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Technology is being used increasingly in sport to assist, and in some cases replace judges and referees. The photo finish has been used to help the steward decide close horse races for more than a hundred years. In some sports, such as swimming, we have seen adjudication enhanced by electronic timing. In tennis we had the electronic service line machine for many years, and now a device for picking up net cords. More recently, some forms of Rugby have used a video referee to decide on the legality of tries. Cricket followed suit, allowing umpires to refer decisions on run outs, stumpings and catches to a third umpire with access to video footage. In many other sports the media use video replays or other technology (such as the hot spot in cricket) to provide evidence for or against the umpire’s decision.

Statistical methods can be useful in rating non-elite tennis players. This paper shows how clubs can use simple optimization techniques to rate their club's players in doubles tennis competitions. Even though clubs lack all relevant information, the effects of home advantage, position played, partner and strength of team opposition can be taken into account and evaluated. The results from all competing clubs, available to the body organizing the competition, are used to rate all players in the competition, and validate the results that were obtained with limited information. We show a home ground advantage exists in non-elite doubles tennis. A simple exponential smoothing method of rating players is then tested, and shown to produce reasonable results.

Cricket teams are usually listed on the scoreboard in expected batting order, and although captains can choose to send in any of the remaining batsmen when a wicket falls, they rarely depart from the usual batting order. By optimizing a simplified model using dynamic programming, this paper shows that in all forms of cricket significant increases in expected score result if captains allow a variable batting order and base their decision on the state of the game, rather than using a set batting order.

Desirable qualities of a tournament are fairness (the better the player, the better his chance of success), balance (few one-sided matches) and efficiency (long enough to benefit the more skillful yet being completed within schedule). The World Professional Snooker Championship is examined to see how well it meets these criteria.

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.

With the growth in sports betting, it is possible to bet, both before and during a match, on a range of outcomes in tennis. This paper shows how the standard statistics published by the ATP can be combined to predict the serving statistics to be obtained when two given players meet. These statistics are then used in a spreadsheet model to predict further match outcomes, such as the length of the match and chance of either player winning. These calculations can be updated as the match progresses. The method is demonstrated by focusing on a very long men’s singles match between Roddick and El Aynaoui played at the 2003 Australian Open.

In cricket, when a batsman is dismissed towards the end of a day's play, he is often replaced by a lower-order batsman (a ‘night watchman’), in the hope that the remaining recognised batsmen can start their innings on the following day. A dynamic programming analysis suggests that the common practice of using a lower-order batsman is often sub-optimal. Towards the end of a day's play, when the conventional wisdom seems to be to use a night watchman, it may be best to send in the next recognised batsman in the batting order. Sending in a night watchman may be good judgement when there are several recognised batsman and several lower order batsmen still to play (say four of each). However, with smaller numbers (two of each, for example), then, with very few overs left to play, it may be better to send in a recognised batsman.

Luck can play a big part in tournament success, and progress is not necessarily the best measure of performance. A linear model is used to fit least squares ratings to margins of victory in the cricket World Cup. The Duckworth/Lewis rain interruption rules are used to project a winning second innings score and create a margin of victory in runs, equivalent to that used when the team batting first wins. Results show that, while the better teams progressed through the first round of the competition, some injustices occurred in the Super-Six round. This appears to be due to the double counting of selected matches. Ordering teams by average margin of victory gives similar results to the more complicated linear model, and its use as a tie breaker is suggested. Publication of the margin of victory as estimated by the Duckworth/Lewis method for second innings victories in all one-day matches would provide a common margin of victory suitable for analysis.

While the official Association of Tennis Professionals (ATP) computer tennis rankings are used to seed players in tournaments, they are not used to predict a player’s chance of winning. However, since the rankings are derived from a points rating, an estimate of each player’s chance in a head to head contest can be made from the difference in the players’ rating points. Using a year’s tournament results, a logistic regression model was fitted to the ATP ratings, to estimate the chance of winning as a function of the difference in rating points. Once the draw for a tournament is available, the resultant probabilities can be used in a simulation to estimate each player’s chance of victory. The method was applied to the 1998 Men’s Wimbledon, 1998 Men’s US Open and the 1999 Men’s Australian tennis championships.

In Australian rules football, points are scored when the ball passes over the goal line. Six points are awarded for a goal when the ball passes between the two centre posts, and one point for a ‘behind’, when the ball passes between a centre post and an adjacent outer post. After a behind, the defending team has a free kick from the goal line. It may be worthwhile, particularly in the closing stages of a game, for a defending team voluntarily to concede a behind, by themselves passing the ball between the two outer posts, either to avert the possibility of an imminent goal or to increase the probability of scoring a goal themselves. A dynamic programming model is used to analyse this situation.

The major winter sport of the southern states of Australia is Australian Rules Football, played between teams of 18 players on oval grounds (the same grounds used for cricket during the summer). A match is played for four quarters, each of 25 minutes duration plus about 5 minutes of extra time. Players can run with the rugby-shaped ball, but it is moved forward more quickly by kicking or punching it to a team-mate, and with no off-side rule, the game is reasonably fast. The scoring region consists of four upright posts. Kicking the ball between the two centre posts scores a goal worth 6 points, while the region between either centre post and the corresponding outside post scores a ‘behind’ worth 1 point. Draws are rare; a typical score might be 18 goals 12 behinds, 120 points, to 12 goals 15 behinds, 87 points, for a winning margin of 33 points. In 1981 the major competition in Australia was organized by the Victorian Football League (VFL), in which 12 Melbourne based clubs played for 22 home and away rounds with a final series of six matches between the top five teams.

Using a dynamic programming formulation, an analysis is presented of the innings of the team which bats first (here referred to as the first innings) and the innings of the team which bats second (here referred to as the second innings). This allows a calculation, at any stage of the innings, of the optimal scoring rate, along with an estimate of the total number of runs to be scored (in the first innings) or the chance of winning (in the second innings). The analysis is used to shed some light on possible batting tactics (in terms of the best run rate at any stage of the innings), to quantify the effects of selecting extra batsmen in a side, and to suggest a method for the development of alternative measures of player performance. Results suggest that scoring rates should be more uniform than at present, and that the team batting second has an advantage. Possible extensions to the model are discussed.