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Bonus Points and Incentives in Rugby

2011 October 23
by Liam Lenten

The 2011 Rugby World Cup has climaxed with hosts New Zealand being crowned champions for the second time last night (joining Australia and South Africa, while England has won it once). They did so by defeating France 8-7 in a tense affair in the Final at Auckland’s Eden Park, in front of (a capacity) 60,000 supporters – certainly not the easy way as most expected, but having endured 24 years of angst since their last title in 1987, all Kiwis will still take it nonetheless! As a tribute to the ‘Shaky Isles’, another post on Rugby seems in order.

One of the most distinctive nuances about the game lies in how in some tournaments (including the World Cup and Super Rugby), there exists a system of ‘bonus’ competition points (in round-robin stages). Specifically, in addition to the standard four competition points for a win (two each for a draw), either team is rewarded with one bonus point if they score four or more tries in a match (irrespective of how many tries the opposition scores). Furthermore, the loser receives an additional (narrow-loss) bonus point if they lose by seven or fewer (match) points. The purpose of these bonus points is to reward attacking Rugby by encouraging teams to score more tries (for example, by running the ball more and kicking it less), and to maintain interest in the game longer in situations where the result has already become highly certain.

A co-author of mine, Niven Winchester (these days at MIT), is a native New Zealander who will no doubt be ecstatic after having been at the game in person. He is primarily a Trade Economist, but also has a penchant for modeling predictions and ranking systems in sport. His 2008 paper in JQAS (abstract here) concludes that the current bonus points system is sub-optimal at his defined objective of revealing the best quality teams over the duration of the season. Instead, he favors altering the narrow-loss bonus threshold from seven to five match points, and changing the try bonus to either a minimum of eight tries, or alternatively, for scoring at least three more tries than the opponent does. The last of these recommendations is particularly compelling when recalling some of the pivotal results from the previous World Cup in 2007. To quote the paper:

Anecdotal evidence also supports our assertion that defensive capability should be included in a try bonus decision rule. In the quarterfinals of the 2007 Rugby World Cup, New Zealand and Australia, two teams heavily favored to advance to the next round, lost to France and England respectively. Several rugby experts, including Australian coach John Connolly, suggested that the attacking style adopted by the two favorites was partly responsible for the unexpected results. In turn, incentive structures in place in the competitions that these teams regularly participate in may influence playing styles. Specifically, New Zealand and Australia compete in the Tri-Nations competition where a (four-or-more) try bonus point is offered, and France and England participate in the Six Nations tournament, where try bonuses are not awarded.

Niven has since adapted this methodology with further modeling improvements to consider a similar question using data for the Australian Football League (AFL) and the National Football League (NFL), with some interesting findings for both.

Perhaps one of the most fascinating questions yet to be explored with Rugby match data is the degree to which such a system effects within-match team and player behavior, compared to what would be observed in the absence of bonus points. In terms of the try bonus, a very simple way to do this would be to look at the distribution of the number of tries scored by teams in matches, and determine whether the frequency of ‘4’s is greater than that suggested by a fitted or stylized distribution. If we look at a histogram of tries scored in all Super Rugby regular-season matches from 1996-2011 (see here), we see that it is not easy to tell from a simple ‘eyeball’ whether this is indeed the case. Even if so, one still needs to control for match-specific factors that may be driving the observed distribution.

As for the narrow-loss bonus, a similar exercise is possible, though arguably more difficult to validate, since there are other factors skewing the incentives simultaneously, and also given the discrete nature of the scoring system. Nevertheless, this is a nice little example of how sports data provides much potential to the Economics profession with respect to the ability to test for incentives and strategies in games.

5 Responses
  1. Duane Rockerbie permalink
    October 24, 2011

    A weakness of the current point system in the World Cup in round-robin play is that it encourages lop-sided scores when a powerful country plays a minnow. This was very evident in this year’s World Cup. The point system is irrelevant in the knockout stages and thus the scoring was much tighter. I suppose some like to watch New Zealand hammer a much weaker opponent to gain scoring points but it is not very sportsman-like. In these types of contests, perhaps the point system could be weighted to reflect the quality of the opponents.

