Musings of a Forensic Statistician

“There are three kinds of untruths, lies, damned lies, and statistics.” Mark Twain is often credited with that statement, but what are the odds?

“Torture numbers enough and they will confess to anything.” Gregg Easterbrook gets the credit for that one, but it might have been lifted from Twain.

I’ve always loved numbers. As a young baseball fanatic, I learned how to calculate a pitcher’s “earned run average” (ERA) by the time I was in the third grade. Baseball has given us some of the world’s greatest multi-dimensional mathematicians. Yogi Berra famously said, “Ninety-percent of the game is half mental.” Top that Stephen Hawking.

Discussions of golf numbers and statistics in the last few days seems to have raised some eyebrows. The USGA applied its PCC (playing condition calculation) to our Monday round. The PCC was triggered by a statistical setpoint in the GHIN system. To address some of the questions, I ran an analysis of golfer’s performances as a function of the course and tees played.

Those that saw the report seemed surprised that with over four thousand data points, golfers playing the yellow tees on the Padre course averaged more than five strokes over their handicap index. Yet, with over six thousand data points from Ambiente’s Camel tees, players averaged about two-and-a-half strokes over their indices.

Is that statistically significant? More than 10,000 data points! Hell yes! The numbers are saying something. The question is “What are they telling us?”

If you’re not a “numbers person”, the answer is “Who cares?” You can stop reading now. But if your curiosity beckons, read on. Who knows? Maybe a more in-depth understanding can lead to your gain.

I’m only going to comment on the performance differences between Ambiente (Camel) and Padre (Yellow). Both courses are roughly 6,100 yards in length. Although they’re admittedly somewhat different in their personalities, both courses are subject to the same weather, winds, temperatures, etc. In a nutshell, we’re comparing apples-to-apples.

(If you’re interested in looking at the numbers associated with the nearly 100 courses played by our golfers over the past six years, you can see them here. I’ll be anxious to hear your thoughts and interpretations.)

Statistically, the difference in the average to handicap between the two courses is huge. A half stroke – maybe not, but it’s nearly double the difference. That is not reasonably possible without further explanation. Here are some possibilities for your consideration:

1. The USGA course rating and slope evaluations are not accurate. If after 10,000 or so rounds, the differences are so pronounced, the obvious conclusion in my mind is that one course is rated substantially too low and/or the other one is rated too high. A statistical analysis of the mathematical structure of the USGA Handicap System strongly suggests that scores should average roughly three strokes over handicap. This neglects performance differences in handicap ranges and some other minor variables. If we drill-down on the question, it may suggest the course slope rating in also in error.
2. Statistical “hysteresis”. Simply put (is it too late for that?), assume a person plays twenty rounds on Padre and ends up with a handicap that is three strokes too high. When that golfer then plays twenty rounds on Ambiente, he’ll be inclined to play significantly better relative to his now elevated handicap. When he completes twenty or so rounds on Ambiente and now returns to Padre, his handicap is too low. In reality, this does “explain” the numbers; it only shines a light on their consequences. The course rating/slope of one or both should be reviewed.
3. Golfers with vanity handicaps prefer Padre. OK, now I’m really stretching it, but let’s not rule it out. Sometimes, it’s the “old guys” (of which I am now one) that are probably more inclined to scrape the four-foot putts, hit “breakfast ball”, and forget how many strokes were actually taken… that prefer Padre. After all, Padre players have access to more bathrooms, fewer fairway traps, and fewer snakes, coyotes, bobcats, and other predators. Play Ambiente and you’re two-and-a-half miles from the clubhouse at the turn. Those are pretty dangerous waters for an old boat.
4. Club “management” is messing with the courses. Frankly, this isn’t speculation; it’s a reality. Most if not all golf course’s management “manipulates” the course a bit to improve pace-of-play. Camelback is no different. The tees on both Camelback courses are periodically moved forward due to a variety of factors, profitability no doubt being the most obvious. In the most egregious case, the green tees on #18 Ambiente occasionally get set forward to take the long shot over the wash out of play. That cuts 70 to 80 yards off the “rated” length of the hole. That alone results in a 0.4 reduction in the course rating. Similar, but less dramatic moves have been made on other holes. After analyzing hundreds of rounds of golf, the rating from the Verde tees when compared to other tee sets is a full stroke-and-half too low… or the tees are intentionally set a full stroke-and-a-half closer than designed when the AGA rated the course.
5. Padre is the preferred course for sand-baggers. I suggest this as a possible explanation, but I don’t really believe it. Nonetheless, if a golfer inclined toward a little padding of his handicap is preparing for an upcoming tournament where a higher handicap would be beneficial, the Padre course would definitely give him an edge in getting his handicap to a competitive level. He could play his best and still get a two to three stroke bump without violating an rules of golf. On top of that, if he’s a proponent of the NMAPYDN school of golf (“Never make a putt you don’t need”), he could work the Padre course into a five or six stroke competitive edge by tournament time.
6. Economics could contribute to some of the performance difference between the courses. The rack-rates and the guest rates are higher on Ambiente than they are on Padre. Perhaps someone who is more cost-conscious tends to reduce expenses on practice and play frequency. If so, his handicap becomes less responsive to change. Non-members also tend to play other courses more often. If those other courses are more fairly rated, performance relative to handicap on Padre will suffer.

