Four ball best ball 1.

In this paper a four-ball-best-ball (4BBB) model for pairs of golf players is set up. The 4BBB match-play scoring system is seen to satisfy a basic requirement of fairness. It is shown that it is not strictly possible to rate individual players as 4BBB players. However, a (reasonably broad) class of individual players is identified such that it is possible to rate them individually as 4BBB players. The capacity of an individual to play birdies is seen to be a very important determinant in being a successful member of a 4BBB pair, but there are other minor factors as well. Consideration is given to equal and unequal 4BBB pairs. The transitive law is seen to apply for 4BBB pairs. Thus, if pair A is better than pair B, and pair B is better than pair C, then pair A must be better than pair C. Correspondingly, if pair A is equal to pair B, and pair B is equal to pair C, then pair A is equal to pair C. Consideration is given to some strategic issues in 4BBB match-play golf. For example, the conditions under which a player should take a greater risk and have a higher probability of obtaining a bogie in order to achieve a higher probability of scoring a birdie, are determined. Also, the conditions under which a player, noting that his partner is about to have a ‘bad’ hole and score only a par or a bogie, should ‘play safe’, are determined. Thirdly, players who can interact in certain ways are seen to have an advantage over those pairs that cannot do this. Finally, one pair’s optimal strategy when they see that their opponents are about to score a par or a bogie, but not a birdie, is analyzed. Key points A model for four-ball-best-ball match-play golf is established, and used to show that, although there can be other factors, the capacity of an individual to play birdies is a very important determinant in that player being a successful member of a four-ball-best-ball pair. Although it is not possible in general to rate play-ers individually as 4BBB players, a class of indi-vidual players is identified such that rating the players within that class is possible. Equal and unequal 4BBB pairs are considered, and the transitive law is seen to apply for 4BBB pairs. For example, if pair A is better than pair B, and pair B is better than pair C, then pair A must be better than pair C. Several strategic issues for individual players and pairs of players are considered, and optimal strate-gies identified. Key words: Strategies for four ball best ball golf, selecting pairs of four ball best ball players Introduction In four-ball-best-ball match-play golf, two players (A and B) play as a pair against two other players (C and D) who also play as a pair. All players play in the usual way. On the first hole, pair (A, B)’s score is the minimum number of strokes A or B took to complete the hole. Correspondingly, pair (C, D)’s score on the first hole is the minimum number of strokes C or D took to complete the hole. One pair wins the hole if their minimum score is less than the other pair’s minimum score, and 1 is added to their match score. The match ceases as soon as one pair has an unbeatable lead and/or 18 holes have been completed. If the match is tied or ‘squared’ after the 18th hole has been played, more holes may be played until a winner is determined by a lead by 1. This is called a ‘playoff’. In this paper several questions are addressed. What is a useful model for studying 4BBB golf? Is the scoring system fair? Can individual players be ranked even though they are playing as pairs? Can pairs of players be ranked or can cyclical relationships (pair A better than pair B, who is better than pair C, who is better than pair A) exist between several pairs? Is it possible for pair A to be stronger than pair B at 4BBB golf, but weaker at other forms of the game? Are birdies particularly important in winning at 4BBB golf? Can two players make strategic decisions to interact in a useful way on a particular hole, and on any hole in general? Can such decisions be usefully made both statically and dynamically? In a recent paper, Hurley (2007) studied how a given set of players might be combined into pairs so as to form a very effective team against an identical opposing team. This is studied in a second paper by the authors (Pollard and Pollard, 2008).