| Long matches can cause problems for tournaments. For example,
the starting times of subsequent matches can be substantially delayed
causing inconvenience to players, spectators, officials and television
scheduling. They can even be seen as unfair in the tournament setting
when the winner of a very long match, who may have negative aftereffects
from such a match, plays the winner of an average or shorter length
match in the next round. Long matches can also lead to injuries to
the participating players. One factor that can lead to long matches
is the use of the advantage set as the fifth set, as in the Australian
Open, the French Open and Wimbledon. Another factor is long rallies
and a greater than average number of points per game. This tends to
occur more frequently on the slower surfaces such as at the French
Open. The mathematical method of generating functions is used to show
that the likelihood of long matches can be substantially reduced by
using the tiebreak game in the fifth set, or more effectively by using
a new type of game, the 50-40 game, throughout the match.
KEY
WORDS: Tennis, scoring systems, sport, generating functions,
long tennis matches.
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