# How does the math work in jdecision?

Jdecision uses the Decision Matrix technique, sometimes called Grid Analysis or Pugh Matrix. In essence, considerations are weighted based on importance and opinions are scored across each consideration. Jdecision then uses a weighted average and shows the winner.

Let's take the *Which car should I buy?* example. You start with some basic considerations and then specify how important each consideration is by assigning a weight between 0 and 5 with 5 being most important. You can see that Style is the most important factor in our decision.

Consideration |
Weight |
---|---|

Style | 4 |

Gas mileage | 3 |

Price | 2 |

You then add some options such as BMW and Camry and score each option across the three considerations. You can specify how well the option satisfies the consideration by assigning a score between 0 and 5.

Consideration |
Camry Score |
BMW Score |
---|---|---|

Style | 1 | 4 |

Gas mileage | 3 | 3 |

Price | 4 | 1 |

Jdecision multiplies the consideration weight by the option's score for that consideration.

Consideration |
Camry: weight*score |
BMW: weight*score |
---|---|---|

Style | 4 * 1 = 4 | 4 * 4 = 16 |

Gas mileage | 3 * 3 = 9 | 3 * 3 = 9 |

Price | 2 * 4 = 8 | 2 * 1 = 2 |

Then add up the products for each option.

Consideration |
Camry: weight*score |
BMW: weight*score |
---|---|---|

Style | 4 | 16 |

Gas mileage | 9 | 9 |

Price | 8 | 2 |

Total | 21 | 27 |

The absolute scores 21 and 27 aren't very meaningful by themselves because we don't know the total possible score. To calculate the total possible score for either car, you multiply each consideration's weight by the highest possible score (5) and then add the products together. So the total possible score in this example is 45.

Consideration |
Weight |
Total possible score |
Product |
---|---|---|---|

Style | 4 | 5 | 20 |

Gas mileage | 3 | 5 | 15 |

Price | 2 | 5 | 10 |

Total |
45 |

To calculate an option's score as a percentage of its potential score, just take the score and divide it by it's highest possible score.

Option |
Score |
Total possible score |
% of it's potential |
---|---|---|---|

Camry | 21 | 45 | 21/45 = 47% |

BMW | 27 | 45 | 27/45 = 60% |

To get the score on a 0-5 star scale, we multiply the percentage by 5 stars to get the final score.

Option |
% of score potential |
Stars |
---|---|---|

Camry | 47% | 47% * 5 = 2.5 (rounded) |

BMW | 60% | 60% * 5 = 3 |