# Science and Golf II: Proceedings of the 1994 World Scientific Congress of Golf

By A. J. Cochran; M. R. Farrally | Go to book overview

29

How to lower your putting score without improving

Middletown, New Jersey, USA

Abstract

While playing golf, after you have mercifully reached the green, you have to decide where to target your putts. You might say that it is obvious-target the hole. But then the probability of being short is about 0.5. The conventional wisdom is to target beyond the hole, so that you won't be short. The pundits use expressions like, “never up never in.” But how far beyond the hole? Here the advice gets diverse and qualitative. Dave Pelz (1989) says 17” for all putts. My pro says, “for long putts target a two-foot cir cle around the hole and for short putts target about one foot beyond the hole.” The purpose of this research is to provide more specific quantitative advice. An approximate solution is to target a distance beyond the hole given by the formula: [Two feet]*[Probability of sinking the putt]. This solution applies to any putt. The dependence on putting ability and the difficulty of the putt is captured by the probability of sinking the putt. This tactic saves about 1 putt per round over conventional wisdom. The solution is derived from a Markov decision model of the putting process.

Keywords: Dynamic Programming, Markov Decision Model, Optimization, Probability, Putting, Simulation, Statistics, Tactics.

1 Introduction

The problem addressed in this paper is introduced in the abstract. To attack the problem, I need a model of a single putt. Associated with a putt, is the position on the green that the ball would stop if there were no hole. I call this the stopping position. Of course, if the putt is sunk, then the ball never gets to the stopping position, because it falls in the hole. The stopping position is modeled as a random position on the green. The proba bility distribution of the stopping position depends on (i) the difficulty of the putt, (ii) the skill of the putter, and (iii) the target selected by the putter. The target selected by the putter is the expected value of the random stopping position. The question addressed in this paper is: what is the optimal target for each putt?

I assume in this paper that the green is flat. The advice derived from the flat green assumption is useful for most non-flat green scenarios. However, there are exceptions. For example, suppose the hole is at the edge of a cliff. Then you would aim short of the hole until the probability of sinking the putt was

Science and Golf II: Proceedings of the World Scientific Congress of Golf. Edited by A.J. Cochran and M.R. Farrally. Published in 1994 by E & FN Spon, London. ISBN 0 419 18790 1

-186-

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