I just wanted to let you know that even though I received the glasses sometime back, today was actually the first day I had a chance to try them out on a golf course. To say I was pleased would be an understatement. For the first time in over a year I was able to follow the flight of my golf ball off the club head without asking a playing partner "did you see where that went?" In all honesty, I was ready to give my clubs away and give up the game I truly love so much. Thanks to you, all that has changed. I plan on playing again tomorrow and even though I am no threat to Tiger, golf has once again become fun....and isn't that what it should be? Thanks again for a great product. Sincerely yours,

IT'S NOT HOW HARD YOU SWING, BUT HOW WELL YOU SWING!

The Swing Speed Radar® is a small, affordable microwave Doppler radar velocity sensor that measures the swing speed of golfers.

Optimize your clubhead speed with your own personal Swing Speed Radar® as you practice on your own in the backyard, garage, basement, etc, as well as on the driving range or during practice rounds.

No need to hit an actual golf ball -use a wiffle ball, Birdie Ball, sponge ball or equivalent to simulate a real ball, but swing at a ball replica to release the club properly.

No need to attach device(s)to the clubhead or shaft. Use any club-switch clubs conveniently and keep swinging.

Going away on a golf holiday with a group? Need a golf draw that pairs each player with each other player exactly once? or twice? or not at all? I have developed draws that meet those requirements. Take a look at them by CLICKING HERE, Golf Draws.

Purchase a Swing Speed Radar and I'll throw in a complimentary pair of Putting Glasses AND Swing Like a Genius T-shirt. Both are valued at $29.95. Or, purchase more individually below at reduced prices.

Purchase a set of 1-iron Golf Clubs and I'll send you both two pairs of glasses and two T-shirts.

Twelve Golfers Golfing -- Optimal Pairings

One of the most common golf tournament size is twelve (12). Well, perhaps not considered a tournament; more like a match or competition. Twelve golfers at the local club that tend to get together on a fairly regular basis. They either play the same game each time, or, they like to mix it up and play different games (stroke play, match play, par points, alternate shot, etc.

The one thing these twelve do want, is to play with a variety of the others over the course of the season. It's very simple to get variety for a few players, ensuring that they be placed in foursomes with different players each round. Unfortunately, this is at the expense of the others, who end up meeting many times just so that those few have optimum variety.

To mix all twelve players up so that they all experience a similar degree of variety is a very complex problem. In mathematics, the topic which describes the different mixings of players is called combinatorics. It has been utilized in golf for many years, centering around the infamous Social Golfer Problem (optimum mixing of players).

Ironically, other size groups (such as 16) which are larger are easier to mix. The problem with twelve is that there are only 3 foursomes to arrange, thus there is limited opportunity to separate players round after round. A 16 player group has another foursome and thus another opportunity of an equitable arrangement of players.

So why is twelve so difficult? Let's take a look at the combinatorics of the problem.

1. How many variations of 12 players are possible? By variation, I mean how many different ways can they be ordered?

1 2 3 4 5 6 7 8 9 10 11 12 and 12 11 10 9 8 7 6 5 4 3 2 1 are just two examples, but, you'll notice that they are the same 3 foursome groups.

To order 12 objects, one must select them one by one. For example, say you're choosing 12 people for a team, which has 12 different roles. You need to choose one person for each role, one by one.

So, for role #1, you have 12 choices. For role #2, you then have 11 choices. If you were choosing only 2 players from the 12, there would be 12x11 = 132 different pairs of people that you could choose for the 2 roles.

In choosing 3 people from the 12, you'd have 12x11x10 = 1320 different triplets.