There are other possibilities and I will delight in hearing your suggestions. But with more than 10,000 data points, it’s irrefutable that something is amiss. As the “forensic statistician”, I’m inclined to argue the Padre course is not rated properly (suggestion #1) and/or Camelback management is lax in its efforts to consistently setup the course according to its AGA rated conditions.

Recognizing the reality doesn’t mean it’s all bad. There sits in the Member’s Lounge a large trophy called “The Camel Cup”. It is currently in possession of the golfers of the J-Golf Group at Camelback in large part because some deceitful and diabolical tournament organizer deemed the Padre course as the field of battle and solicited the help of the Camelback ground’s crew in setting the pins in devilish locations prior to the tournament. The poor guys from Gainey Ranch never knew what hit them. I guess it makes sense that an unfair situation puts one side at a disadvantage, but the other side ends up with the advantage. Having a grasp of statistics can pay dividends, especially when you realize that it is said, “Four out of three people have trouble with fractions.”

Meet the World Handicap System

Most golfers have heard that change is in the wind. The USGA Handicap System will undergo some very significant modifications sometime in early 2020. I recently became “certified” through the USGA in the new Handicap System and will share with you the most significant aspects of the new program.

If you’re not particularly concerned with the minutia of the new system, you can simply go with … the new system, like the old system, is designed to level the playing field when golfers with different skill levels compete against one and other. The old system does a good job; the new system (probably) does a slightly better job.

If you’re inclined to know a bit more, here you go.

1. The old system used the best ten of your last twenty rounds to calculate your handicap index. That result was then reduced to 96%. In the new system, your index will be based upon your best eight rounds. The result will NOT be reduced to 96%.

2. In the old system, your “course handicap” was calculated by taking your playing index, multiplying by the course slope and dividing by the average slope of all golf courses, i.e., 113. In the new system, your course handicap is calculated in exactly the same way – except that it is totally different! The new system is keyed to the total course par whereas the old system was keyed to the course “rating”. If there’s a difference between course par and course rating, you will now adjust your course handicap accordingly. For example, with the old system, if you had an index to 10.0 and you played a course with a slope of 126, your course handicap would be (126/113) times 10.0, i.e., 11. In the new system, the calculation remains the same except you now adjust for the difference between course rating and course par. If the course you’re playing is rated 69.0, you deduct an additional three strokes from the old system’s course handicap. You become an 8 handicap.

