but it absolutely increases the likelihood of the end set having high numbers.

 

[FrogReaver]

you do realize that removing low sets from the new subset does actually increase the probability that any given combination of higher stats will see play.

A simple example. Let's take the equal distribution of 1,2,3. If I discard the initial result of one then my chance of ultimately ending up with a 2 increases to 50% instead of 33.3333%. Same for a 3. It's imperative that you admit that discarding certain results and rerolling them increases the probability that The non discarded is ultimately selected.

In this equal distribution it's easy to calculate. The chance of getting a 2 plus the chance of getting a 1 times the chances of getting a 2 + the chance of getting a 1 squared times the chance of getting a 2, etc... This is the geometric series with r = 1/3 and constant 1/3. Which is 1/3 * 3/2 = 1/2.

There. A provable example that shows you are incorrect.

Since the average set of six 4d6k3 is around 16/14/13/12/10/9, discarding sets whose modifiers add up to less than +1, and sets that don't have any stat of 14+, we are not 'only keeping sets that are well above average'.

If we think of rolled sets as either 'low', 'medium' or 'high', where 'low' is what gets discarded, then the only thing discarding does is prevent low sets from being played. This does indeed increase the observed average of played sets (without affecting stat generation), it does not do this by increasing the likelihood of high numbers being generated, or even by increasing average scores and making them any higher. It only removes low sets from play, not make any played set any higher than it would be without the discarding rule; the discarding rule does not get used at all for any set that is played.

 

[FrogReaver]

Yet the re-flip is 50-50.

Not one person here has said it isn't. Yet you keep bringing that up like its an important point.

 

[Arial Black]

Not one person here has said it isn't. Yet you keep bringing that up like its an important point.

It is the important point!

We all agree that the observed average (post rolling) is higher with the discard rule.

We all agree (don't we?) that each re-roll of an entire set follows the same expected distribution (pre-reroll) of the first, and also of the same method (say, 4d6k3) with or without any discard rule.

Where we disagree is the relevance of each fact to character creation.

The reason I keep banging on about it is that the method we use (3d6, 4d6k3, whatever) has a certain probability curve and has an expectation of delivering a certain average (around 16/14/13/12/10/9 for 4d6k3, for example), and that this curve/expected average of stats generated by that method is identical whether or not a discard rule is in place.

This is because no set that is actually rolled and played has been affected by the discard rule at all! With or without a discard rule, there is the exact same probability of rolling high, medium, and low sets!

This is the point: the fact that low sets are not played if there is a discard rule does not affect the chances of generating medium or high sets! Medium and high sets are rolled with exactly the same frequency with or without discards, and no set that is played is affected by the discard rule because that set has not been discarded!

So no DM has to worry about loads of 18s hitting his table caused by any discard rule. The observed average is higher not because medium sets are improved in any way, or because it's easier for 4d6k3 to generate 18s, but simply because the low sets are not played!

The only real affect that a discard rule has is to eliminate low sets, not make medium or higher sets more likely to be rolled. The observed average post-rolling has no effect whatsoever on the scores actually played, beyond simply eliminating low sets!

 

[pdzoch]

According to the old D&D 3.5 rules, stats are allowed to be rerolled. "If your scores are too low, you may scrap them and roll all six scores again." Of course, it also defines "too low": "Your scores are considered too low if the sum of your modifiers (before adjustments because of race) is 0 or lower, or if your highest score is 13 or lower." I am sure this rule or option has been carried throughout other editions and games by players and game masters.

I once read somewhere, and I wish I could find it again for this post, that ditching the low rolled stats was acceptable because the characters are supposed to be heroes and the average person (low rolls, or a REALLY bad roll in one stat) might not have taken up the call to adventure.

I do not mind a character with a couple or high stats, are even a collection of really good stats, but when I see more than one great stat, I do become suspicious. My rule with rolled stats is I have to see the rolls. Otherwise, it is point buy or array.

Personally, I do not mind a bad roll or two. I think it makes for a fun (or at least, interesting) character to play.

 

[Maxperson]

It is the important point!

We all agree that the observed average (post rolling) is higher with the discard rule.

We all agree (don't we?) that each re-roll of an entire set follows the same expected distribution (pre-reroll) of the first, and also of the same method (say, 4d6k3) with or without any discard rule.

Where we disagree is the relevance of each fact to character creation.

I fail to see how the stats you end up with are not the most important fact of rolling for character creation. That end result that is very much higher than average because of all the re-rolls is all the matters.

 

[FrogReaver]

Proof by contradiction:

Suppose there was a d6 that we rolled. if we always rerolled results of 1,2,3,4,5 then the only thing that is ever played is a 6. According to you we still have the same probability of rolling low as we do high with or without this discard and reroll rule. This is obviously false. There is a 100% chance a 6 the high value) gets played with this rule. End of proof.

keep in mind you just claimed DM's don't need to worry about seeing more 18's in play due to your claims. In my example this Dm has to work about only seeing the highest possible roll every time given the adopted discard and reroll rules.

I think you are getting confused between what affects each roll of the dice and what ultimately gets to see play.

It is the important point!

We all agree that the observed average (post rolling) is higher with the discard rule.

We all agree (don't we?) that each re-roll of an entire set follows the same expected distribution (pre-reroll) of the first, and also of the same method (say, 4d6k3) with or without any discard rule.

Where we disagree is the relevance of each fact to character creation.

The reason I keep banging on about it is that the method we use (3d6, 4d6k3, whatever) has a certain probability curve and has an expectation of delivering a certain average (around 16/14/13/12/10/9 for 4d6k3, for example), and that this curve/expected average of stats generated by that method is identical whether or not a discard rule is in place.

This is because no set that is actually rolled and played has been affected by the discard rule at all! With or without a discard rule, there is the exact same probability of rolling high, medium, and low sets!

This is the point: the fact that low sets are not played if there is a discard rule does not affect the chances of generating medium or high sets! Medium and high sets are rolled with exactly the same frequency with or without discards, and no set that is played is affected by the discard rule because that set has not been discarded!

So no DM has to worry about loads of 18s hitting his table caused by any discard rule. The observed average is higher not because medium sets are improved in any way, or because it's easier for 4d6k3 to generate 18s, but simply because the low sets are not played!

The only real affect that a discard rule has is to eliminate low sets, not make medium or higher sets more likely to be rolled. The observed average post-rolling has no effect whatsoever on the scores actually played, beyond simply eliminating low sets!