The "3 to 7 Range" Cliche - Volatility as a Guiding Design Principle?

[Kevin Lynch]

I've often heard the statement that "XXXX is a good hole, it brings 3 to 7 into play."  Usually it's used in terms of half-par Par 5s.  While analyzing the Players Championship for my Fantasy Pool, I noticed a few things that started me thinking about Volatility and its "value" in terms of design.  Forgive me if I don't present a clear opinion about this volatility below - I'm just looking to get some thoughts on the issue with some questions below (even if it doesn't generate any good discussion, you may find Glover & Watson's scoring anomalies interesting).

Glover Hits for the Cycle
I don't know if anyone else noticed, but on Sunday morning, Glover was standing in the 16th fairway with a 6 iron in hand, staring at an Eagle opportunity.  Instead, he dumped it in the water and walked away with a double-bogey 7.  It kick-started a stretch in which Glover notched a score of Eagle through Quadruple Bogey over the next 18 holes.

Quadruple Bogey:  8 on Par Four 4th
Triple Bogey:  7 on Par Four 18th
Double Bogey:  7 on Par Five 16th
Bogey:  6 on Par Five 11th
Par:  Many
Birdie:  3 on Par Four 12th
Eagle:  3 on Par Five 16th

It seems a cruel and ironic twist of fate that Glover completed his cycle with the Eagle on the Par Five 16th, the same hole where the volatile run began.  However, it fit in perfectly with the "3-7" description.

Bubba's "Beta"
During the Player's Championship, Bubba posted rounds of 76-66-76-68, a pretty high level of Volatility.  Even more interesting, if you break down the 4th round, he was -7 under through 13, and threw in 3 bogeys on the last 4 holes.  BTW, if you add in the last two rounds at the Masters (67-78), Bubba's on a pretty wild ride in "bigger" events.


Is Volatility Good Design or Contrived?

From my year's of watching Majors (incl. Players) and analyzing numbers for my Pool, it seems like TPC Sawgrass produces the widest variance in scoring than other major events.  I'm curious of others' impressions regarding this volatility. 

Is it an indicator of good strategic design or is it simply the result of an overabundance of penalty strokes throughout the course (or a combination of both)?  For example, you can get a wide range of scores on a half-par hole like the 16th (a function of options), but the 17th & 18th can generate a similar wide range, with very little in terms of options.  Do you consider the former to be good design, while the latter instances may be contrived?


When people use the "Eagle to Double" criteria, do you feel differently if the high end of the range includes penalty strokes, or are you more impressed if it can be accomplished without penalty strokes?  For example, do you prefer a hole like Riviera's 10th, which can extract a severe penalty without losing a ball, as opposed to a hole like Augusta's 15t or 13th?


From a Architect's Point of View, how much do you focus of the potential scoring volatility of a hole design?  Is it a principle that you are consciously thinking about, or is it simply a fortunate by-product?  When RTJ speaks of "Hard Par, Easy Bogey," it seems like a conscious principle meant to LOWER volatility.  Do you have a preferred philosophy in terms of "desired volatility?"  I suppose that if you make a conscious effort to increase volatility, you could run into risk of "forcing" options or potential penalties onto a design.


Again, I apologize if the above questions seem a bit rambling, but I'm hoping this will open some dialogue that may become more focused through the course of the comments.

[Carl Nichols]

Kevin:
You could add in Graeme McDowell, who was leading the entire field by 3 strokes before his last 19 holes, which he played 9 over par!

[David Harshbarger]

I definitely think holes that can manage to elicit a range of scores makes for sound design, and as you say, Riviera 10 is a great example of that, without being penal.

Anytime enticement enters the equation, and players find their limits pitted against their greed, there's an opportunity for an exciting hole.  Setting up these types of situations is a fantastic design principle, IMHO, and when executed well, deliver holes where 3 to 7 isn't just a cliche.  

In theory, when the penalty isn't penal, but some form of extremely challenging recovery, I think that makes the hole extra interesting.  First, water and OB are obvious penalties so they will often weigh too heavily on the mind of the player to entice them to take a risk.  Severe recovery areas into un-holdable greens, hidden bunkers, blind shots, false fronts and short grass, when these are the elements that make up the penalty, their benign nature from afar is more likely to entice players to take the risks.  To me, that's what makes this particular type of hole construct interesting.

I don't think you necessarily want 18 holes of this, but a few a round?

[Mark Bourgeois]

Kevin,

Good post. Rather than use par to benchmark volatility I would use player volatility relative to the field -- or, for the case of measuring volatility of individual holes, and therefore "half par-ness," distribution of scores for a particular hole on a particular day. That's a better benchmark as it incorporates the play of the day, taking into account tee and hole locations, weather conditions, etc.

