What is the Correct Way to Seed a Knockout Tournament?

2000 ◽  
Vol 107 (2) ◽  
pp. 140 ◽  
Author(s):  
Allen J. Schwenk
Keyword(s):  
Knockout Tournament

Some Monotone Almost Balanced Knockout Tournament Plans

1993 ◽  
Vol 7 (3) ◽  
pp. 361-368
Author(s):  
R. W. Chen ◽  
F. K. Hwang ◽  
Y. C. Yao ◽  
A. Zame
Keyword(s):  
Real World ◽  
General Class ◽  
Binary Tree ◽  
The Real ◽  
Random Labeling ◽  
Knockout Tournament ◽  
Rooted Binary Tree

Knockout tournaments are often used in sports (or experiments where preferences are registered by comparisons instead of measurements) to determine the champion of an event. A knockout tournament plan (KTP) for n players is a rooted binary tree with n leaves to be labeled by the n players. Each subtree of two leaves represents a match between the two players labeling the two leaves; the winner of the match then moves on to label the root of the subtree. While there are many KTPs to choose from for a given number of players, in the real world an almost balanced KTP is usually chosen. One reason could be the perception that a balanced KTP is “fair” to the players, in the sense that, given a random labeling of leaves by players, a stronger player has a better chance to win the tournament. Surprisingly, it has been shown that not all KTPs have this property, and it is difficult to prove this property for any general class of KTPs. So far the property has been shown to hold only for balanced KTPs. In this paper we extend it to some classes of almost balanced KTPs.

Game Outcome Uncertainty and Television Audience Demand: New Evidence from German Football

2018 ◽  
Vol 19 (2) ◽  
pp. 140-161 ◽  
Author(s):  
◽  
Benno Torgler ◽  
Sascha L. Schmidt
Keyword(s):  
Decision Making ◽  
Economic Literature ◽  
Game Outcome ◽  
European Football ◽  
Knockout Tournament ◽  
Television Audience ◽  
New Evidence ◽  
Uncertainty Of Outcome

Abstract Despite its prominence in the economic literature, our knowledge regarding the role of game outcome uncertainty (GOU) in spectator decision-making is fairly limited. Even worse, studies testing the uncertainty of outcome hypothesis (UOH) by exploring TV demand for European football have further intensified the original ambiguity. In this paper, we revisit the role of GOU in spectator decision-making by testing the UOH with regard to two different sporting products: (1) domestic league and (2) knockout tournament games. Analyzing TV demand for almost 1,500 German football games, we find support for the UOH in league, though not in knockout tournament games.

A Random Knockout Tournament (D. E. Knuth)

SIAM Review ◽  
1987 ◽  
Vol 29 (1) ◽  
pp. 127-129 ◽  
Author(s):  
D. E. Knuth ◽  
O. P. Lossers
Keyword(s):  
Knockout Tournament

scholarly journals NO TRUMP!: A statistical exercise in priming

2016 ◽  
Author(s):  
andrew gelman
Keyword(s):  
North American ◽  
Donald Trump ◽  
Significant Difference ◽  
Knockout Tournament

How are people unconsciously influenced by the rise of Donald Trump? We test the theory that Trump’s rise has irrationally changed the behavior of one group of people: elite bridge players, whom we assume are otherwise completely typical. We examine the hands played in one of the premier North American bridge events, the Vanderbilt Knockout Tournament, in 1999 and 2015. We find that players had significantly higher probabilities of making No Trump contracts in the 2015 period compared with the earlier periods. We conclude that in the latter period, defending players are subtly deranged by the prospect of Trump and play their hands worse. By contrast, a 2015 European tournament shows no significant difference with the earlier 1999 tournament. This strengthens our conclusion.

DIFFERENCES IN PUTTER TRAJECTORY AND PSYCHOPHYSIOLOGICAL VARIABLES BETWEEN PROFESSIONAL AND AMATEUR GOLFERS UNDER STRESS CONDITION

2018 ◽  
Vol 18 (07) ◽  
pp. 1840008
Author(s):  
JIN SEUNG CHOI ◽  
JEONG WOO SEO ◽  
GYE RAE TACK
Keyword(s):  
Heart Rate ◽  
State Anxiety ◽  
Stress Condition ◽  
Maximum Velocity ◽  
Professional Group ◽  
Maximum Speed ◽  
Psychological Variables ◽  
Self Confidence ◽  
Professional Golfers ◽  
Knockout Tournament

