Shop Distribution - The Nerdiest Post you’ll read today
商店分布 - 您今天将读到的最书呆子的帖子

Hey folks. Mort here with what is going to be the nerdiest game design post you’ll see in a while, but I wanted to share it with you. Generally in all aspects of life, even if you’re confident in something, it’s helpful to double check your biases and make sure you’re actually correct or not. So that’s what I did.
嘿伙计。 Mort 在这里发布的内容将是您稍后会看到的最书呆子的游戏设计帖子，但我想与您分享。一般来说，在生活的各个方面，即使您对某件事充满信心，仔细检查您的偏见并确保您实际上是否正确也是有帮助的。这就是我所做的。

We’ve all seen posts where a player rolls down 50 gold and doesn’t see the uncontested unit they’re looking for, heck you may have even been on that end yourself (sorry, but wait for the punchline). Sometimes, this experience can be so stark that you’re concerned with the reliability of the system. Could this be bugged? I can’t really be that unlucky—is something wrong with the game? Now, my initial reaction is that this is a common thing called “confirmation bias” where a recent experience is being weighted more heavily. This, in conjunction with negativity bias, where negative experiences are seen to have a higher impact, become the fuel for many “Mortdogged” experiences. But even with knowledge of these biases, is everything fine? I mean, TFT has had its share of bugs, so let’s take a deep dive in the design space to make sure everything works as it should.
我们都见过这样的帖子：玩家滚下 50 金币，但却看不到他们正在寻找的无争议单位，哎呀，您自己可能也遇到过这种情况（抱歉，请等待笑点）。有时，这种体验可能非常严峻，以至于您担心系统的可靠性。这能被窃听吗？我不可能真的那么倒霉——是游戏出了问题吗？现在，我的最初反应是，这是一种常见的现象，称为“确认偏差”，其中最近的经历被更重视。这与消极偏见（消极经历被认为具有更大的影响）相结合，成为许多“颓废”经历的燃料。但即使了解了这些偏见，一切都好吗？我的意思是，TFT 也有一些缺陷，所以让我们深入研究设计空间，以确保一切都能正常工作。

For this experiment, I focused on 4 costs. We pulled out 6 copies of nine of the Four Costs (these are our contested units), and left the other three Four costs as our uncontested units, with all 10 copies in the pool. At this point, this means there are 4 copies of the contested units (36 contested units total) and 10 copies of our three uncontested units (30 uncontested units total). If we do a large extensive roll down, we should see uncontested champions (30/66) 45% of the time approximately.
在这个实验中，我重点关注了 4 个成本。我们从四种成本中的九种中取出了 6 个副本（这些是我们有争议的单位），并将其他三种四种成本作为我们无争议的单位，所有 10 个副本都在池中。此时，这意味着有 4 个有争议单元的副本（总共 36 个有争议单元）和 10 个 3 个无争议单元副本（总共 30 个无争议单元）。如果我们进行大规模的滚动，大约 45% 的时间我们应该会看到无争议的冠军 (30/66)。

We ran this experiment for the first time, with Ornn, Ashe, and Kaisa as the three uncontested units (lol, Ornn is uncontested, right?), and here are the results.
我们第一次进行这个实验，以奥恩、艾什和佳兆业为三个无争议单位（哈哈，奥恩是无争议的，对吧？），结果如下。

• Ornn: 136  奥恩：136

• Ashe: 168  艾什：168

• Kaisa: 120  佳兆业：120

• Lillia: 58  莉莉：58

• Morgana: 52  莫甘娜：52

• Kayn: 58  凯：58

• Lee Sin: 61  李仙：61

• Syndra: 38  辛德拉：38

• Nautilus: 53  鹦鹉螺号：53

• Galio: 61  加里奥：61

• Annie: 50  安妮：50

• Sylas: 46  塞拉斯：46

The total 4 costs seen was 901, and the uncontested ones made up 424. This is (424/901) 47% of the time, which is within expected variance for something of this sample size, and matches our expectations. Good news. But of course, one time isn’t enough, so let’s run the experiment two more times. 
所看到的总共 4 项成本为 901，无争议的成本为 424。这是 (424/901) 47% 的时间，这在该样本大小的预期方差之内，并且符合我们的预期。好消息。当然，一次是不够的，所以我们再进行两次实验。

• Ornn: 154  奥恩：154

• Ashe: 141  艾什：141

• Kaisa: 178  佳兆业：178

• Lillia: 57  莉莉：57

• Morgana: 72  莫甘娜：72

• Kayn: 48  凯：48

• Lee Sin: 53  李仙：53

• Syndra: 57  辛德拉：57

• Nautilus: 52  鹦鹉螺号：52

• Galio: 62  加里奥：62

• Annie: 52  安妮：52

• Sylas: 41  塞拉斯：41

• Total: 473/967 = 48.9%
  总计：473/967 = 48.9%

And again  然后再次

• Ornn: 150  奥恩：150

• Ashe: 140  艾什：140

• Kaisa: 152  佳兆业：152

• Lillia: 63  莉莉：63

• Morgana: 58  莫甘娜：58

• Kayn: 55  凯：55

• Lee Sin: 48  李仙：48

• Syndra: 54  辛德拉：54

• Nautilus: 47  鹦鹉螺：47

• Galio: 60  加里奥：60

• Annie: 64  安妮：64

• Sylas: 55  塞拉斯：55

• Total: 442/946= 46.7%  总计：442/946= 46.7%

So yeah, generally we’re seeing the results we’d expect with a sample size this big. It’s not EXACTLY 45%, but the law of large numbers shows that this is expected, and if we dramatically increased the sample size, we would likely converge to that expected 45%. From a purely mathematical standpoint, it seems like our shop is working as expected. Huzzah!
所以，是的，一般来说，我们会看到如此大的样本量所期望的结果。这并不完全是 45%，但大数定律表明这是预期的，如果我们大幅增加样本量，我们可能会收敛到预期的 45%。从纯粹的数学角度来看，我们的商店似乎正在按预期运行。好哇！