Choosing all 12 people yields 12x11x10x9x .... x3x2x1 = 479 001 600 or about 479 million different arrangements. In combinatorics, we have a shorthand for representing this: it's 12! which is read 12 factorial (6! = 6 factorial = 6x5x4x3x2x1 = 720)

As demonstrated with the two examples of 12 players above, many of these 479 million arrangements are the same 3 foursomes. Let's call the foursomes A, B and C. In the example above,

A = 1 2 3 4 B = 5 6 7 8 C = 9 10 11 12 and then A = 9 10 11 12 B = 5 6 7 8 C = 1 2 3 4

So basically, I've just rearranged the order of the foursomes and not changed the foursome at all.

ABC --> CBA

How many different orders are there for the foursomes which would be the same foursomes? How many ways can one order 3 objects? Answer? 3! = 3x2x1 = 6

In the 479 million arrangements, there are 6 repeats with the same foursomes (same golfers grouped together). So, we need to divide 479 million by 6.

479 001 600 / 6 = 79 833 600 or about 80 million

But each foursome of players can be the same foursome but with a different order.

Foursome A = 1 2 3 4 can also be A = 4 3 2 1 and A = 2 4 3 1, etc. There are 4! = 24 different arrangements of each of the four players in a foursome. So, the original 479 million also has 24 repeats of the same foursomes. We need to divide by another 24.

79 822 600 / 24 = 3 326 400 different arrangements of the 12 golfers that are different. But in those arrangements, there are foursomes which has players that met in many of the different foursomes of the different arrangements. For instance, the foursomes 1 2 3 4, 1 8 9 4, and 1 5 10 4 are all different but all contain players 1 and 4 so these players meet three times (say in successive rounds).

What also needs to be considered is how many "pairings" of different players are possible? What we want is to minimize the number of pairings of golfers.

For 12 golfers there are 66 different pairings:

1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-10 1-11 1-12 (12 unique pairings with Player 1)

2-3 2-4 2-5 2-6 2-7 ........ 2-12 (11 more unique pairings with Player 2 (1-2 repeat)

3-4 3-5 3-6 3-7 ......... 3-12 (10 more cause 1-2, 2-3 already counted)

this pattern continues until finally 11-12 (1 more unique pairing)

One can also calculate this using factorials. 66 = 12!/(10!2!) = 12 C 2 called a combination

Let's consider Round 1. Foursome 1 2 3 4 has 6 different pairings. The other two foursomes would also have 6 for a total 18 pairings in the first round: A: 1 2 3 4, B: 5 6 7 8, C: 9 10 11 12

To ensure as few repeats as possible in the second round, as many players as possible need to only play with players from a different foursome (1 plays with anyone from foursomes B and C). But if player 1 plays with a player in foursome A, then player 2 must play with a player from foursome B to avoid a repeat with player 1. As you can see, repeats are unavoidable.

If you jumble the numbers above even a little bit, you'll end up with more than 3 repeat pairings. The minimum number of repeat pairings in successive days is 3. So the best one can achieve is 15 new pairings (18 - 3 repeats).

In Round 3, the same would hold with a minimum of 3 repeats with Round 1 and 3 more repeats with Round 2, so 18 - 3 - 3 = 12 more unique pairings. Note that a minimum of 3 is harder to obtain in Round 3 than in Round 2.

So, the total unique pairings possible in the first 4 rounds is 18 + 15 + 12 = 45 leaving another 11 to achieve (11 + 45 = 66). Round 4 would have a potential 9 unique pairings (if you chose the previous 3 rounds just right) which leaves at least 2 more pairings to achieve in Round 5.

It ends up that it actually takes 6 rounds to achieve all 66 unique pairings, but at the expense of having multiple repeats with other pairings (twice and thrice).

See if you can work it out. I've given you some information to get started above. Or, if you'd like to get your hands on this fully optimized solution, go to the one of these:

How is your putting from over 30 feet? Do you 3-putt too often? How often?

The intent of this article is to provide some statistics from the professionals as a comparison and then provide some tips and strategies for improvement.

As a start, below are statistics for professional golfers, the best in the world. P1 are the probabilities of one putting from the various distances. P3 are the probabilities of three putting from various distances.

Note that from 30 feet, the pros only sink 7.6% of their putts and 3-putt 5.4%.

