Competitiveness

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?

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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

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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.

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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.

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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.

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Beware printyourbrackets.com

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 printyourbrackets.com.

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.

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All That Luck

In Skill and Luck in Backgammon, I described the process by which I settled on the parameters tourneygeek should use to simulate backgammon tournaments. The result was that the luck factor should be set to three, which implies that backgammon is 75% luck, and only 25% skill.

This does not mean, however, that backgammon is an easy game – a game in which a few small, easily learned heuristics will allow you to play at a high level. Open any of the many more advanced monographs on backgammon strategy and tactics, and you’ll soon see that there’s an enormous body of knowledge that expert players have and others do not. There’s plenty of skill in backgammon, it’s just that this skill is regularly overwhelmed because there’s even more luck.

Is there really that much luck in backgammon? How do players cope with it?

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