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Golf and the Six Sigma Statistics

-Anuj Medtiya

Have you heard these words “six sigma process” or “six sigma strategies“? In this article, I will be explaining you what it actually means with a simple and lovely example of golf. This article will also provide you with a brief understanding of normal distribution. So let’s hop onto the golf cart and travel to our first step.

Sigma ‘σ’, which ironically looks like the ‘6’ turned rightwards by 90 degrees is used to represent the variation in a data set. It measures the deflection of the data points from the mean i.e. how far is each point from the mean on an average. The following example will provide a much clearer view.

So, we have arrived where the ball is placed on the golf course. And we are required to hit the ball in the hole marked with the red flag which is pretty obvious. The hole is 330 yards away which is too long to be covered in a single shot. There are 2 sand traps in between which will lead to a penalty if our ball goes into the trap. Thus the best way to go about this game will be to hit the ball to the center between the sand traps, i.e. in the green area between 150 to 250 yards. The best shot will be at around 200 yards.

Now suppose you had 20 tries, with 20 different golf clubs and you are a beginner. The balls went to different locations covering a wide area of the golf course.

We start by understanding the 1 Sigma process.

So this is basically where you hit around 30% of your shots (6 shots) within the correct distance (between 150 and 250 yards). And the remaining 70% are spread over a wider area. There is a lot of scope for improvement. You will notice the dark green shaded curve at the left. This shaded area represents the probability. The mean is usually at the center of the probability distribution which in our case is 200 with the highest probability. Variation is possible on either side of the mean. As you can see, some shots have crossed the 250 yards mark while some didn’t reach the 150 yards mark. The probability curve is flatter and quite stretched as the shots are distributed over a wide area.

We now travel to the 2 Sigma process.

You have practiced a little which made you slightly more accurate with your shots. You also ruled out a few golf clubs which you didn’t like. The 2 sigma process is where you hit around 70% of your shots (14 shots) within the correct distance. The rest 30% are spread outside the target but with smaller deviations from the mean as compared to the 1 Sigma process above. You will notice that the green probability distribution curve is less stretched and the probability of the center part inclusive of the mean has increased and is more curvy then the previous one.

Now we arrive at the 3 Sigma process.

You have become much better at the game. You can now understand the effect of wind on your shots to some extent. You filter out some more golf clubs from the set. The 3 sigma process is where around 93% of your shots (18.5 shots) are within the correct distance. The remaining 7% are deviated from the mean even lesser now. The probability distribution graph has become taller and thinner at the center. The red line representing the spread of shots has shortened considerably.

Now we jump onto the 4 Sigma process.

You have become so good at golf that you are thinking of converting your passion into a career. The 4 sigma process is where 99% of your shots are within the correct distance. Now, you also try to hit the ball closer to the mean of 200 yards. The tails of the probability distribution curve mostly fall within the range. The distribution has become even taller at the center as the probability of achieving the mean has increased greatly. The spread has reduced further.

Now we arrive at the 5 Sigma process.

You have started playing professionally. You only use your 3 favorite golf clubs which you are comfortable with. The 5 sigma process is where 99.97% of your shots are within the correct distance. There is a negligible probability (0.03%) of you making an error at this stage. The probability distribution is concentrated tightly at the center. The variation around the mean is also very small. You must be wondering what the 6 sigma process would be if the 5 sigma process is so tight.

Finally we arrive at the 6 Sigma process.

You have mastered the game of golf. You have identified your best golf club out of the 3 which you played with. You use the direction of the wind at your advantage more accurately. The 6 sigma process is where 99.9997% of your shots are within the correct distance. All your shots are concentrated in the center. They’re either at the mean distance of 200 yards or very close to that. The variation is so less that your probability distribution looks like the Eiffel Tower; triangular, tall and thin. The 6th sigma is the variation of 0.0003%!

Six sigma has wide industry applications where it is used for improving the product, process or the service and eliminate the defects. Our golf example had experience, practice, wind, quality of the golf club as factors affecting the variation and thus the Six Sigma. Similarly, different industries have different factors affecting quality of their product or service which they can improve with the help of Six Sigma techniques.

This concept was developed by an engineer Sir Bill Smith working at Motorola in 1986. Six sigma can be thought of as a measure of performance with Six Sigma being the goal. For example, for a product manufacturing company, Six Sigma can be used in the following manner to reduce defects.

Now that you have understood the Six Sigma, let us understand what we learnt about the normal distribution in a brief summary.

The different sigma processes used in the example above showed us some important characteristics about the normal distribution.

  1. The mean is at the center with the highest probability. In our case, each sigma process had the same mean of 200 yards.
  2. The normal distribution is a symmetric distribution. This means that the variation about the mean are symmetrically distributed on either side of the mean. Some shots crossed the 250 yard range while some couldn’t reach the 150 yard mark.
  3. The greater the accuracy about the mean,-
    • lesser the spread of the distribution
    • taller will be the probability distribution curve at the center
    • thinner will be the probability distribution curve

I hope you enjoyed the article. Stay tuned!



Published by mscnm

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