35 ft putts have about the same likelihood of 1-putts and 3-putts at about 6%.

A great study on putting to read is "How to Catch a Tiger: Understanding Putting Performance on the PGA Tour" by Fearing, Acimovic & Graves. Click on the title for a link where you'll find it if you have interest. Some of the mathematics is pretty deep but you'll still get a lot out of the graphs and explanations.

The study revealed that professionals tend to get all of their first putts within 3 feet of the hole up to about 30 foot lengths. This explains why they tend to 2-putt these lengths and rarely 3-putt them. They have excellent distance control. For longer putts, their distance control is not as good. For those putts that miss, the average distance-to-go after the first putt increases as well as the range of distances (short, long and wide of the hole) increases. I can explain this best using the chart below. All values are in feet.

putt length

10

20

30

40

50

60

average distance-to-go

1.8

2.1

2.6

3.4

4.5

5.2

std deviation dist-to-go

1.2

1.9

2.0

2.8

3.2

4.2

So, for a 30 foot putt, 7.6% of pros would sink and 93.4% of pros would miss. Of the 93.4% that miss, on average, the 2nd putt is 2.6 feet long. 68% of the misses would finish between 0.6 and about 4.6 ft away. The 5.4% of pros that 3-putt from 30 feet would be the ones that miss the hole by more than 3 feet.

Those putters that are better at sinking short putts (6 feet and under) can still 2 putt if there distance control is not the best. So, just because a player rarely 2-putts from long distances doesn't necessarily mean his/her distance control is excellent. He/she might be an excellent short putter to compensate.

Golf Balls & Temperature -- Learn how temperature affects the distance a golf ball carries. Fall temperatures mean less distance.

How to Improve Your Long Putting

The average PGA Tour Pro hits way more greens and hits it closer to the hole than amateur golfers. As I've pointed out before, Riccio did a study some years back and found the following:

AVERAGE SCORE

CATEGORY

71

75

79

81

85

89

91

95

99

GIR

12

10

8

7

5

3

2

0

0

% Fairways

81

71

61

56

46

36

31

21

11

Putts per Round

29.0

30.3

31.7

32.3

33.7

35.0

35.7

37.0

38.3

For example, a 90 shooter (about a 20 handicap) will only hit about 3 greens per round. Usually, this golfer then has a longish putt for birdie. Isn't frustrating that it's highly likely that he/she will 3-putt for bogie?

You can improve your long putting game by improving the following:

1. Your Distance Control (hit the ball the distance required more consistently reducing the average distance the ball falls short or long)

2. Improve Your Green Reading (reduce the amount you miss your putts left or right)

3. Improve Your Putter Alignment and Stroke Mechanics (so you start the ball off on the right line)

4. Improve How Solidly You Hit Your Putts (more contact off the center of the putter face)

Below, I'll provide you with some instruction/tips on distance control and will follow-up with the others in my next newsletter.

Distance Control

Improving distance control requires practice. It's all about feel. The distance a putt rolls is highly correlated with the length of the backstroke. The longer the backstroke, the greater will be the speed of the putter at impact and thus the farther the ball will roll.

I strongly recommend you do a little experimenting to determine how distance is correlated to the length of your backstroke as it all depends on the amount of acceleration you have with your forward stroke which depends on how much forward force to exert on the putter.

Before proceeding however, I do advise that no matter what the length of your stroke, you try to maintain the same tempo (time from pulling the putter back to the time of impact). Research of the best putters in the world has shown that tempos remain the same and the length of the backstroke is about twice the length of the forward stroke to impact.

I like to use a count 1-2-3-4. I count 1 at the beginning of my backstroke, and then 2-3 to complete my backstroke and transition to my forward stroke and then 4 is impact. So, if the time between counts is 0.5 seconds, the total stroke to impact takes 1.5 seconds (count1 = 0 sec, count 2 = 0.5 sec, count 3 = 1.0 sec and count 4 = 1.5 sec). The exact time depends on your natural tempo (this is related to the length of your arms and putter, the weight of you arms and your muscular build). The total time and tempo should be the same for a 10 foot putt as it is for a 30 foot putt; the with which the putter moves is just faster.