On that score, a true beta is not a naive distribution (variance / st dev) but rather the measure of a player's volatility relative to the field.

Congrats for using The Players to bring up this topic as hopefully it will generate some light. Normally it comes up Masters week and sparks fun discussions, eg: http://www.golfclubatlas.com/forum/index.php/topic,34103.0.html

[Kevin Lynch]

David,

I like your point regarding the effect the varying hazards can have in the "enticement factor".  I always prefer the "potential" penalty (sand, severe slopes, short grass) vs. the "absolute" penalty (OB / Water), even if the reality is they will extract the same number of strokes.  I don't mind the unfortunate discovery of "Man! That recovery was much more difficult than I ever imagined from the fairway" because I appreciated the opportunity to take the risk.

For example, the 11th at Tobacco Road is one of my favorite holes because the entire right side is sand.  I don't dread the thought of an extremely difficult explosion shot up a 30 foot wall.  But, if you filled the right side with water, it would become a fairly boring hole for me, since I'd rarely attempt the gamble.

In terms of TPC Sawgrass, it appears that most of the Volatility comes from the penalty stroke, rather than the extremely challenging recovery.  Perhaps this explains some of the pro criticisms over the years.

I am still curious to hear from Architects how much the "range" of scores enters their thought process during the design phase.  Perhaps it's just a matter of designing the hole in a way where there can be a wide range of set-up options to accentuate the "volatility" on certain days, but serve as a less "volatile" hole on other days (perhaps allowing other holes the chance to provide the volatility on those days).

[Kevin Lynch]

Kevin,

Good post. Rather than use par to benchmark volatility I would use player volatility relative to the field -- or, for the case of measuring volatility of individual holes, and therefore "half par-ness," distribution of scores for a particular hole on a particular day. That's a better benchmark as it incorporates the play of the day, taking into account tee and hole locations, weather conditions, etc.

On that score, a true beta is not a naive distribution (variance / st dev) but rather the measure of a player's volatility relative to the field.

Congrats for using The Players to bring up this topic as hopefully it will generate some light. Normally it comes up Masters week and sparks fun discussions, eg: http://www.golfclubatlas.com/forum/index.php/topic,34103.0.html

I see from your link that you have done quite a bit of quantitative analysis, far beyond the level I have performed.  Thinking about TPC Sawgrass vs. Augusta, I'm not sure there is as much of a "Risk / Reward" ratio to analyze at Sawgrass.  Rather, there may be a "Penalty / Difficulty Ratio."   For example, the ratio of Birdies / Bogeys on #17 isn't a function of risk vs. reward, as opposed to the severity of penalty weighed against a relatively short hole.

I did do some analysis on the Volatility at the Players (as well as Masters / PGA) relative to the rest of the field (instead of vs. Par).  I didn't attempt to measure in terms of Standard Deviation - rather I simply calculated the average Absolute Variance of each player's score vs. the Field Average for that particular day.  To weed out the "strugglers" from Day 1/2 who missed the cut, I only used the scores for people who played all 4 rounds (helps provide better apples-to-apples comparison between Round 1/2 vs Round 3/4).

Sawgrass:
Round 1:  Field Average 70.41   Average Variance: 1.80
Round 2:  Field Average 70.60   Average Variance: 1.86
Round 3:  Field Average 71.55   Average Variance: 2.37
Round 4:  Field Average 71.85   Average Variance: 2.35
All Rounds: Field Average 71.10   Average Variance: 2.09

Augusta:
Round 1:  Field Average 71.04   Average Variance: 1.92
Round 2:  Field Average 70.53   Average Variance: 1.70
Round 3:  Field Average 72.08   Average Variance: 2.21
Round 4:  Field Average 71.67   Average Variance: 2.20
All Rounds: Field Average 71.33   Average Variance: 2.01

Whistling Straits:
Round 1:  Field Average 71.65   Average Variance: 1.59
Round 2:  Field Average 70.38   Average Variance: 1.68
Round 3:  Field Average 70.96   Average Variance: 2.16
Round 4:  Field Average 73.62   Average Variance: 2.13
All Rounds: Field Average 71.65   Average Variance: 1.89

I'm not sure what all that means, but I find the following interesting:

- The Volatility increased in all cases quite a bot for the weekend rounds.  Is this a function of weekend pressure or "riskier" Course Set-up?

- Whistling Straits had the lowest volatility of the last 3 courses.  I suppose that makes sense, since there are less 1/2 par holes at WS and the hazards at WS rarely come into play (really, #5 is the only place where a penalty stroke occurs.  Well, there plus random bunkers on #18).

[Jeff_Brauer]

2 shots a round over 4 rounds?  pffffft!  For volatility, how about the old 2 or 20 hole? 

[Mark Bourgeois]

Remember, Jeff, "These Guys Are Good."

