Competitive balance in a quasi-double knockout tournament

ABSTRACT

In 2001, the All-Ireland Gaelic Football competition changed from being a singleknockout tournament to a quasi-double knockout competition. Similar natural experiments in economics and operational research theory suggest such a change should reduce the competitive balance in the competition. Using a Hirschmann–Herfindahl Index measure of concentration and a bootstrapping approach, we confirm that the new structure leads to a less competitive outcome and, importantly, this outcome is less uncertain. Our bootstrapped results show that in the long run, with larger samples, there is less competitive balance in the new competition structure than in the older structure competition structure. Finally, we also consider a stochastic dominance approach to evaluating the change in tournament structure, but the low power due to the presence of ties in our small sample leads to an inconclusive outcome.

KEYWORDS:

• Sports economics
• competitive balance
• bootstrapping
• operation research
• stochastic dominance

JEL CLASSIFICATION:

• L83
• C15

Acknowledgements

The authors would like to thank the editor of Applied Economics and also the two referees who provided valuable comments that were incorporated into the final draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Edwards (1996) gives an example of a quasi-double knockout tournament that was held in Great Falls, Montana, in February 1990.

² The smaller average attendances at League of Ireland soccer games can be found in Reilly (2015) and Jena and Reilly (2016).

³ The Hirschmann–Herfindahl Index (HHI) is a measure of market concentration used in the anti-trust literature and in the sports economics literature.

⁴ It should be noted that there is an important strand in the economics literature on tournaments that evaluates tournaments on their ability to get the contestants to expend effort. Rosen (1986) is a prime example of this literature in the context of competitors in sport. For much of the literature discussed in this section, it is implicitly assumed that competitors’ effort is constant.

⁵ It is not always in the interests of the competition organizer to improve the chances of the ‘best’ team. Mastromarco and Runkel (2009) illustrate how F1 organizers seem to have introduced rule chances that hampers the better teams but increases competitive balance.

⁶ The maximum value is 1 where market shares are expressed as decimals, e.g. 0.1 for 10%.

⁷ Other levels of confidence (percentiles) are available on request from the authors.

⁸ The increased concentration of titles arising from the double knockout structure is still revealed in the higher mean HHI measures, compared to that of the single knockout structure.