So all is good right, and there’s nothing to be done…right? Well…no actually. Just because it is mathematically correct does NOT mean the design is perfect. If you’ve ever watched my stream, I’ve talked about how good design doesn’t just let RNG take the wheel, and designs around the core player experience. In this case, the player is not rolling down 1000 times and letting the law of large numbers do its job…instead, it’s rolling down 60 gold and expected results that are intuitive, which is that uncontested units show up more.
所以一切都很好，对吧，没有什么可做的……对吧？嗯……实际上没有。仅仅因为它在数学上是正确的并不意味着设计是完美的。如果你看过我的直播，我已经谈到了优秀的设计不仅仅让 RNG 掌舵，而是围绕核心玩家体验进行设计。在这种情况下，玩家不会滚动 1000 次并让大数定律发挥作用……相反，它会滚动 60 枚金币和直观的预期结果，即无争议的单位出现更多。

Let’s repeat the experiment, but instead of 1000 rolls, let’s only do 40 and see what happens. Same thing, with Ornn/Ashe/Kaisa as our uncontested units, and see what happens.
让我们重复这个实验，但我们只进行 40 次，而不是 1000 次，看看会发生什么。同样的事情，以奥恩/阿什/佳兆业作为我们无争议的单位，看看会发生什么。

• Ornn: 8  奥恩：8

• Ashe: 6  艾什：6

• Kaisa: 1  佳兆业：1

• Lillia: 6  莉莉：6

• Morgana: 0  莫甘娜：0

• Kayn: 1  凯：1

• Lee Sin: 6  李仙：6

• Syndra: 2  辛德拉：2

• Nautilus: 4  鹦鹉螺：4

• Galio: 4  加里奥：4

• Annie: 0  安妮：0

• Sylas: 2  塞拉斯：2

• Total: 15/40 = 37.5%
  总计：15/40 = 37.5%

Because the sample size is so low, the variance expands pretty dramatically. Much like if you flip a coin 10 times and hit heads 7 times, 70% is way higher than 50%, but the reality is when the sample size is lower, the variance is higher. Again, this all lines up from a mathematical sense…but from a game design standpoint it’s pretty rough. Kai’Sa is uncontested here and is seen one time, while Lee Sin has 6 copies out of the pool, and is seen 6 times! These are the experiences people have that feel off, and make them not trust the game.
由于样本量很小，方差会急剧扩大。就像抛硬币 10 次，正面朝上 7 次一样，70% 远高于 50%，但实际情况是，当样本量较小时，方差会较高。再说一遍，这一切从数学意义上来说都是一致的……但从游戏设计的角度来看，它相当粗糙。卡莎在这里没有任何争议，只出现过一次，而李仙则有 6 份出池，出现过 6 次！这些都是人们感觉不舒服的经历，使他们不信任游戏。

Nintendo games do a lot of fudging behind the scenes I’ve talked about before, to try to make expected outcomes more likely to happen. Famously one of the most basic versions of this is in Fire Emblem, where they double roll odds, so if something says 75%, it’s actually 87.5% so it FEELS more like 75% to people (A 95% chance in Fire Emblem is much closer to 99%!) Based on this, I think there are improvements we can and should make here, so the game behaves closer to what you would EXPECT it to, even if it is within acceptable outcomes.
任天堂游戏在我之前谈到过的幕后做了很多捏造的事情，试图让预期的结果更有可能发生。众所周知，最基本的版本之一是在《火焰纹章》中，他们将掷骰子的几率翻倍，所以如果有东西说 75%，它实际上是 87.5%，所以对人们来说感觉更像是 75%（《火焰纹章》中 95% 的几率要高得多）接近 99%！）基于此，我认为我们可以并且应该在这里进行改进，因此游戏的行为更接近您的期望，即使它在可接受的结果范围内。

Personally, this was awesome for me to confirm and was a good use of time yesterday. I like constantly challenging our game design to see if we can do better, and I think this confirms we can. It won’t be easy, it won’t be overnight, and it may not even be soon…but I think it is worth exploring, and I think we’ll start doing that as soon as possible. 
就我个人而言，这对我来说非常棒，而且昨天的时间得到了很好的利用。我喜欢不断挑战我们的游戏设计，看看我们是否可以做得更好，我认为这证实了我们可以。这并不容易，不会一蹴而就，甚至可能不会很快……但我认为这是值得探索的，我认为我们会尽快开始这样做。

Thanks for reading all. Hope your roll downs are within expected variance, and take it easy :)