Haven’t Posted in a While

I’m a bit disappointed. Not with the game itself, but with the playerbase.

Anyways, I’m currently pretty busy with college. I may revisit this blog when more patches come out or the expansion, or when I am less busy. It has been a good time. For now, I’ll be posting on my real-life blog, A Reasoner’s Miscellany.

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Confirmation Bias and the Stealth Nerf Delusion

From a thread I posted in the forums.

Confirmation Bias. 

It is the tendency of humans to to only consider evidence that supports their own theories, while ignoring or pushing aside evidence that goes against their theories. It is most prominent in the “Drop rates were stealth nerfed” threads.

Consider a person who has an unshakable belief that a fair die is rigged to roll a 1 less often than it should. Now suppose the person conducts 6 tests of 6 rolls.

4 2 5 6 1 3
3 2 1 6 2 5

1 1 6 2 3 4
2 4 1 5 1 3

5 2 4 5 2 6
6 4 2 5 3 2

Statistically, this is far too small of a sample size to indicate anything wrong with the die. In fact, in total, the die rolled a 1 exactly 6/36 times, as expected. A statistician will look at this and conclude that the experiments show no evidence of the die being rigged. However, humans are not fully rational, and most humans are not statisticians, and thus do not think of the roll in a rational way.

Instead, if a person already had the pre-conceived notion that the die was rigged to roll 1’s less often, he would only consider experiments 5 and 6, in which 1’s rolled less often, to be relevant experiments. When you ask him, “What about the experiments 3 and 4?”, he will come up with some explanation such as, “It is just luck” or “That’s just a few cases and it does not indicate that the die is not rigged.”


This applies a double standard because his own good cases, experiments 5 and 6, were likewise based on luck and do not indicate anything about the die.

Stealth Nerf Delusions

Now, replace rolling a 1 with rolling an ilvl 63 rare, with proper adjustment for the actual drop rate percentages.

What goes through the mind of someone who is already assuming that the drop rate was nerfed? Basically, when this person has a “normal” run, such as experiments 1 and 2, he do not notice it. When he gets a “good” run, such as experiments 3 and 4, he dismisses the evidence because it is just randomness and luck. But when he gets a bad run, such as experiments 5 and 6, it suddenly becomes solid evidence of a drop rate nerf.

Just based on those two runs, a biased sub-sample of the data, they believe that the drop rate has been stealth nerfed.

This bias is a self-propagating. The more posts there are claiming drop rate nerfs, the more likely it becomes for someone who was previously skeptical to join in despite the lack of evidence. They start only noticing when they get unlucky streaks and start dismissing lucky or normal runs. When enough people believe in such a claim, it becomes a mass delusion.

Of course, under a delusion, people often become overly defensive about their position even though they have no rational reason to agree with it. When questioned, they start making even more ridiculous claims to support their original claim, akin to making up more lies to cover up the original lie. Only, they aren’t aware that it is a lie and they genuinely believe what they are saying to be the truth.

Randomness and Statistics

Besides confirmation bias, many people just don’t seem to understand what randomness is. People mistakenly think the following statements are true:

  • If the drop rate says 5% ilvl 63, then most of the time in a set of 100 random items, I should find 5 ilvl 63 items.
  • If I don’t get an ilvl 63 drop for a long time, then I am due to get one soon.

The first point is statistically not true. In fact, most of the time (82%), you will find less than or more than 5 ilvl 63 items in 100 runs. The Act 1 drop rates for ilvl 63 were analyzed in this post.

The result is that out of 100 random items from Act 1 Inferno, with a drop rate of 5% (rounded up from 4.8%), the chances to get exactly N ilvl 63 drops is the following:

0 : 0.592%
1 : 3.116%
2 : 8.118%
3 : 13.958%
4 : 17.814%
5 : 18.002% (Expected Value)
6 : 15.001%
7 : 10.603%
8 : 6.487%
9 : 3.490%
10: 1.672%
11: 0.720%

When you scale this up to 100,000 players, there should be hundreds of players (0.592%) who should find zero ilvl 63 drops in a random set of 100 drops in Act 1. Here the selection bias kicks in hard. These people who don’t find any ilvl 63 drops become much more likely to complain on the forums, thus becoming a vocal minority and vastly over-representing their actual distribution (0.592%) and try to make it seem as if they a much larger proportion (50%+) of players.

As far as the second point goes, that an event should be “due” when it hasn’t happened for a while, it is simply the Gambler’s fallacy. When an independently random event does not happen for a while, people erroneously assume that it is bound to happen soon. For example, if a coin has landed 10 Heads in a row, people will erroneously bet significant amounts of money on Tails because the chance to get 11 Heads in a row is tiny. This misses the real issue, as the chance for the next flip to be Tails is still 50-50. The chance to flip Tails does not increase when there is a Heads streak.