Kevin, thanks for running the numbers. The really cool thing I see is The Masters, where volatility goes up but average score holds steady or even drops.

Seems to me when both average scores and volatility rise, the increased volatility is due to just making the course harder. I would guess more difficult courses have higher volatility.

In contrast, volatility up but scores steady / down says the course isn't playing harder but is offering more temptation.

Maybe somewhere in there is support for your point about how hazards and features can be used to change the volatility.

[Jeff_Brauer]

Mark,

At first blush, I would agree with your basic assessment above.

As to the basic question, I always ask just how much differentiation/volatility do you really need?

If we are thinking about tournament golf (at almost any level, not just the Tour) what is more exciting to compete in - a tourney where you may make a 12 and be out of it (assuming stroke play) or one where a bad hole costs you just one stroke to the competition?

A tournament tightly bunched or with a few runaway contenders?

[Kevin Lynch]

In contrast, volatility up but scores steady / down says the course isn't playing harder but is offering more temptation.

I think that's true, but I suppose you would really have to look at that on a hole-by-hole to see the impact of "temptation" in set-up (which is quite a bit like what you did in your Augusta thread). 

I had looked at the Players Championship because it seemed like the type of course that could really grab a player and cause them to ride the roller coaster.  In terms of my Golf Pools, I have a format where you pick any 10 golfers and your score on the weekend is best 7 of 10.  In all my years running it, the event where the most "big names" miss the cut is the Players.

I suspect that may be more a function of "punitive" volatility, as opposed to "temptative" volatility (not sure if "temptative" is a real word, but if Shakespeare and Sarah Palin can make up new words, why not?)

Maybe somewhere in there is support for your point about how hazards and features can be used to change the volatility.

I don't think there's any doubt that they do change the volatility.  I guess I'm curious about a few things:

-  Is this type of volatility something we desire as golfers?  as viewers?

-  Is the desire for volatility something that an Architect consciously tries to build in (or uncover from the land, for the minimalists)?

-  Is this volatility more a function of design, or a matter of set-up?  On the PGA Tour, some of these pins are set so tight to edges, that they can create a "temptation shot" out of even the most vanilla designed holes.  Similarly, the course can be set up to create punitive volatility by pushing the envelope (e.g. McDowell's 3rd round approach to 18, which never warranted the punishment of water in proportion to the execution of his shot).

[Kevin Lynch]

Mark,

At first blush, I would agree with your basic assessment above.

As to the basic question, I always ask just how much differentiation/volatility do you really need?

If we are thinking about tournament golf (at almost any level, not just the Tour) what is more exciting to compete in - a tourney where you may make a 12 and be out of it (assuming stroke play) or one where a bad hole costs you just one stroke to the competition?

A tournament tightly bunched or with a few runaway contenders?

Good question, Jeff, and the type of question I was hoping would develop in this thread.

Personally, I don't like the type of hole where you can play yourself out of a tournament in one hole.  Sawgrass' 17th is a potential culprit here.  Another example could be the 14th at Pebble Beach.

But, at the same time, I wouldn't want the biggest variation between a "bad hole" and the average hole to just be a stroke.

I guess that's where the whole "3-7" cliche comes into play.  At Augusta's 13th, you're never going to play yourself out of the tournament, because you don't have to "keep trying until you get it" (like you do at TPC's 17th).  But, at the same time, since your competitors have a good chance of picking up Eagle or Birdie, you feel compelled to bring the risk of 6 or 7 into play.


As for whether I want a tournament tightly bunched vs. a few runaway contenders, I suppose I don't mind either way.  What I'm more concerned about is that there be a decent potential for movement so there's no "coasting" in.

What I don't like are closing holes where the pin is in a nearly inaccessible position for birdie, but there aren't significant challenges elsewhere on the hole to make bogey a big risk.  For example, the 18th at Bethpage Black can be a real sleeper in certain pin positions.  Also, before technology made it reachable in 2, the 18th at Pebble Beach was a similar letdown when they would tuck the pin just past the bunker with baked out greens.

Sawgrass is one of those courses where I'm torn.  Although I'm not a huge fan of water as a penalty, you really can't argue with the drama from a spectator standpoint from 16-18.  Anyone within 3-4 shots of the lead entering that stretch still has a chance, from the potential of moving up (16/17) or moving back (16/17/18).

[Mark Bourgeois]

Absolutely as golfers and viewers we desire volatility -- but the key is your word "temptation." Hero shots over water where the golfer has a choice are one thing; forced / punitive shots where choice is absent is another.

Chip Beck (wimp) and David Toms on 16 Sunday (uh, Tin Cup hero?) are two examples.

Jeff and Kevin, it's one thing for a golfer to shoot himself out of a tournament, it's another thing entirely when those wounds are not self-inflicted.

Mark