TY - JOUR
T1 - Catch-Up
T2 - A Rule That Makes Service Sports More Competitive
AU - Brams, Steven J.
AU - Ismail, Mehmet S.
AU - Kilgour, D. Marc
AU - Stromquist, Walter
PY - 2018/10/21
Y1 - 2018/10/21
N2 - Service sports include two-player contests such as volleyball, badminton, and squash. We analyze four rules, including the Standard Rule (SR), in which a player continues to serve until he or she loses. The Catch-Up Rule (CR) gives the serve to the player who has lost the previous point—as opposed to the player who won the previous point, as under SR. We also consider two Trailing Rules that make the server the player who trails in total score. Surprisingly, compared with SR, only CR gives the players the same probability of winning a game while increasing its expected length, thereby making it more competitive and exciting to watch. Unlike one of the Trailing Rules, CR is strategy-proof. By contrast, the rules of tennis fix who serves and when; its tiebreaker, however, keeps play competitive by being fair—not favoring either the player who serves first or who serves second.
AB - Service sports include two-player contests such as volleyball, badminton, and squash. We analyze four rules, including the Standard Rule (SR), in which a player continues to serve until he or she loses. The Catch-Up Rule (CR) gives the serve to the player who has lost the previous point—as opposed to the player who won the previous point, as under SR. We also consider two Trailing Rules that make the server the player who trails in total score. Surprisingly, compared with SR, only CR gives the players the same probability of winning a game while increasing its expected length, thereby making it more competitive and exciting to watch. Unlike one of the Trailing Rules, CR is strategy-proof. By contrast, the rules of tennis fix who serves and when; its tiebreaker, however, keeps play competitive by being fair—not favoring either the player who serves first or who serves second.
KW - 91A20
KW - MSC: Primary 60J20
KW - Secondary 91A80
UR - http://www.scopus.com/inward/record.url?scp=85056143309&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85056143309&partnerID=8YFLogxK
U2 - 10.1080/00029890.2018.1502544
DO - 10.1080/00029890.2018.1502544
M3 - Article
AN - SCOPUS:85056143309
VL - 125
SP - 771
EP - 796
JO - American Mathematical Monthly
JF - American Mathematical Monthly
SN - 0002-9890
IS - 9
ER -