  2. Liam Lenten permalink
    October 24, 2011

    Duane, I must admit the Pool Stage stage in the World Cup is really too short for bonus points to make much of a difference – that bonus points overcomes an extra win (the way that has happened on the odd occasion in Super Rugby) , though it is worth noting that with the only pairing of teams that finished on equal wins (France and Tonga in Pool A), France still would have progressed even if Tonga had beaten Canada like they should have (ALL other things being equal). Hence, perhaps the incentive effect is not so strong in RWC, but it still present in Super Rugby.

  3. David permalink
    October 25, 2011

    A similar system exists in ranking high school football teams for post season playoffs in Oklahoma. For all the details you can check out the OSSAA website for official documents, but I will do my best to summarize here.

    In each classification, there are 4 districts of 8 teams each. Each team plays all other teams in its district, and their win-loss record in those district games determines seeding for playoffs (the 4 top-seeded teams in each district make playoffs). In the (frequent) event of 3-way tie in district win-loss records, Teams are further ranked by the sum of their marginal points in those 7 district games, up to +/- 15 points a game.

    In other words a Win is a Win, first and foremost. But among teams with the same number of wins, the “most convincing” teams get the nod for the post season. For example:
    * Team A wins 4 games, each by 15+ points, and loses 3 games by 3 points each, then Team A’s district record is 4-3, and their marginal points score is 51 (15+15+15+15-3-3-3)
    * Team B wins 4 games, each by 7 points, and loses 3 games by 7 points each, then Team B’s district record is 4-3, and their marginal points score is 7 (7+7+7+7-7-7-7)
    * Team C wins 4 games, each by 3 points, and loses 3 games by 15 points each, then Team C’s district record is 4-3, and their marginal points score is (3+3+3+3-15-15-15)
    The OSSAA system will rank Team A as the winner of the tie created by the 4-3 records, because they defeated their opponents handily (by 15 or more points), and their losses were close games.

    Whether or not Team A, in it’s 4 wins, scored 15 points or 115 points is of no consequence, only that they scored 15 more than their opponent. This rewards teams for winning by more than two touchdowns, but does not require offenses to be especially high scoring or aggressive, provided a team can play well on defense. No team can overcome a losing record against common opponents, but it is unlikely that a team is unfairly eliminated from the post-season based on a single, closely-contested ballgame when an otherwise sound body of work has been put together.

  4. October 25, 2011

    Duane, I must admit the Pool Stage stage in the World Cup is really too short for bonus points to make much of a difference – that bonus points overcomes an extra win (the way that has happened on the odd occasion in Super Rugby) , though it is worth noting that with the only pairing of teams that finished on equal wins (France and Tonga in Pool A), France still would have progressed even if Tonga had beaten Canada like they should have (ALL other things being equal). Hence, perhaps the incentive effect is not so strong in RWC, but it still present in Super Rugby.
    +1

  5. Rob Macdonald permalink
    October 27, 2011

    Great post Liam. Winchester’s work is interesting; though I doubt we’ll see bonus points in other football codes any time soon.

    This notion of having incentives within a game (beyond merely the incentive to win) is very important to consider at the moment. Some pundits have suggested a monetary incentive to go from back to front of the field may have contributed to Dan Wheldon’s death at Las Vegas recently.

    http://blogs.findlaw.com/tarnished_twenty/2011/10/dan-wheldon-dead-was-indy-car-track-too-crowded-badly-designed.html?DCMP=NWL-cons_sportslaw

    Duane, is your causality right in saying:

    “The point system is irrelevant in the knockout stages and thus the scoring was much tighter.”

    I’m not so sure about that.

    The scoring was much tighter because of the relative team quality. I doubt very much that the lack of bonus points is the determinative factor. As for blowouts; look at the major vs minor nations scorelines and you’ll see that quite often there were far more than 4 tries: http://www.rugbyworldcup.com/home/fixtures/poolstage.html

    Sure, it is relevant and interesting to look for these incentive effects; but sometimes the supposed incentive effect becomes a bit of an urban myth and we don’t see the woods from the trees by underplaying the relevance of the absolute differences in the quality of the teams in the first place (we see the same problem on the flipside when people lament teams tanking. No, oftentimes, they are just pathetic teams playing better teams).

    A proposal to weight the system of bonus points on the basis of team quality is not appropriate on sport integrity grounds.

    Nor is is practicable. It would require a team of handicappers going from match to match, deciding upon the appropriate bonus point criteria based upon the weather, team lineups, significance, home ground advantage etc.

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