Go out to a flat putting green with a tape measure. Measure out putts of 20 feet, 30 feet, 40 feet and 50 feet if you can. The putts should be relatively straight (no severe breaks).

Place the tape measure down in line with your target line so that you can measure the length of your backstroke. For the 20 foot distance, start hitting balls with the focus of tempo and solid contact only. Take note of the length of your backstroke for the ball to roll 20 feet. For instance, if it appears to be 10 inches (depends on the speed of your putter and the speed of the green), place a tee at the 10 inch mark as a guide. Then, hit some more putts focusing on tempo, solid contact and taking the putter back to the tee. If the ball consistently falls short, then you need to increase the backstroke and move the tee back to say 11 inches. If the ball falls long, then adjust the backstroke shorter.

Do the same for 30 feet and then for 40 feet. You should now have 3 pairs of backstroke lengths and distances. You can test these by choosing a distance in between the distances, like 25 feet, 35 feet and 45 feet. The length of your backstroke for 25 feet should be about half way between the length for 20 feet and 30 feet, etc.

This will give you a gauge for the length of the backstroke and the length of the putt. You could even modify it to be in terms of an object instead of length, such as a putter head length, a dollar bill length, a cell phone length, etc. That way you don't need the tape measure to practice.

In your practice sessions, you could put down two one dollar bills end to end and determine how far the ball will roll, then three bills, four bills, etc

You could even produce your own gauge on a piece of cardboard or make purchase like the one below.

Golf Ball Trajectory Rules

Last week, I found an excellent explanation of the different types of trajectories you can get with your golf ball and what causes them.

Proper alignment can be learned. It can be mastered. You just need to know how you're aligning. You need a measuring tool to let you know.

You need a Laser Putting Alignment System.

Take a look at the Laser Putting Device that I use and consider getting one for yourself

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The slope of the green is the single biggest factor in how much your putt will break on the way to the hole, but the fact is: most golfers have a hard time reading break.

The number one tool chosen by more and more Tour Pros and Caddies to measure greens is the BreakMaster Digital Green Reader.

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Stages of the Golf Swing

Review the different important stages of the golf swing. Are you getting into the proper positions?. Click on the links below.

No shipping charges on orders over $75. If you want some more details about a Golf Digest Study of Used Golf Balls in which they had Golf Laboratories use their Golf Robot to hit the balls, click on this link:

1. Go to my Frequently Asked Questions (FAQ) page. There's a link to it on my pages from the left hand menu near the top of the page, just below the Search icon. It's called "FAQs." You then click on the graphic icon and you'll be taken to my database page. For your convenience, here it is: FAQI've answered hundreds of questions over the past 6 years and have created a fairly large database. You can search it out. If you can't find the answer you're looking for, submit a question and I'll answer it.2. On all of my web pages, there is a search feature in the top left section, right underneath my LOGO. Just place your search keywords in the search box, select "This Site" below it, and then press "Search." What will come up is a Google search of the pages on my site with relevance. You can also search the entire internet by selecting "Web" instead.
Go to my main page now: Home or just check the top left menu of this page. 3. Also, directly under the Google Search area, you'll find a pop down menu called "Your Topic." Select the topic of interest and press "Go."I would suggest you bookmark my main page and/or your specific areas of interest so that you can find them easily in the future. On each page at the very top, there is a link you can click on:
"Click here to add this page to your favourites"Hope you find all you're looking for.You can learn more from NEW Titleist Pro-V1 by clicking HERE.

A list of resources that have been used to produce
this newsletter can be found on my web site here.

Hope I provided some useful ways for you to
become better prepared for you best golf season
ever.

Ken Tannar

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