You're Reading: Playing the Percentages in Golf (with Calculator)
It’s not always your golf swing, short game, or even putting stroke that holds you back from shooting your best scores. Over the course of 18 holes, course management decisions will have some effect on your scorecard. Typically, the concept of poor course management on the golf course is associated with golfers choosing riskier shots and not playing safe. While this is true, the goal should be to achieve the smart play or the shot that result in the best overall probability to make the lowest score on a given hole.
Put simply, playing the percentages or playing the percentage shot in golf is choosing a given shot type, approach, strategy, etc., that has the highest likelihood of success.
For instance, while we do not always listen to reason in the moment, the shot from within the woods over the trees and over a pond onto the green has a low likelihood of success. What’s more, in this case, with the threat of penalty from the pond, the odds are high that the result will be a disastrous score for that hole. Instead, the shot with (hopefully) a far greater chance of success is punching out to the fairway and proceeding to finish the hole from there.
This is an obvious example, and certainly in golf there are situations that involve options with considerably more uncertainty. Furthermore, playing the percentages and factoring the odds into your course management, should extend beyond an isolated shot consideration, particularly when the right decision is not as clear as it is in the above hero-or-zero scenario.
The issue with making isolated decisions is that while they might produce a safe alternative and avoid a big number, they risk the mistake of leaving something on the table. Furthermore, it is not always the safe play now that will serve as the safe or smart play for the entire hole.
To put this to extremes, imagine the reliability of hitting your pitching wedge off the tee. You will almost certainly hit more fairways and avoid the danger off the tee. However, this is obviously not the correct strategy as it makes any effort to achieve a green in regulation or even being greenside in regulation difficult.
Risk-reward holes by design are intended for either a riskier play or a safer play that avoids the hole’s danger. As golfers, the risky shot with greater potential reward is more enticing but this is not say that it is not the correct approach. A lot depends on the situation, weather conditions, and your comfortability with the shots you have to pull off. Leading a tournament or a match provides an additional consideration.
So, where does this leave us? To truly make an educated and accurate course management decision, we must analyze a hole’s strategy 1) among the different alternatives from the tee, 2) the alternatives that extend from each tee shot option, 3) the shot alternatives that extend from those shots and so on.
For example, on a par 4, you consider hitting either your driver or 3-wood. Let’s say that 15% of the time you will pull/hook your driver, 40% of the time you will push/slice, and the remaining 45% of the time you will hit your drive down the middle. Assuming slightly better accuracy with your 3-wood, the respective percentages may be 10% hook/pull, 30% push/slice, 60% down the middle.
So far, it sounds like 3-wood is the better option.
Now, after hitting your driver, let’s say that from the left or right woods, 75% of the time you will just punch out and the other 25% of the time you will go for the green, hitting the green 10% of the time and missing 15% of the time.
From the fairway with your driver, you will hit the green with your first shot 80% of the time and miss the green 20% of the time.
Since 3-wood will leave a longer approach, the same shots will have different and worse probabilities: from the woods, punch out 80% of the time, hit the green 5% of the time, miss the green 15% of the time. From the fairway, after hitting 3-wood, you will hit the green 65% of the time and miss the green 35% of the time.
After the punch out, for both the driver and 3-wood scenarios, you will hit the green 90% of the time and the other 10% you will take two shots. When failing to hit the green from the woods, you will hit the green 50% of the time and the other 50% of the time it will take you two shots to hit the green.
With this information, conditional probability and expected value are needed to determine the best play on the hole.
“Conditional Probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.”
Using the definition of conditional probability, we need to define our events and their associated probabilities.
In our case, the different events are:
The ideal scenario is hitting the fairway and then the green. With driver, the odds are 45% of hitting the fairway and 80% of hitting the green from there.
Put differently, of the 45% of the time that driver finds the fairway, the next shot will find the green 80% of the time. In mathematics, “of” means to multiply.
Therefore, before playing a shot on the hole, the odds of hitting the green in two is .8 x .45 = .36 or 36%.
A similar process must be computed for all the other scenarios and child scenarios (a child scenario, e.g., would be hitting or missing the green after punching out from the woods).
To calculate an actual score (or average score) from the Driver or 3-Wood alternatives, we must use expected value.
“Expected Value is the weighted average of all possible outcomes.”
The following are the expected values or expected strokes for hooking left, slicing right, and down the middle when hitting driver off the tee along with the initial odds of hitting each:
Note: Slice right and hook left have the identical expected number of strokes. This is strictly due to the fact that we treated the shot options from both scenarios identically. This can be fine-tuned or tailored to a specific hole or any other factors.
To be clear, these are the average (weighted average) number of shots required to hit the green including the stroke used to hit the tee shot.
Consequently, to calculate the expected value of selecting driver off the tee, we use the following calculation:
Similar calculations were performed for the child scenarios of each tee shot to arrive at the expected strokes used above.
Note: For the sake of simplicity, the above does not consider putts. If you want, you can simply assume two putts. However, more practically, we know that if we hit driver and are closer to the green, we not only have a better chance of hitting the green but will likely leave a shorter (and more makeable) putt than when we are approaching the green from a further distance. To be complete, the odds of a one putt, two putt, and three putt should be determined and entered into the overall calculation.
It should quickly become apparent that the process of calculating conditional probability is cumbersome to say the least. Instead, calculations such as these are much better suited for a computer than a human. That is why you should use Golf Surfer™’s conditional probability golf calculator shown below.
The video tutorial will indicate how to use the calculator. For further questions, refer to the guide towards the end of the article. Ultimately, though, you can extend the scenarios as much as you want and tailor the shot types to the particular hole you are playing. Obviously, it works best when you know the probabilities of each shot based on your game and ability.
Okay, so using the calculator to determine the best possible strategy is great for planning out your round beforehand. During the round, though, the average golfer will not be capable nor benefit from performing such an in-depth calculation.
Nevertheless, this same thought process should be practiced. Do not worry about deciding between club selections based on a difference of one hundredth of an expected stroke. However, make an approximate calculation that you know you can trust the majority of the time.
In winning interviews on the PGA tour, it is typical for the golfer to comment on his playing one shot at a time and how that helped him in his victory. Staying present is important. A big number can crop up at any time during a round of golf. This is true for professional golfers and amateur and recreational golfers alike.
Thinking ahead to the finish line and failing to concentrate in the moment can come back to hurt you.
However, considering your strategy for the entire hole should be included for every shot even when focusing on the present shot at hand. Making these considerations is important for two reasons.
First and foremost, if done properly with an accurate portrayal of a golfer’s ability and tendencies, the best shot will be chosen more often. Second, while this may depend on the type of player and personality you have, your confidence in the shot you select and your commitment to the shot should improve knowing that you carefully and rationally weighed the expected or likely score from each possible shot. You will not have to second guess whether the shot you hit now will place you in the optimal position for your next shot.
In the end, you can achieve a one-shot-at-a-time mentality while also playing the percentages.
While this article may have seemed like a little bit of a math class, hopefully everything was simple enough to grasp. Making a thorough analysis of your abilities and appropriate strategies based off them will improve the mental and course management aspects of your game.
