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Why all the mathematicians favor VRR/MWC tournaments over PR tournaments

Posted By: Rick Janowski
Date: Wednesday, 9 January 2013, at 9:09 a.m.

In Response To: Why all the mathematicians favor VRR/MWC tournaments over PR tournaments (Timothy Chow)

I agree that a tournament based on wholly PR-based (error rate) criteria is an extreme case and has the undesirable quality that winning the match is not necessarily the primary goal. However, it is possible to devise a hybrid approach without the negative quantities you identify, based on some normalisation of win-rate. Let’s look at the two possible criteria:

A. Actual Win Rate: This is simply, the normal criteria from a conventional win-rate based tournament.

B. Predicted Win Rate: From the average PRs of players and their specific opponents, the predicted win-rate may be evaluated from conventional Elo-based formulas and the relationship of PR difference to Elo difference.

A hybrid win rate can then be established as some relative weighting of the above two approaches, (eg, 67/33) which effectively guarantees that the primary goal of the tournament is winning the most matches, whilst reducing the extreme luck element.

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