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

[Arial Black]

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.

No. There have been absolutely zero re-rolls of the set that you keep!

The set that you keep was rolled using the very same (say) 4d6k3 that you would roll even if you didn't have any discard rule at all.

The set you actually use has not been touched by the discard rule.

 

[Maxperson]

No. There have been absolutely zero re-rolls of the set that you keep!

The set that you keep was rolled using the very same (say) 4d6k3 that you would roll even if you didn't have any discard rule at all.

The set you actually use has not been touched by the discard rule.

Touched by it? No. Exists because of it? Yes. It's extraordinarily unlikely that such a high numbered set was the first roll. In virtually all cases, the set you keep ONLY EXISTS because of the re-rolled sets.

 

[Arial Black]

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.

I concede your point here. I was about to edit my post to mention this, but I'm at work and my break was over, so I'll clarify now.

The discard only kicks in when the set you roll is...low! This prevents low sets being played without making the sets you roll that aren't low any better than if you didn't have a discard rule.

However, if you set the discard threshold so high that it not only eliminates low sets but also eliminates medium sets, then this will mean that the PCs you play are higher than you would expect for that method.

As a specific example, take the 4d6k3 method, with its average expectation of 16/14/13/12/10/9, and re-roll any set without any stat of 14+ and any set whose modifiers add up to less than +1: this rule doesn't touch the average expectation of 4d6k3, so we should expect the same medium and high sets as we would without a discard rule. It's just the low sets that have gone.

But if you set the discard threshold to higher than the average expectation of 16/14/13/12/10/9, then you must play higher than average sets.

 

[FrogReaver]

The statement that no set that is played is affected by the discard rule because that set had not been discarded is demonstratably false.

Suppose I first roll A set that I discard and then reroll. Let's say I roll high. It is not true that me playing with high stats was independent of the discard rule in this scenario.

Anytime you would roll stats that you discard and reroll the discard rule has affected what was played.

 

[FrogReaver]

Care to explain how this concession fits with your other claims. If it is wrong in this example why should we have faith that your argument will hold in any other case? What is special about the case I cited that your general statements regarding these probabilities failed to explain it? Could it not be that this is evidence that probabilities of high played stats actually increase due to the discarding and rerolling like we claimed?

I concede your point here. I was about to edit my post to mention this, but I'm at work and my break was over, so I'll clarify now.

The discard only kicks in when the set you roll is...low! This prevents low sets being played without making the sets you roll that aren't low any better than if you didn't have a discard rule.

However, if you set the discard threshold so high that it not only eliminates low sets but also eliminates medium sets, then this will mean that the PCs you play are higher than you would expect for that method.

As a specific example, take the 4d6k3 method, with its average expectation of 16/14/13/12/10/9, and re-roll any set without any stat of 14+ and any set whose modifiers add up to less than +1: this rule doesn't touch the average expectation of 4d6k3, so we should expect the same medium and high sets as we would without a discard rule. It's just the low sets that have gone.

But if you set the discard threshold to higher than the average expectation of 16/14/13/12/10/9, then you must play higher than average sets.

 

[Arial Black]

Touched by it? No. Exists because of it? Yes. It's extraordinarily unlikely that such a high numbered set was the first roll. In virtually all cases, the set you keep ONLY EXISTS because of the re-rolled sets.

What 'extraordinarily high' roll are you talking about? If you mean 16/14/13/12/10/9, this is the average set produced by rolling 4d6k3 six times.

And the reason for rolling a set has no impact on the expected results of any particular method.

 

[Arial Black]

Suppose I first roll A set that I discard and then reroll. Let's say I roll high. It is not true that me playing with high stats was independent of the discard rule in this scenario.

Yes it is true, because that re-roll is a separate event from rolling the first set, and the 4d6k3 method from the first set is totally identical to the 4d6k3 of the second set.

 

[Valetudo]

Ive noticed that groups who use rolling 4d6d1 for stats tend toend up far above the average, and in a edition that asi and feats compete for the same upgrade. It really changes the game.

 

[FrogReaver]

Actual black,

You said: 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.

This statement is demonstrably false. The probability of all possible played sets must add up to 1. If we eliminate even a single possibility with a probability > 0 then the that probability no matter how small must go somewhere. It can't just vanish or we would be left with a total probability of possible playable stats less than 1 and that is not possible. So some probability higher than the discarded probability must increase which demonstrates that as sets are discarded then the probabilities of the higher non discarded stats does in fact increase.

 

[FrogReaver]

Yes it is true, because that re-roll is a separate event from rolling the first set, and the 4d6k3 method from the first set is totally identical to the 4d6k3 of the second set.

no. The reroll is not an independent trial but is dependent upon the the first roll being low.

if you always got a reroll no matter how well you rolled that would make the reroll truly independent. But it is not because the rerolls very existence is tied to you rolling something specific in the first place.