Juletip #9 - The Optimal Drive becoming better at golf using proc optmodel

[OMH]

The Optimal Drive: Solving Bogstad Golf Course with Mixed Integer Linear Programming

By “The Data Caddie”

Golf is often described as a game of art and feeling. But at its core, it is a physics engine governed by strict constraints: distance, friction, aerodynamics, and probability. For the data scientist, a round of golf isn't just a walk down the fairway, it’s a resource allocation problem waiting to be solved.

In this post, we break down how we utilized SAS PROC OPTMODEL to build a "Digital Caddie" for Oslo Golfklubb (Bogstad). By treating the course as a mathematical network and the player’s bag as a set of constrained resources, we moved beyond simple heuristics to find the mathematically optimal path to the hole.

This blog is of course not a complete guide of how to become Tiger Woods – it is merely a fun Christmas project showing how SAS procedures can hopefully support your improvement and simulate how to become a better golfer.

I do not take any responsibility if You are not improving your swing – that is done by practicing for You. I understand there are numerous numbers of options we could model into the optimization – however I believe we need to set a limit at some stage. This blog post will describe my approach to it. Don’t shoot the messenger – at least yell FORE before - so I can duck away.

Golf is a game played on a six-inch course—the one between Your ears. A perfect, optimal strategy is useless if the player cannot execute the required shot consistently under pressure. The optimization of strokes is a powerful data problem, but the real game is one of mental resilience, muscle memory, and managing the inevitable "noise" of a bad shot.

Our model might prove that a 3-Wood and a 9-Iron is the "optimal" path to the green. But this is worthless if the player's 3-Wood is their least consistent club, one they only hit purely 1 out of 5 times. The true best strategy for that player might be a "sub-optimal" 4-Hybrid and an 8-Iron, which they can hit confidently 9 out of 10 times.

So, what is the purpose of our PROC OPTMODEL caddie if it can't account for this human element?

The answer is that our model is not a replacement for the golfer; it is a decision-support tool designed to reduce cognitive load.

The average golfer is already processing dozens of variables: "Is the pin in the front or back? Is the wind helping or hurting? Will this lie cause a hook? Is a 5-Iron enough to clear that bunker?"

Our model's job is to solve all the complex physics before the round begins. It takes the "Plays Like" distance, the dynamic wind, the elevation, and the player's scaled ability and provides a clear, data-driven recommendation. It removes the guesswork.

By having a trusted, optimal plan, the player is freed from the burden of calculation. They can step up to the ball with a single, clear-minded task: focus on execution.

This post is not about replacing the art of golf with a cold algorithm. It's about using a powerful algorithm to handle the complex science, so the player can be free to perform the art.

Let's build the model.

The Objective: From "Greedy" to "Optimal"

Most GPS watches and casual golfers use a "Greedy Algorithm" approach: Hit the longest club that doesn't go over the green. While simple, this heuristic fails to account for complex trade-offs. I believe this approach will go for most amatures and even pros at some holes on a course.

We have a lot of help from study the course we are playing – however remember everything and to be prepared with data - will this make me a better player? I must say maybe, – as the most critical factor wrt. nailing that course is You. What I’m aiming for is to help you so that You can be prepared and hopefully improve your score based on the modelling of the course and Your stats et such.

Figure 1 Bogstad Golf Course overview of course

For example, on a 310-meter Par 4 with a strong tailwind:

• Greedy Strategy: Driver (240m) + Lob Wedge (70m).
• Optimal Strategy: 4-Iron (180m) + 9-Iron (130m).

Why might the second be better? Perhaps the Driver brings a hazard into play, or the 4-Iron landing zone is flatter. To solve this, we need Mixed Integer Linear Programming (MILP). We aren't just looking for a valid sequence of shots; we are looking for a set of shots that minimizes risk and effort while adhering to a strict stroke budget.

The Constraints: Topology and Meteorology

Optimization requires precise input. We defined the Bogstad course using vector mathematics rather than just static lengths.

1.   The Setup: Three Core Data Inputs

Our model relies on three key pieces of information:

1. work.hole_data (The Course): This dataset defines the challenge.
   • Hole, Par, Length: The standard scorecard data.
   • HoleIndex (HCP/STI): This is the critical variable. It ranks the holes from 1 (hardest) to 18 (easiest) and is essential for fairly distributing handicap strokes.
     
