TY - JOUR

T1 - Serving strategy in tennis

T2 - Accuracy versus power

AU - Gerchak, Yigal

AU - Kilgour, D. Marc

N1 - Publisher Copyright:
© Mathematical Association of America.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - In tennis, the server has an advantage—the opportunity to serve again without penalty, if the attempt results in a fault. A common strategy is to hit a powerful or “tricky” first serve followed, if necessary, by a weaker second serve that has a lower probability of faulting even if it is easier to return. Recently, commentators have argued that this standard strategy is flawed and that the second serve should be as difficult to return as the first. This advice contradicts Gale’s theorem, which we reformulate and provide with a new (analytic) proof. Then we extend it with a model of the rally that follows the successful return of a serve, providing additional insight into the relative effectiveness of the “two first serves” strategy. The only tools we use are basic probability and introductory calculus.

AB - In tennis, the server has an advantage—the opportunity to serve again without penalty, if the attempt results in a fault. A common strategy is to hit a powerful or “tricky” first serve followed, if necessary, by a weaker second serve that has a lower probability of faulting even if it is easier to return. Recently, commentators have argued that this standard strategy is flawed and that the second serve should be as difficult to return as the first. This advice contradicts Gale’s theorem, which we reformulate and provide with a new (analytic) proof. Then we extend it with a model of the rally that follows the successful return of a serve, providing additional insight into the relative effectiveness of the “two first serves” strategy. The only tools we use are basic probability and introductory calculus.

UR - http://www.scopus.com/inward/record.url?scp=85032832747&partnerID=8YFLogxK

U2 - 10.4169/math.mag.90.3.188

DO - 10.4169/math.mag.90.3.188

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AN - SCOPUS:85032832747

SN - 0025-570X

VL - 90

SP - 188

EP - 196

JO - Mathematics Magazine

JF - Mathematics Magazine

IS - 3

ER -