Measuring Competition

Measuring the competitiveness is, in some ways at least, easier than measuring fairness. Fairness is a complex notion, and even if you’ve clearly identified the aspect of fairness you’d like to measure, it may be difficult to know how fair a result is. Fairness (C), for example, is defined as rewarding merit. In my computer models, merit is simply a number, and so fairness measures relating to it can be calculated precisely. But in the world, what constitutes merit is not so clear.

Competition, in contrast, is more readily visible, though there are still some serious questions about how it might be measured. In this post, I’ll work through some of the issues, and suggest a couple of competition measures that I plan to test further. Continue reading “Measuring Competition”


Fairness is such a complicated and compelling topic that it seems to have a way of taking over tourneygeek. But let’s leave it to one side, at least for a post or two. Recall that fairness is only one element in the FEPS framework for the goals of tourney design: Fairness, Efficiency, Participation, and Spectacle. Let us, in honor of March Madness – that great annual spectacle of a tournament – shift attention to the fourth element, spectator appeal, and see whether we can reach into tourneygeek’s bag of tricks and find something that will help us design tournaments that are compelling to watch.

What can we do to make our tourneys produce close games? In particular, can anything be done about the NCAA basketball tournaments ridiculous tendency to produce blowouts in its early rounds?

Continue reading “Competitiveness”

Exotic Brackets Spotted in the Wild

Here’s a bracket I found in the unfamiliar morning paper I read this morning in the hotel restaurant. (Please excuse the crude rendition – I’m on the road (at a tournament, naturally), and the laptop I brought doesn’t have my good drawing tools on it). See if you see what it is about this bracket that caused me to steal its page from the paper:

Lakeville South                  5
–                                                Lakeville South
#2 St. Thomas Academy 2

#3 Moorhead                      4
–                                               Moorehead
Hill-Murray                        2

#1 Eden Prairie                  3
–                                               Eden Prairie
Wayzata                               1

#5 Grand Rapids               6
–                                               Grand Rapids
#4 Maple Grove                4

Continue reading “Exotic Brackets Spotted in the Wild”

Rounds and Skill Progression

After looking a quite a number of analyzed brackets, I’m finally beginning to see some patterns that should have been obvious long ago. I now begin to think that I can explain why the bracket shift works for some events, and not for others.

I’ve been distracted by the question of bracket balance. Balance is, to be sure, important, and I’m not going to lighten up on my crusade against bad drops and grouped byes. But two other features are more important: the number of rounds in the path to success, and the progression of skill levels.

Continue reading “Rounds and Skill Progression”

Follow the Money

Today, a different kind of analyzed bracket.

Most of the brackets posted here have shown the prospects of the player occupying a certain line in terms of the chance of winning the tournament as a whole from that line. In this new bracket, the outlook is couched in terms of expected prize money – the player’s aggregate chance of winning any of six prizes.

The bracket I’ve analyzed is one of the possible brackets for the main even at this weekend’s Viking Classic backgammon tournament in Minnesota. The analysis gives me a chance to show a few new things besides the money, also.

Continue reading “Follow the Money”

Fairness ($)

For some time, I’ve been a little unhappy with my fairness measures. It’s time, I think, to try something new.

Something along these lines:

Fairness (D): Fairness is the correlation between the skill level of the player, and the player’s mean reward.

The reward could be expressed in dollars and cents if it is evaluated in terms of prize money (hence fairness ($) in the title to this post). But I’d like to to be a little more flexible than that – to cover situations where the reward is couched in terms of ranking points, the opportunity to play additional matches, or prize money, or whatever else, including various combinations.

Continue reading “Fairness ($)”


I’m planning to play Viking Classic backgammon tournament in Minnesota next weekend, and contacted the director to see if he needed any brackets. He allowed as how he thought he had things well in hand because he’d found what he needed on

After some back and forth, he’s decided to let me draw some brackets for the tourney. The stuff he’d found on PYB was pretty awful.

Continue reading “Beware”