D&D 5E Great Weapon Mastery - once more into the breach! (with math)

[Yunru]

So the fighter barbarian with elven accuracy and using precision (assuming I added precision maneuver into the equation correctly) is telling me that the fighter barbarian with a greatsword does more damage than your crit fisher in most situations. No magic weapon. No other abilities used except barbarian rage, reckless attack and precision attack. Requires 11 levels of fighter and 2 levels of barbarian. I am looking at level 20 DPR. Any other classes can be used afterwards.

AC DPR
11 89.35
12 89.27
13 89.07
14 88.68
15 88.03
16 87.05
17 85.70
18 83.90
19 81.58
20 78.69
21 75.16
22 70.92
23 65.92
24 60.08
25 53.35
26 45.66
27 36.94
28 27.13
29 16.18
30 16.18

Had to come back to this again to ask: What are the numbers with a Barbarian 2/Champion 15?

 

[Ovinomancer]

Averaging is not a fallacy, it is a law.

What? No, just... no. Not saying the Capn is right, just that this is wrong. The law of averages is a mathematical thing and has very precise language -- it's not a law like something you just do because it's a law. Averaging can, quite often, present fallacious results. If I have 12 men, for instance, 11 of whom are 6 feet tall and one who's 2 feet tall, the average of their heights provides a false representation of the truth -- almost all of them are tall but one's a brownie.

 

[Yunru]

What? No, just... no. Not saying the Capn is right, just that this is wrong. The law of averages is a mathematical thing and has very precise language -- it's not a law like something you just do because it's a law. Averaging can, quite often, present fallacious results. If I have 12 men, for instance, 11 of whom are 6 feet tall and one who's 2 feet tall, the average of their heights provides a false representation of the truth -- almost all of them are tall but one's a brownie.

That's a matter of sample size and statistics. The 3 foot tall one would be ommited as an outlier, giving a accurate representation of the truth.

 

[Ovinomancer]

That's a matter of sample size and statistics. The 3 foot tall one would be ommited as an outlier, giving a accurate representation of the truth.

No... your sample size is the 12 men. You can't just say that sample sizes are whatever works best for your result -- the data is the data. And, if you're omitting outliers, then you're still presenting a fallacy -- you're now saying that the sample was men who were tall and there was no brownie.

Averages are NOT the data -- and, since they're not the data you can reach fallacious conclusions using averages. Statistics are not the truth, although they can be useful sometimes. Being 100% aware of the fact statistics don't measure data they measure the model of your data, including all of the assumptions you've built into your model, is critical to avoiding the trap of lying to yourself with statistics.

Example: I build a model of GWM ignoring advantage and crits and maneuvers and multiclassing and only at AC 12 with 13th level characters with 20 STR and +1 weapons. I get an average that proves, conclusively, that GWM is better than a longsword. The law of averages doesn't mean jack, here, despite me having an average. And no one in this thread believes for a moment that my model, and it's assumptions, actually shows how it is. And so it goes. You may have a better model than mine, but averages aren't your friend any more than they were mine. The law of averages is just another statistical structure, built on it's own assumptions. Forget those assumptions at peril of lying to yourself and becoming overconfident in your answers.

 

[Yunru]

No... your sample size is the 12 men. You can't just say that sample sizes are whatever works best for your result -- the data is the data. And, if you're omitting outliers, then you're still presenting a fallacy -- you're now saying that the sample was men who were tall and there was no brownie.

Clearly you don't understand statistics. The sample is still the 12 men the tall and the brownie all. But the brownie is ommited from the averages as being an outlier - an exception.

 

[Ovinomancer]

Clearly you don't understand statistics. The sample is still the 12 men the tall and the brownie all. But the brownie is ommited from the averages as being an outlier - an exception.

Which is not presenting all of the data and leads to fallacious conclusions. Are you certain it's me not understanding how you can lie with statistics? Most lies with statistics aren't intentional, and come from trusting statistics too much.

 

[Yunru]

Which is not presenting all of the data and leads to fallacious conclusions. Are you certain it's me not understanding how you can lie with statistics? Most lies with statistics aren't intentional, and come from trusting statistics too much.

No it's presenting all the data and accounting for exceptions. It's literally year 1 statistics. You list all the data, including what you deem outliers, but you only work with the interquartile range.

 

[FrogReaver]

Which is not presenting all of the data and leads to fallacious conclusions. Are you certain it's me not understanding how you can lie with statistics? Most lies with statistics aren't intentional, and come from trusting statistics too much.

Removing outliers is a common statistical technique.

 

[Yunru]

I looked into the math on that. I didn't redo everything but it looks pretty accurate after getting a chance to check it out.

I wonder how an elven accuracy Barbarian Fighter using a greatsword and GWF would stand?

I think, if we fill up the last levels with Rogue, we might be able to pass 100 average damage:
https://1drv.ms/x/s!At-zPv0cZTn6hkonA-UHyfNu5Tek

(EDIT: Oh! I forgot to account for GWF too!)

But lets take this to it's rightful thread?
http://www.enworld.org/forum/showthread.php?553760-Repeatable-DPR-Kings

 

[lkj]

Removing outliers is a common statistical technique.

I'm going to hate myself for stepping into this-- But removing outliers needs to be justified. Selective removal of outliers is precisely the kind of manipulation that can lead to incorrect statistical representations. Yes, sometimes it is ok to remove outliers-- often there is technical and even statistical justification for it. However, one does not simply automatically remove any values that fall in the tails.

In the case of 12 individuals with 1 short and 11 tall, the real problem is you almost certainly don't have enough samples to form a statistically valid representation of your population. Because, chances are, it isn't inherently normally distributed. Or, you just got a wonky sample.

Averages are great. They are lovely. But they are a tool like any other and their use needs to be examined in the context of the data.

And anyway, that particular contrived example can be easily modified to make the point better. Imagine a population of 100. 50 are 6 feet tall. 50 are 2 feet tall. The average is 4 ft tall. But the average is not an adequate representation of your data. In fact, no one in your population is 4ft tall. In that case, if you simply presented the average, you wouldn't be providing a useful statistical representation of your data. In fact, by itself, it would be a misrepresentation.

Disclaimer: I have made no examination of the data in this case. I have no idea whether using the average is justified. Just don't have the time to go through it. But I couldn't help myself responding to the general idea that averages are always a good representation.

AD