Games of Chance, Games of Skill, Probability and the Kerry-Dublin replay

Games of chance are those in which the outcomes is governed by a probability over which the participants have no control. The probability of a specific outcome depends on the game. For example, the probability of “heads” in a coin toss is 1/2 whereas the probability of a "6" from the roll of a dice is 1/6. People have made wagers on games of chance for centuries and the payout for a particular wager is proportional to the probability of the outcome. Because the outcome in these games is entirely governed by chance or luck, and are independent of the skill of the player, in the long run it is impossible to make money by gambling in this fashion.

The most common form of betting is on games of skill in which the skill or the participant(s) is a major determinant of the outcome with chance playing a greater or lessor role depending on the game. In poker, for example, the cards that the player receives are determined by chance but the outcome is significantly influenced by the skill of the player. Horse racing is a game of skill in which each animal has its specific set of racing skills that are impossible to quantify exactly but can be estimated based on ‘form’ which is a qualitative variable related to racing history, pedigree etc. The form of a horse relative to other horses in the race determines its probability of winning and the odds of winning offered by bookies and betting houses are directly related to this probability. For example, a horse thought to have a 1/2 (or 50:50) chance of winning is likely to have 1/1 odds or ‘even money’, one with a less than 50% chance will be given long odds (2/1, 3/1 etc.) and one with a greater than 50% chance will have short odds (1/2, 1/3, etc.). Though the relative skill of the horses is a major determinant of the winner of a horse race, chance can also have a significant influence; the most skillful horse may not win the race on a particular day.

Team sports are also games of skill but the outcome of any specific match has a certain element of chance just as with horse races. This brings us rather circuitously to predicting the winner of the Kerry-Dublin All-Ireland final replay. The current betting odds for the replay on September 15th are 1/4 for a Dublin win and 7/2 for Kerry which translates into a 0.8 probability of Dublin winning the game. The probability of Dublin winning the original match based on the betting odds was approximately 0.82. Therefore, the fact that Dublin could only draw a closely contested game that they were generally expected to win has had virtually no effect on the expectations and predictions of the betting community on the outcome of the replay. Given the information about the respective strengths of the Dublin and Kerry teams that can be gleaned from the drawn game, are the current expectations about the outcome of the replay rational? I think not.

The unchanged predictions (and betting odds) for the replay are presumably driven by the fact that in repeated matches between two teams that differ significantly in skill, the more skillful team will tend to win more of the matches. This reasoning assumes that Dublin is clearly the more skillful team and that this conclusion is not changed in any way by the new information provided by the last match between the teams. The information provided by the last match is that Dublin are not invincible, that the Dublin forwards can be shut down by the Kerry backs, that Dublin were prevented from turning the dynamic of the game mid-way through the second half, and most importantly that Kerry managed a draw in a game in which their star forwards (Clifford, Ganey) significantly underperformed. I believe that the prediction and the betting odds are not consistent with the information we have about the teams and that Kerry will win the replay by three or more points.