Interestingly enough, we’ve been doing this exact same thing when competitors play from different tee sets. Those playing from the more forward tees lose the difference in course rating from the two tee sets from their handicaps. With the change in the Handicap System, there will no longer be a need to adjust handicaps when playing different tee sets. The adjustment is automatic in the course handicap calculation. On the downside, in days gone by, many have been confused by the adjustments for different tees. Now everyone can be equally confused every day they play. However, there are a couple of extra considerations that make the system easier to understand and slightly more equitable. If you’re interested, ask. I’ll be happy to belabor the topic a bit more for you.

3. Many have been asking about ESC (equitable stroke control) where you have certain maximum scores you can post depending upon your handicap range. In the new system, the maximum score that may be posted for handicap purposes is “net double bogey”. For example, if you take a seven on a par three hole and you get one stroke on that hole, you are allowed to post a six, i.e., a “net double bogey”. If you take a twelve on a par five hole and you get two strokes on that hole, your posting maximum is nine, i.e., “net double bogey”.

4. Handicaps will be updated on a daily basis. The rules have always called for “timely” posting of scores. With the daily updates, “timely” takes on a new meaning. You are obliged to post on the same day as you played the round.

5. The new “World Handicap System” has a number of not so obvious features that the USGA is calling “safeguards”. I won’t get into the details of “hard caps”, “soft caps”, and the like here, but most of these features are intended to constrain the activities of those who have historically had a problem with their handicaps increasing as tournament appeared on their horizons. Some of these features are rather cute, but all you need to know at this point is that your handicap will generally be prevented from rising by more than five strokes in any given twelve month period. So, if you’re going to sandbag, plan well in advance.

One component of the new system that has raised a lot of eyebrows is the system for compensating for abnormal course conditions. If you’re playing in winds gusting to forty miles-per-hour, chances of you shooting a net 65 are pretty close to zero. The USGA will be attempting to correct postings for rounds played under such conditions. Heavy rains, locust plagues, armed insurrections, civil unrest, even cases of extremely slow play (like Friday the 18^th at Camelback) may be adjusted by the USGA.

This is a noble goal and in theory possible; time will tell. But it certainly raises a lot of questions. No, they will not be checking the local weather report. They will not have a weather station on the course. Drones and satellite surveillance will not be used. At this point, you may be wondering if they’ve established a partnership with Santa Claus; after all, only he knows who’s been naughty and who’s been nice.

To find out how they’re going to do all of this, you might also suspect the best way to find out would be to simply ask the USGA. Not so fast Ferdinand. To paraphrase their response, “it’s none of your business!” They’re trying to keep this a closely guarded secret.

As a mathematician, I’m pretty confident I can tell you exactly how they intend to do this. Frankly, I like their approach despite its minor flaws. In a nutshell, if for the past fifty days, you’ve had perfect weather. During that time period, postings have consistently hovered around say three strokes over handicap with a standard deviation of a half stroke. Then on one given day, the USGA computer looks at scores and sees they’re solidly six strokes over handicap with a standard deviation of one full stroke. Guess what … something’s amiss. There a good chance a monsoon just blew through or the laws of gravity were suspended on that day or … whatever. But from a statistical standpoint, there was very clearly an “abnormal course condition”. The USGA plans on automatically adjusting if the deviations were what they consider to be “significant”. The definition of “significant” may still be up in the air, but you’ve got the gist of their system.

There are some interesting potential consequences of this system. One I envision will occur at Camelback Golf Club where two eighteen-hole courses are played. One of those courses is reasonably rated by the Arizona Golf Association (as long as management doesn’t keep moving tees dramatically closer to holes than they were when the course was rated). The other course is – in the studied opinion of this writer – not properly rated at least from one of the common tee sets. The end result is that when golfers play Ambiente, their postings fall within the statistically expected range. However, when golfers play Padre, postings typically fall two to three strokes higher than statistically expected.

