*T*, and then create a 350x1 matrix containing an initial guess at the ratings of all the teams, which we call π. We then perform the following calculation iteratively:

πUntil π reaches a steady state. (In this case, 8 iterations gives us accuracy to 4 digits.) With a 350x350 transition matrix, it is also feasible to solve this analytically as a system of linear equations, but I didn't have a library handy for that computation._{k+1}= π_{k}T

Here are the comparative results of the two different implementations:

Predictor | % Correct | MOV Error |
---|---|---|

TrueSkill + iRPI | 72.9% | 11.01 |

LRMC (random walkers, 2006) | 71.3% | 11.65 |

LRMC (matrix, 2006) | 71.5% | 11.65 |

LRMC (random walkers, 2010) | 71.8% | 11.40 |

LRMC (matrix, 2010) | 72.2% | 11.37 |

(2006 and 2010 here refer to the two different LRMC functions from [Sokol 2006] and [Sokol 2010].)

This shows some small differences between the implementations (probably due to different degrees of accuracy) but no significant errors. So it would appear that despite its good showing in predicting recent NCAA Tournament results, LRMC is not as accurate as TrueSkill, IMOV and some of the other ratings.

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