Hypergeometric Distribution: How and Why

There’s been so much discussion recently (which was lead by Dayani here and I’ve been trying to contribute to) in the theorycraft community about how Chain Heal works and how it will affect High Tide. One of the problems that the theorycraft has run into so far is expressing exactly how the random selection process affects the average of Chain Heal’s healing. I suggested previously that a specific kind of distribution might help, and later showed that the this distribution provides a good estimate of real (simulated) Chain Heal and High Tide interaction. In addition, I’ve been talking at length about why we should be caring about statistical ideas in Warlords of Draenor – especially because it will evidently inform our understanding of the value of Stats.

We know that this distribution – known as the “Hypergeometric” distribution – gives a good description of how High Tide interacts with Riptides and Chain Heal, in both imaginary and “realistic” situations, and for any number of applied Riptides upon the raid. It’s pretty damn useful, so it’s fairly clear that we should be using it.

However, so far I haven’t actually explained (successfully) what this distribution is and how to use it! This post is dedicated to explaining (in part) what the Hypergeometric distribution does and how to actually use the thing. I think that this is important to getting it more widely used in the community.

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To Craft a Sim – Part 4

In this series of posts, I’m talking about putting together a simulation I’ve built called CHsim. It’s designed to simulate the way Chain Heal will behave in Warlords of Draenor – including interactions with player positioning, talents, incoming damage, Riptide, and Mastery bonuses.

My first post in this series discussed why I’m developing CHsim, and I left off by pointing out some good reasons why I’m not using SimCraft to achieve my goals. The second post talked about raid positioning and how I’ve modelled a “realistic” raid. The third post discusses the way I’m making Chain Heal bounce from person to person, and was supposed to talk about what that means for High Tide modelling. However, I didn’t get as far as that before; this post is extending on the Chain Heal mechanism I talked about earlier.

CH_Bouncing1

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Simulating Chain Heal – Preliminary Results

Sim, simming me/sim, simming me/sim, sim, simming you.

As I’ve been going on about for ages, I’ve been developing a simulation of Chain Heal’s application in Warlords of Draenor raid-type situations, including the variation on raid positioning and decision making. Today, I’ll be taking a look at some preliminary results of the simulation which I spent the Easter weekend simming and analysing.

CH_Bouncing2

Not long ago Dayani posted a nice first analysis of Chain Heal and it’s interaction with Riptide and High Tide. If you haven’t read it already, it’s fantastic and you should. Either way, she made an interesting point about how Chain Heal’s mean healing changed as the number of Riptides on the raid increased. However, by her own admission she wasn’t able to mathematically extend her analysis to any size of raid or number of Riptides;

To analyse the full range of possible number of injured targets versus possible number of Riptides on the raid would take me way too much brainpower, and that’s what I’m hoping the computer models being worked on by Stoove and Haileaus will allow us to do in a more efficient manner.

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To Craft a Sim – Part 3

In this series of posts, I’m talking about putting together a simulation I’ve built called CHsim. It’s designed to simulate the way Chain Heal will behave in Warlords of Draenor – including interactions with player positioning, talents, incoming damage, Riptide, and Mastery bonuses.

My first post in this series discussed why I’m developing CHsim, and I left off by pointing out some good reasons why I’m not using SimCraft to achieve my goals. The second post talked about raid positioning and how I’ve modelled a “realistic” raid. This post discusses the way I’m making Chain Heal bounce from person to person, and what that means for High Tide modelling.

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To Craft a Sim – Part 2

In this series of posts, I’m talking about putting together a simulation I’ve built called CHsim. It’s designed to simulate the way Chain Heal will behave in Warlords of Draenor – including interactions with player positioning, talents, incoming damage, Riptide, and Mastery bonuses.

My last post in this series discussed why I’m developing CHsim, and I left off by pointing out some good reasons why I’m not using SimCraft to achieve my goals. Today, I’ll be expanding upon a feature which CHsim does have which SimCraft doesn’t really; player positioning. CHsim simulates the positioning of a raid in 2D space (like a top-down view of the fight) whereas I have it from Theck that SimCraft doesn’t track positions in 2D space.

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To Craft a Sim – Part 1

In this series of posts, I’m talking about putting together a simulation I’ve built called CHsim. It’s designed to simulate the way Chain Heal will behave in Warlords of Draenor – including interactions with player positioning, talents, incoming damage, Riptide, and Mastery bonuses.

Anyone following me on Twitter recently will have seen me talk endlessly about something I call CHsim. I’m super excited to show off my work right now, not only because it stands to give us a way to investigate optimal strategies for Chain Heal, but also because this is some of the best work I’ve ever done… ever!

What & Why

The idea for CHsim came when I was trying to hash out how Chain Heal will behave in Warlords of Draenor. This turns out to be extremely difficult – there are so many variables in the mix and variations of questions that you want to ask. We need some creative solutions! There are, essentially, three ways to find out what we want;

  1. TheoryCraft – write down a formula (or several!) to describe the way your heal works
  2. SimulationCraft – write a program to crunch numbers and spit out some statistics for you
  3. ExperimentalCraft – go run a combat log analysis or check your Recount after your raid

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Statistics in Warlords of Draenor

Why You Should Care About Statistics in Warcraft

Last week I mentioned that the statistics of raid health in Warlords of Draenor are going to be important because of the changes to smart heals (now dumb heals) in the expansion. Today, and because I think a lot of people will be suspicious of this claim, I’m going to show you why I said that. Hopefully, you will walk away convinced that we should be caring about the way health is distributed throughout the raid in Warlords of Draenor raiding.

I’m going to run through a couple of interesting demonstrations of statistics applied to questions that we might reasonably want to ask. They are questions which have intuitive answers, but which so far haven’t been proven in any real sense as far as I can tell.

Furthermore, although I will be making some assumptions, the assumptions that I make in these examples are not restrictive in the way the results are applied. I think that this is the most important thing to note, because it means that these results reflect real situations which we will see

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