Matrix Multiplication in Excel — Markov Chains

This post is part of the “Matrix Multiplication in Excel” series. It’s composed of a math introduction, a silly interlude and an interactive tutorial (you are here). By the end of the series, you’ll learn how to perform Markov Chain calculations, which are used in some damage calculations.

Now that we know some of the basics, I’m going to introduce a toy problem where one would use matrix multiplication, step through how to calculate it in Excel and then give an example used forensic economics.

Click here to download Matrix Multiplication.xlsx.

Scenario 1: Ping Pong Problem

Suppose two ping pong players (labelled left and right) are tied near the end of a game. In order to win, one of them has to have a two point lead. Suppose that, on any given volley, the left player has a 55% chance of winning.

The game can be thought of as having five states:

  1. (2,0) – The left player wins.
  2. (1,0) – The left player is winning by one.
  3. (0,0) – The game is tied.
  4. (0,1) – The right player is winning by one.
  5. (0,2) – The right player wins.

Graphically, the transitions between these states can be seen as follows.

ppFig1

The left player increases his score with the probability p(LW), in this case 55%. How do we calculate the probability that the left player wins? Continue reading →

Matrix Multiplication in Excel — What is the Matrix?

This post is part of the “Matrix Multiplication in Excel” series. It’s composed of a math introduction, a silly interlude (you are here) and an interactive tutorial. By the end of the series, you’ll learn how to perform Markov Chain calculations, which are used in some damage calculations.

‪‎Trigger Warnings‬: Authorial Self-Insertion, In Medias Res, Movie References, Fake Trigger Warnings

neo_morpheus

Just a few days ago, I had been lying on my back, surrounded by doctors, atrophied and struggling to gasp for breath. This man wanted billions of humans to experience the same process. A note of discord rang through my heart as I tried to imagine the whole of humanity simultaneously squinting as they adjusted to their new eyes.

Morpheus misinterpreted my discomfort and didn’t miss a beat. Continue reading →

Matrix Multiplication in Excel — Math Introduction

This post is part of the “Matrix Multiplication in Excel” series. It’s composed of a math introduction (you are here), a silly interlude and an interactive tutorial. By the end of the series, you’ll learn how to perform Markov Chain calculations, which are used in some damage calculations.

A matrix (plural matrices) is a rectangular array of numbers, symbols or expressions arranged in m rows and n columns. For matrix A below, the element at row i and column j is indexed as a_{i,j}.

mmFig1 Continue reading →