With your nominal understanding of the way the USGA will be handling “abnormal course conditions”, it will tend to have two pronounced effects. The first is that these semi-automatic adjustments to postings will tend to mitigate the consequences of an improper course rating. It’s sort of a self-correcting rating system. The other result is that meteorologists will be driven to drink heavily after seeing that the Ambiente course basks in perpetual paradise from a weather standpoint. Yet Padre will appear to be at the epicenter of a never-ending typhoon of biblical proportions. Invite someone from the USGA to play Camelback and they’ll say, “With pleasure, but only if it’s Ambiente.”

Enough said about the new WHS (World Handicap System). However, for a future topic of discussion in the Acacia Lounge, ask yourself … “Why is the USGA keeping the details of the abnormal course conditions calculation so secret?”

Golf Scorekeeper’s Primer

What follows is applicable to our immediate golf group. It is recommended for all golf groups. It’s a combination of policy and “The Law” of the USGA Handicap System. If you find yourself keeping score in our regular golf group, please make certain you are familiar with these guidelines and adhere to them rigorously.

We putt everything out – all the way out. A ball that stops a quarter inch from the hole MUST be putted INTO the hole. Admittedly, few (with the possible exception of this writer) has more than a one-in-a-million chance of missing that putt, but it still must be putted into the hole.

Golf Erotica for Mathematicians

I recently received an email from one of our golfers asking for an explanation of the “Odds” column on the Gross Score Report found at the bottom of the “Match Sign-Ups” page on this site. It dawned on me that others may have that same question. What follows is a copy of my response to the email.

If you have something important to do, like watch your grass grow or look for dust bunnies under your couch, skip everything in black below and go directly to the answer in red at the bottom of this diatribe. Either way, let me know if you have any other questions. Cheers.

What time is it, you ask? Let me tell you how to build a watch!

Lateral Hazards – A Footnote

The previous post (Camelback Golfers – Read This or Else; December 14, 2017), has generated far more “interest” than I had anticipated. Almost every response came to me in private rather than as a comment on this blog. After reviewing the responses, I can assure you that we not only have some good golfers in the group, we’ve also got some golfers that carry a sense of humor that can be used like a scalpel to surgically extract the essence of a situation and describe it in a fashion that make my sides hurt from laughter. I can’t share all the comments because they were sent in private. However, I will give the award for best humor to Dr. John Raines. Barbara must spend half her time doubled over in laughter.

I will share one comment and my response to it without mentioning any names (not even my own). One golfer said:

“I assume you believe there are those that fudge?”

Here’s my response.

“Three answers …

Going Native on Ambiente

With a few new members and a few whose memories come into and out of focus from time-to-time, let’s review the rule associated with playing out of the “native grass” areas on the Ambiente course at Camelback.

Native grass areas are deemed “lateral hazards”. This means:

1. YOU MAY NOT ground your club when addressing your ball. You MAY lightly touch the grass, but you MAY NOT do anything that alters the swing path such as taking practice swings that tear or uproot the grass or plants near the ball.

2. YOU MAY NOT move any loose impediments in the hazard. You MAY NOT brush any rocks or pebbles aside. YOU MAY NOT pick up or move any twigs, pine needles, coyote droppings. You DO NOT get relief from “obstructions” if you’re in a hazard without incurring a penalty stroke. This includes things like the fire hydrant on the ninth hole.

3. YOU DO NOT get free relief from standing water if you are IN the hazard. That’s sort of why it’s called a “hazard”. After the rains, many of the native grass areas become native rivers. No relief without penalty.

4. YOU MAY NOT “build a stance”. You can place your feet firmly on the ground, but you may not uproot plants or kick big rocks around while taking your stance.

Relief from a lateral hazard is covered under Section 26 of the Rules of Golf. You have five options:

1. Play the ball where it lies without penalty and subject to the prohibitions outlined above. Obviously, you have to find the ball to do this. No penalty.

2. Stroke and distance. Return to the spot from which you hit the ball. You incur a one stroke penalty. If you hit the ball from the teeing ground, you are now hitting your third shot from the teeing ground.