This study compared the differences in the putter trajectory and psychophysiological variables of winners and losers in a competitive putting game that targeted professional and amateur golfers under stress. Eight professional golfers (handicap: [Formula: see text]) and eight amateur golfers (handicap: [Formula: see text]) participated. To maximize the tension of the competition, the putting game was held in a single-elimination one-on-one knockout tournament with a single 2.1[Formula: see text]m putting competition for each group. In the case of a hole-in or a failure by both golfers, the game resumed until the winner was determined. To compare the golfers during the game, the maximum speed, moving length, and amplitude of the putter head during the back-swing and the follow-through were set as the motion variables; and psychological variables (heart rate, heart rate variability (HRV), and Competitive State Anxiety Inventory-2 (CSAI-2)) were analyzed. The results showed significant differences between the putter trajectory variables (maximum velocity and amplitude of the putter head during follow-through) of the groups, but no differences in the psychophysiological variables. In comparing winners and losers within each group, however, the professional group showed a difference in only the psychophysiological variables (HRV and self-confidence of CSAI-2), whereas the amateur group showed a difference in only one putter trajectory variable (follow-through length). It was quantitatively confirmed that factors that determine the outcome of the game differed at a technical level.

Bayesian optimal design of fixed knockout tournament brackets

2016 ◽  
Vol 12 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Jonathan Hennessy ◽  
Mark Glickman
Keyword(s):  
Monte Carlo ◽  
Simulated Annealing ◽  
Optimal Design ◽  
Expected Utility ◽  
Partial Information ◽  
Direct Computation ◽  
Monte Carlo Estimate ◽  
Bayesian Optimal Design ◽  
Knockout Tournament ◽  
Carlo Estimate

AbstractWe present a methodology for finding globally optimal knockout tournament designs when partial information is known about the strengths of the players. Our approach involves maximizing an expected utility through a Bayesian optimal design framework. Given the prohibitive computational barriers connected with direct computation, we compute a Monte Carlo estimate of the expected utility for a fixed tournament bracket, and optimize the expected utility through simulated annealing. We demonstrate our method by optimizing the probability that the best player wins the tournament. We compare our approach to other knockout tournament designs, including brackets following the standard seeding. We also demonstrate how our approach can be applied to a variety of other utility functions, including whether the best two players meet in the final, the consistency between the number of wins and the player strengths, and whether the players are matched up according to the standard seeding.

scholarly journals When Rigging a Tournament, Let Greediness Blind You

2018 ◽  
Author(s):  
Sushmita Gupta ◽  
Sanjukta Roy ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Decision Making ◽  
Parameterized Complexity ◽  
Algebraic System ◽  
Black Box ◽  
System Of Equations ◽  
Standard Format ◽  
Feedback Arc Set ◽  
Fpt Algorithm ◽  
Knockout Tournament ◽  
Greedy Solution

A knockout tournament is a standard format of competition, ubiquitous in sports, elections and decision making. Such a competition consists of several rounds. In each round, all players that have not yet been eliminated are paired up into matches. Losers are eliminated, and winners are raised to the next round, until only one winner exists. Given that we can correctly predict the outcome of each potential match (modelled by a tournament D), a seeding of the tournament deterministically determines its winner. Having a favorite player v in mind, the Tournament Fixing Problem (TFP) asks whether there exists a seeding that makes v the winner. Aziz et al. [AAAI’14] showed that TFP is NP-hard. They initiated the study of the parameterized complexity of TFP with respect to the feedback arc set number k of D, and gave an XP-algorithm (which is highly inefficient). Recently, Ramanujan and Szeider [AAAI’17] showed that TFP admits an FPT algorithm, running in time 2^{ O(k^2 log k)} n ^{O(1)}. At the heart of this algorithm is a translation of TFP into an algebraic system of equations, solved in a black box fashion (by an ILP solver). We present a fresh, purely combinatorial greedy solution. We rely on new insights into TFP itself, which also results in the better running time bound of 2^{ O(k log k)} n^{ O(1)} . While our analysis is intricate, the algorithm itself is surprisingly simple.

scholarly journals Inference From a Knockout Tournament

1968 ◽  
Vol 39 (2) ◽  
pp. 583-592 ◽  
Author(s):  
J. A. Hartigan
Keyword(s):  
Knockout Tournament

scholarly journals Universal statistics of the knockout tournament

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Seung Ki Baek ◽  
Il Gu Yi ◽  
Hye Jin Park ◽  
Beom Jun Kim
Keyword(s):  
Knockout Tournament
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