     

The Course Data

We utilized the official Oslo GK Slope/Scorecard to determine the Course Handicap (Spillehandicap), which gives us the "Allocated Strokes" per hole based on the hole's difficulty index (HCP Index).

We then modeled the physical properties of every hole:

• Bearing: Compass direction from tee to green (0-359°).
• Elevation: Elevation changes in meters (affecting "Plays Like" distance).
• Length: Official measured distance.

2. work.pro_golf_bag (The "Pro" Baseline):
   • This dataset defines the "100%" distance for each club (Driver, 3-Wood, etc.). We use this as a "pro" or "scratch golfer" baseline to scale against.
3. %let Player_HCP = 18; (The Player):
   • This macro variable is the main control. It defines the player whose game we are simulating.

The Physics Engine

Before the optimization runs, we calculate an Effective Distance Factor. This is not a static variable; it is calculated dynamically for every hole based on the interaction between the hole's bearing and the live weather data.

We use trigonometry to decompose the wind vector relative to the hole direction:

SAS

/* SAS Logic for Dynamic Wind */
AngleDifference = abs(HoleBearing - WIND_DIRECTION_DEGREES);
Headwind_Component = cos(AngleDifference_Radians);
Sidewind_Component = sin(AngleDifference_Radians);

/* Penalize distance for headwind, penalize accuracy/distance for sidewind */
Hole_Wind_Factor = 1.0 - (Headwind_Component * WIND_STRENGTH_FACTOR);

This means a 15 km/h wind from the West will shorten a West-facing hole, lengthen an East-facing hole, and apply a sidewind penalty to North/South holes.

2. The Solver: PROC OPTMODEL

This is the heart of the operation. We use the SAS Optimization procedure to formulate the problem.

The Decision Variables

We define an integer variable NumberOfStrokes[h, k], representing how many times club k is used on hole h.

The Objective Function

We want to minimize the total strokes. However, to prevent the solver from simply picking the longest clubs that "just barely" pass the hole, we introduced a secondary objective: Minimal Overshoot.

This tiny penalty ∑ forces the solver to choose the combination of clubs that lands closest to the pin without being short, rather than just any combination that covers the distance.

The Constraints

The model must obey two strict physical laws:

1. Distance Coverage: The sum of the effective distances of the chosen clubs must equal the hole length plus the calculated overshoot.
2. Stroke Budget: The total strokes used must be less than or equal to the player's "Personal Par" (Course Par + Handicap Strokes - 2 Putts).
   
   

SAS

/* The MILP Model formulation */
min TotalObjective =
    sum {h in HOLES, k in CLUBS} NumberOfStrokes[h,k]
  + sum {h in HOLES} (Overshoot[h] * 0.0001);

con MakeHole {h in HOLES}:
   sum {k in CLUBS} Effective_Club_Distance[h,k] * NumberOfStrokes[h,k]
   = Plays_Like_Distance[h] + Overshoot[h];

con ParConstraint {h in HOLES}:
   sum {k in CLUBS} NumberOfStrokes[h,k] <= par[h] - PUTT_BUDGET[h] + AllocatedStrokes[h];

3. The Output: From Inventory to Sequence

PROC OPTMODEL returns an Optimal Inventory. For Hole 1, it might tell us: {Driver: 1, PW: 1}. It tells us what to use, but not when.

To generate the final "Caddie Card," we post-process this inventory. Since we assume a standard strategy of maximizing distance off the tee, we sort the optimal inventory by club distance (descending). This transforms the raw optimization data into a human-readable sequence:

Hole 1 (Par 4, 321m) - Headwind

1. Shot 1: Driver (Effective Dist: 196m) -> Remaining: 125m
2. Shot 2: Pitching Wedge (Effective Dist: 125m) -> On Green
3. Shot 3: Putter
4. Shot 4: Putter
   
   

Reports you can get:

And these can be available on your phone or tablet to bring on to the course. Even on your watch I presume.

Conclusion

By combining PROC OPTMODEL with robust data preparation, we created a system that adapts to the player's handicap, the course's specific layout, and the live weather conditions. It demonstrates that golf strategy isn't just about intuition; it's a solvable linear programming challenge.

For those playing Bogstad GK, remember to check your Course Handicap before running the model—parameters matter!

Happy holidays with coding and golfing.
/Ole-Martin Hafslund - novice green card golf player

[BeStibolt]

I'm impressed, Ole Martin! I didn't even know you played golf! This is so interesting! Thank you for sharing!