Similarly, when you don’t find an ilvl 63 item in a while, that does not mean the next item you find has more than a 4.8% chance to be ilvl 63. It still has the same chance as before.

Final Notes

The truth is often painful. But as life works, ignoring the truth does not make it false, and believing in a lie really hard does not make it true. A bunch of people believing in a lie also does not make it true. Someone might have all the faith in the world that the Earth is flat, and cite all the other people who believe this to be the case, but unfortunately, that does not make his theory correct.

Summary

  • Due to confirmation bias, players tend to ignore lucky streaks and normal runs, and only include unlucky streaks as evidence. This is wrong. All evidence should be included.
  • The above confirmation bias builds on itself, leading more and more people to “notice” the same thing, creating a mass delusion.
  • By the binomial distribution, the chance to actually obtain the expected number of ilvl 63 drops (for instance) is very low in any given run.
  • Not getting the expected number does not imply any stealth nerfs.
  • Those who get very unlucky streaks are much more likely to post, and thus over-represent themselves on the forums.
  • Good drops are never “guaranteed” to occur after an unlucky streak. Expecting that a certain item must drop soon is the Gambler’s fallacy.
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Even the Slightest Upgrade Feels Great

I thought this was pretty amusing. It was the first time in a very long while that I found a strict upgrade. I’ve found plenty of decent upgrades along the way that sacrificed one or two stats to gain others, like losing 30 strength to gain 50 vitality. But I’ve never found an upgrade before that was strictly better statwise than my previous item after hitting Inferno. This was pretty epic.

Click the image to enlarge.

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Patch 1.0.4

Well, patch 1.0.4 launched earlier today, with many, many changes. Here is a very brief summary:

  • Inferno nerf.
  • Class buffs.
  • New Legendaries.
  • Improved drop rates from white mobs.
  • Paragon levels.
  • Auction House 6-prop search.
  • Co-op easier.
  • Numerous bug fixes.

After about 5 minutes of playing in the new patch, I found this:

The lifesteal affix was originally capped at 3%, but now apparently it can go up to 6%. This is pretty neat.

The Paragon level mechanic forced me to choose a character to main. I decided to go with the Wizard, as I feel it is the most diverse class.

Now I’m interested in what the next patch, 1.0.5, will bring.

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1.0.4 Datamined Changes

Diablofans has datamined numerous changes to come in patch 1.0.4.

My prediction holds that a lot of abilities after the patch will still be useless. They did numerous buffs to certain abilities, but did not address core mechanics besides the Witch Doctor mana change, which is definitely a correct decision. It is sad to see, however, that Monks will have largely the same spirit regeneration as before. The new set bonuses on items are also not too appealing.

Who will benefit the most from the patch? Just judging by the datamined notes, it will be:

  1. Barbarian
  2. Wizard
  3. Demon Hunter
  4. Witch Doctor
  5. Monk

The Barbarian is going to absolutely stomp Inferno, and the Wizard has numerous new tricks up their sleeves. Demon Hunters got some well-rounded buffs, Witch Doctors will have many new playstyles, but Monks will mostly play the same as they do now.

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1.0.4 Demon Hunter and Witch Doctor Changes

Demon Hunter info here, Witch Doctor info here.

  • Buffs to Bola Shot and Entangling Shot.
  • No buff yet to Grenades.
  • Buff of Hatred spenders, including Chakram, Cluster Arrow, and Rain of Vengeance.
  • Buff to pet survivability via pet scaling with vitality and a “Force Armor” type defense, as well as innate regeneration.
  • Buff of innate Mana regeneration from 20 to 45.
  • Redesign of Vision Quest to grant 30% bonus mana regeneration after using a Primary skill. Overall the system is more fluid.
  • Buff of numerous abilities.
  • Splinters and Zombie Bears are not being nerfed.

The pet changes are great, and the Demon Hunter buffs look decent. I just hope that the Wizard and Monk end up being great as well.

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1.0.4 Wizard and Monk Buffs

Wizard info here, and Monk info here.

  • Hydra runes are being buffed to compete with Venom Hydra.
  • Energy Twister is having its proc coefficient reduced.
  • Various other buffs.
  • Meteor and Arcane Torrent are being buffed.
  • Exploding Palm is being significantly buffed.
  • Seven-Sided Strike and Wave of Light are receiving significant buffs.
  • One With Everything is not being nerfed.

Though these are previews only, they certainly do not outline enough changes to significantly increase the number of builds.

Energy Twister’s proc coefficient is nerfed with the new legendaries in mind. In addition, it is just obviously too powerful in its current state, like pre-nerf Nether Tentacles.

Overall these will be good buffs, but as I mentioned in my post about the Barbarian changes, the buffs shown are hardly enough.

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