3. Drop a ball within two club lengths of the point where the ball crossed the margin of the hazard. You take a one stroke penalty.

4. Drop a ball within two club lengths of a point on the opposite side of the hazard, but no closer to the hole than where the ball first crossed the margin of the hazard. You take a one stroke penalty.

5. Drop a ball as far back as you wish on a line from the point of entry and the flagstick. You take a one stroke penalty.

Admittedly, it is called a “lateral hazard”, but this DOES NOT MEAN you can drop a ball laterally out of the hazard. You MUST drop within two club lengths of the point where the ball first crossed the margin of the hazard (assuming you’re taking relief as defined by #3 above).

What are the native grass areas? For most golfers, it’s pretty apparent that the arroyo area on the starboard side of the course is a “native grass” area. However, some golfers lose their clarity when they end up in a little “island” area of native grass. If it looks like native grass, you’re safe assuming it is a hazard. This includes places like (1) the tall grass between the cart path and the sand traps on the left side of the #3 fairway, (2) the grass areas running the entire length of the port side of pretty much every hole on the course, (3) the grass areas above and to the left of the traps on #18, (4) the tall grass area between the cart path and the #16 green, (5) the grassy area above the trap at the end of the dogleg on the #1 hole. These are just a few of the “native grass” areas. If it’s got flowers, it’s not fairway, it’s not rough, it’s native.

A couple of final comments on this topic: if you’re playing the Padre course and hit a ball into a native grass area that’s part of the Ambiente course, e.g., the area behind the twelfth green, IT IS NATIVE GRASS and deemed lateral hazard.

Consider this a “local rule” for The Jones Boyz Group. I don’t recall if Camelback has addressed this issue, so don’t claim it as an “official” local rule for the club without checking. There are areas on the course where the cart path runs through native grass areas. For example, on #3, #5, #6, #7, #8, #9 and other holes, there are sections of the cart path with native grass areas on both sides of the path. Technically, with a ball on the path or a ball adjacent to the path where the concrete interferes with your swing and the finish on your $100 club, you are NOT entitled to relief. However, by Executive Decree of the Tournament Committee, i.e., me, we will play with our own local rule. You MAY take relief from the cart path without penalty. However, you MAY NOT take relief out of the hazard. The free drop must be within a club length of the nearest relief from the cart path, but within the hazard.

We’ve got a great golf group and we should be proud that we have fostered a culture where we play by the rules. We don’t improve our lies. We don’t bump the ball. We’re pretty much “by the book”. Hopefully, this helps some of the newer members of the group to stay on the high road.

In the final analysis, the best way to avoid conflicts with these and other rules is to hit your shots into the fairway. I’m thinking about trying that approach. I’m always open to new things.

Why Play the Ball “Down”?

From time-to-time, competitors approach me before a match and suggest that because it rained the day before or the course was over-seeded a month ago or the mower blades need to be sharpened or the tides have been running higher than normal in Malaysia or their grandmothers have been ill or their balls don’t like bad lies or blah, blah, blah. In all but the rarest of circumstances, we elect to play the ball “down”. No winter rules. No improving the lie.

Why? Because the rules of the game say play it down!

However, I don’t opt to play it down solely so I can be a “good boy” and play by the rules. You know me better than that. The rules say “play it down” for reasons. And here they are – straight out of the USGA Handicap System Manual, Section 7-2.

1. Such a Local Rule conflicts with the fundamental principle of playing the ball as it lies;
2. Preferred lies is sometimes adopted under the guise of protecting the course when, in fact, the practical effect is just the opposite – it permits moving the ball to the best turf, from which divots are then taken to injure the course further;
3. Preferred lies generally tends to lower scores and a Handicap Index, thus penalizing players in competition with players whose scores are made without preferred lies;
4. Extended use or indiscriminate use of preferred lies will place players at a disadvantage when competing at a course where the ball must be played as it lies.

