Thoughts on the Golf Handicap System

I love golf.  For so many reasons.  It’s a metaphor to life - as much as you perfect your swing, you will get the occasional bad bounce, and sometimes a lip-out.  Every shot you hit is different - the lie, the wind, how fast the greens are, where the pin is.  It is such a hard game, but so rewarding at the same time, when you see a ball sail through the air, just the way you visualized.

Among all these reasons though, I especially love that in golf, you can have a close, fun, competitive match with anyone no matter your skill level.  This is enabled by the golf handicap system, which measures a player’s potential, based on the recent scores they have submitted.  

How does the current golf handicap system work?

The current golf handicap system, in my opinion, is reasonably good. For each round, it factors in the difficulty of the golf course to determine what a player at a particular skill level (determined by their handicap) would typically score.  A golf course’s difficulty is determined by two numbers:

• Course Rating:  This number describes what a scratch golfer (i.e. 0 handicap) would shoot on a good day.  (e.g. if the course rating is a 72.5, then a scratch golfer would shoot a 72.5 on a good day)

• Slope Rating:  This number describes how difficult the golf course is for a handicapped golfer.  More specifically, this number divided by 113 (don’t ask me why but it is what it is) quantifies for each handicap increment, how many more strokes a golfer would shoot.  For example, if the slope rating is 135, then a 10 handicapper is expected to shoot 135/113 = 1.2 more strokes than a 9 handicapper

Combining the two numbers together, you can create a graph of what a golfer at any handicap is expected to shoot.  The blue line below describes what player of various handicaps would typically shoot on a par 72, 72.5 course rating, 135 slope rating course:

Looking at the graph initially, this line makes sense.  Since this course is relatively difficult given its slope rating (significantly higher than 113), the expected score gets significantly higher than the “45 degree line”, as the handicap goes higher.  (for example. a 20 handicapper is expected to shoot 25 over par on this course).

However, if we look at the scratch / plus handicap side of the spectrum, this is where the graph starts to not make sense.  The line actually dips below the 45 degree line, meaning that in the current golf handicap system, advanced / plus handicap golfers are expected to shoot lower at a more difficult golf course than an easier one.  While plus handicap golfers are great golfers, this shouldn’t be the case, and suggests that the golf handicap system doesn’t work well for very advanced golfers.  In fact, it can lead to cases where advanced golfers are unfairly penalized when playing a match against golfers with higher handicaps.

So, what do we do about this?  Is there a solution?

A Potential Alternative Golf Handicap Calculation

To search for a reasonable solution, we need to go deeper into what the USGA does currently to evaluate courses.  Looking into more detail, we see that they essentially estimate (1) what a scratch golfer would shoot, and (2) what a bogey golfer (i.e. 18 handicap) would shoot to generate course and slope ratings.  These are the two data points that the USGA spends the most effort on, and likely the most accurate.  For that reason, I propose that any handicap system we propose must preserve the scratch and bogey golfer ball score estimations

Another observation is that we should create a system where plus-handicap golfers are expected to shoot worse on more difficult courses (unlike what we see today).  This would mean that the slope of the graph will have to be different depending on the handicap level, and that our equation will have to be non-linear.  

With these observations in mind, I propose an equation that maps the relationship between golf handicap and expected score on a golf course as follows:

f(x) = a x^2 + bx + c

where x is the golf handicap, and f(x) is the score relative to par expected on that golf course

Choosing a quadratic equation allows for two advantages:

• It allows for different slopes at different values

• It ensures that the rate of change is smooth (for quadratic relationships, the rate of change is linear, and you can infer that by using calculus :) )

With this structure, we can solve for a, b, c by knowing a few things:

• f(0) = c = course rating.  The expected score of a scratch golfer needs to match the current course rating

• f(18) = 324a + 18b + c = course rating + slope rating / 113 x 18.  In other words, the expected score of a bogey golfer should match the current score implied by the course and slope rating (and we saw before that the USGA spends significant effort estimating this)

• f’(0) = b = 1.  This is a little harder to explain, but essentially the logic is as follows:

• Let’s say we are looking at a difficult golf course.  At handicaps > 0, the slope should be greater than 1, as higher handicap golfers will tend to deviate further from their expected skill level for harder courses

• On the other hand, for plus-handicappers (handicap < 0), the slope should be less than 1, as lower handicap golfers are also expected to shoot above their expected scores

• For both of the above to be true, that means at handicap = 0, the slope must be 1 

Putting all these together (we essentially now have 3 equations with 3 unknowns) yields that:

• a = (bogey golfer score - 18 - scratch golfer score) / 324

• b = 1

• c = scratch golfer score

So for example, a 72.5 course rating, 135 slope rating, par 72 course, would yield the equation:  Expected Score = 0.011 x Handicap^2 + Handicap + 0.5, and becomes the red line in the graph below:

Notice that:

• The red and blue lines intersect at 0 and 18 handicaps, which preserves the scoring estimations that USGA does for each course for scratch and bogey handicappers

• The red line curves up in the plus handicapper region and stays above the 45 degree line, which matches our intuition and objective

• One potential downside / change that this equation introduces is that it penalizes mid-handicappers a little bit (i.e. 10 handicaps are expected to shoot better than before).  That said, looking at average scores by handicap published by the USGA, we already see a similar pattern to what we observe here, so this is a change (as a 6-8 handicapper myself) that I’m willing to accept

To sense check the new system, we also ran some simulations for 73 course rating, 100-150 slope ratings with the new equation vs. the old system.  We can quickly see that the new methodology preserves the “difficulty” expectation for plus handicappers (i.e. the green lines are still above the blue lines), unlike the old methodology, while ensuring that the curve for higher handicaps, don’t change significantly.

By no means do I think this is a perfect handicap system (and it never will be!), but I feel like it does address some of the flaws that the handicap system provides for advanced amateur golfers! Would love thoughts on whether this alternative method resonates and if there are even better solutions!