Using ShotLink data that records information on every stroke taken on the PGA Tour, this paper introduces a new metric to assess putting. The methodology is based on ideas from spatial statistics where a spatial map of each green is constructed. The spatial map provides estimates of the expected number of putts from various green locations. The difficulty of a putt is a function of both its distance to the hole and its direction. A golfer’s actual performance can then be assessed against the expected number of putts.
We provide the details associated with the Markov chain Monte Carlo implementation briefly discussed in Section 3.
In a Markov chain approach, it is typical to first consider the construction of a Gibbs sampling algorithm. In a Gibbs sampling algorithm, we require the full conditional distributions of the model parameters. A little algebra yields the following full conditional densities:
Referring to the full conditional distributions in (10), we observe that sampling σ is straightforward. Most statistical software packages facilitate generation of a random variate v from the required Gamma distribution, and we then set
The remaining distributions in (10) are nonstandard statistical distributions, and we therefore introduce Metropolis steps, sometimes referred to as “Metropolis within Gibbs” steps for variate generation (Gilks, Richardson and Spiegelhalter 1996). A general strategy in Metropolis is to introduce proposal distributions which facilitate variate generation and yield variates that are in the “vicinity” of the full conditional distributions. For the generation of λi, we consider putting data obtained from the 2012 PGA Tour up to and including the Ryder Cup on September 30, 2012. The data were obtained from the website www.pgatour.com and are summarized in Table 3 by considering the median putting performance by PGA Tour professionals at a distance of r feet from the pin. From Section 2.1 of the paper, we recall that the expected number of putts is given by
|Putting distance r (in feet)||Proportion of||E(Z)|
For the generation of βj, we consider the Normal
corresponding to putting angles of average difficulty. Using similar constraints at other distances r, we obtain knots for the piecewise linear function g. To be precise, we set
For the generation of δ, we need to be aware of the constraint δ>0. We consider the proposal distribution Gamma(0.25, 1.0). This is based on a subjective estimate δ=0.25 and a sufficiently large variance to capture the true value of δ.
Reaching a par 3/4/5 hole in regulation indicates that a golfer has landed on the green in 1/2/3 shots.
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