In a book entitled “How to Cheat in Golf – Confessions of the Handicap Committee Chairman”, the author (one of my favorites) dedicates Chapter Four to “The Biggest Cheat in Golf”. He makes it clear the biggest cheater is the golfer that takes steps of any kind that result in a unjustified lowering of his handicap index. Bumping your ball, improving your lie, and playing “winter rules” means that the biggest cheat in golf is you!

Let’s play it down.

The Pope and the Slippery Slope

I recently noticed a posting on the bulletin board of the locker room at the Scottsdale club at which I play golf. Obviously posted by a higher handicap golfer, it heralded the claims of Dean Knuth, “The Pope of Slope”, that low handicap players retain a distinct advantage in head-to-head competition over higher handicap players. Although I have a lot of respect for the opinions of Dean Knuth, I took some issue with the article as printed in Golf Digest. Below is the original piece as taken from the bulletin board as well as my response. I then went into my database of golf matches and analyzed nearly one million head-to-head matches. I’ll present the empirical data upon request. What do you think?

Taken from Golf Digest June 2014 Issue

Another Reason to Ask for More Strokes

You would think that a golfer with a course handicap of 12 would have a decent chance of beating a scratch golfer, provided he was given his full 12 shots. But that golfer has only a 25 percent chance of winning, says Dean Knuth, former Director of the USGA’s Handicap Department. “The USGA set up its system to favor better players with a built-in bonus for excellence,” Knuth says. “It’s a philosophy that handicaps should be based on potential rather than average ability.” For every six strokes in handicap difference, the better player has a one-stroke advantage, Knuth says. So in a match between an 8 and a 14, the 8 handicapper has a 60 percent chance of winning. You might want to remember that before wagering.

But now (as Paul Harvey used to say), The Rest of the Story …

Dean Knuth is unquestionably one of the experts in the world of golf handicaps, however, he may be sugar-coating this one and allowing us middle to high handicappers to cry foul when there isn’t one.

The slight-of-word about handicaps being based on “potential” rather than “average” ability is a semantic dance with roots buried in the “USGA Handicap System”, but those roots are clouded and misunderstood. They are part and parcel of a circular argument that doesn’t make a lot of mathematical sense.

I suspect Mr. Knuth is alluding to the fact that for the purposes of handicap calculation, the differential for any given round is multiplied by 96% which the USGA calls its “Bonus for Excellence”, an “incentive for players to improve their golf game.” On the surface, it appears to favor the lower handicap players. But does it really?

I challenge you to go to the driving range and question one, ten or a thousand golfers as to why they’re practicing. I don’t believe any of them will respond they’re there because of the USGA’s “Bonus for Excellence”. They’re there because they lost two balls in a water hazard the previous day and they can’t afford to lose two more tomorrow. To suggest the “Bonus for Excellence” incents golfers to improve or for that matter that the USGA should concern itself with your level of motivation is delusion.

The “Bonus for Excellence” does tend to mitigate a statistical advantage that the higher handicap players have over the lower handicap players. Generally speaking, the higher the handicap, the greater the variability of scores. A scratch golfer’s net scores generally fall within a couple of strokes of par. A twenty handicap golfer’s net score will usually fall within four or five strokes of par – both over and UNDER. In other words, a twenty handicap golfer has a much higher probability of shooting a net 65 than a scratch golfer.

On any given day, in a head-to-head match, the scratch golfer may have a miniscule statistical edge over the high handicapper. However, it’s not the big edge Mr. Knuth suggests.

In a recent tournament at a nearby club, eighty-eight golfers competed where prizes were awarded to the best twenty-two net scores, i.e., 25% of the field. Slightly more than 20% of the field carried single-digit handicaps. If Mr. Knuth’s claims are valid, wouldn’t you expect the list of winners to carry more than 20% of the single-digit handicapper’s names? Alright, how about close to 20% of the winners come from the group of low handicappers? How would you explain only 10% of the winners being single-digit? The fact of the matter is that of the twenty-two prize winners, not a single one came from the single-digit list. With a closer look at the probabilities, this outcome was not unexpected.

No matter how you cut the math, here’s my conclusion. With all due respects to Mr. Knuth … If you come to me and ask for an extra stroke because your handicap is six strokes above mine, you’ll be talking to yourself. Play well.

Howard Jones

Handicap Committee Chair – Camelback Golf Club

Pay No Attention to that Man Behind the Curtain

I have a much greater understanding of one of the most famous quotes from the 1939 Hollywood spectacular, “The Wizard of Oz”. For I have indeed looked behind the curtain. As a result, rumors fly that I am no longer a member of Gainey Ranch Golf Club. I have received numerous calls and emails asking me if it is true. So allow me to put the rumors to rest.

Tales from your Handicap Committee

If you’re not a “math guy”, this may be of little interest. Unless that is, you’re interested in reading a simple “how to piece” on how to manipulate your handicap. Before I get started, let me point out that there are those – on and off the Handicap Committee – that don’t believe the “numbers” can reveal anything. What follows is an example of what the numbers can tell us. You be the judge. And yes, this is very real data for a very real golfer at Gainey. It may have been moved to slightly to mask the identity of this golfer, but it is real.

This particular member plays a fair amount of his golf on courses other than his home course. The chart below shows his posted differentials for a substantial (read: statistically significant) period of time. The blue diamonds show his differentials when playing on Gainey Ranch G.C. The red squares are his posted differentials when playing at away courses.

A couple of things immediately jump out at you. Home differentials are clearly randomly distributed around roughly thirteen. The actual number isn’t the important thing; it’s the distribution that is significant. You can see they range from a low of around seven to a high of roughly twenty. If you analyze the distribution, it is what you would expect for someone in this golfer’s handicap range, i.e., standard deviation of around three strokes. Ninety-five percent of the differentials should (given the laws of statistics) fall between approximately seven and nineteen. What an amazing coincidence – they do!

Now look at the away scores. Their average is closer to sixteen, nearly three strokes higher than those recorded at Gainey. Does this fact imply handicap manipulation? Maybe – maybe not. It can certainly be argued that Gainey Ranch’s handicap doesn’t “travel well”. I’m confident there’s an element of truth to that. You can also make a case that a golfer isn’t as familiar with away courses and a lack of course knowledge results in higher scores. Perhaps this is true, but how many times can that excuse be used? After all, once you’ve played a particular course four or five times, you should have a pretty good level of familiarity and that excuse tends to evaporate into the morning mist.

For the sake of this discussion, let’s temporarily accept that a three stroke difference in the scoring average is acceptable. If that’s the case, shouldn’t the entire grouping of data points move up approximately three strokes? For this golfer, it does, but . . .

The “randomness” disappears! It’s as if the entire bottom half of the distribution is missing! Could it be that the scores weren’t posted “properly”? Hell yes. That’s one possible explanation. The standard deviation of away postings is approximately one stroke! This seems to be statistically “improbable” (for those of you not paying attention, this is called a gross understatement).

An average differential of sixteen with a standard deviation of one stroke means that ninety-five percent of this golfer’s away differentials fall within the range of fourteen and eighteen. This is well within the “you must be joking” range of statistical probabilities.

There are possible explanations. For example, it could be that by playing a more difficult course with which you have no familiarity whatsoever magically makes you a much steadier and more consistent golfer than you are at home. To me, that’s like saying the more you drink, the better you drive.

There are a couple of other explanations. I’ll sit back and see if any of you come up with them and post them as comments here. In the meantime, I continue to do battle with those who say numbers don’t prove anything and I’ll watch to see how this golfer performs in the upcoming Member/Member tournament. This golfer isn’t alone. He has company. I’d love to say, “If you don’t mind, I don’t mind”, but I do. It’s my job.