Full House, or the Trouble with Tiger Woods

How do you explain the existence of golfer Tiger Woods? He is the leading moneywinner on the PGA Tour, the winner of seven consecutive PGA events, the winner of his third consecutive Buick Invitational tournament, at 31 is well on his way to passing Jack Nicklaus for career major tournaments won, and on and on.

As the late Stephen J. Gould pointed out in his book Full House, one of the hallmarks of a human-centered dynamic system over time is the spread of excellence. In other words, participants in the activity — he used baseball as his example — get better with the result being a decrease in standard deviation and an increase in the overall level of play. That is how Gould explained the disappearance of Ted Williams-like 0.400 hitters in baseball: It is an example of overall improvement, not of some late lamented baseball period with better hitters.

Fair enough, but why should golf be different? In other words, shouldn’t the dominance records set in the days of yore (read: days of high standard deviation) be unassailable, like Byron Nelson’s 1945 mark of 11 consecutive wins?

Interestingly, golf is a funny case. If you look back at average scores for professional golfers over the last 25 years you find that it hasn’t changed much, despite reputedly better equipment, with 70.5 (give or take 0.03 or so) having been the scoring norm on 18 holes for more than 15 years. At the same time, the standard deviation in scoring has gone nowhere, sitting at 0.54 in 2006, which is pretty much where it was in 1980, more than 25 years ago.

So, if scoring isn’t improving and standard deviations aren’t tightening, what does that mean? You could reasonably argue that it means pro golfers aren’t really improving, which is possible, even if it feels unlikely if you compare the state of play today to that of 50 years ago. (Note: I’ll concede straight away that we amateurs aren’t getting any better, but that’s a different issue). Pros today hit it longer, have more shots in their repertoire, and generally do things that pros of fifty years ago couldn’t imagine. Then again, golf is a strange sport, one designed, it often seems, just to piss participants off.

You might also argue that courses have gotten longer and more difficult, mitigating new equipment’s advantages and making a pro’s 70.5 today very different from a 70.5 in 1980. Fair enough, and I put considerable credence in that argument, although I’m still not convinced tricked-up and Tiger-proof courses are enough to explain the non-improvement in golf demonstrated in frozen deviations.

Anyway, I got to thinking about all of this last weekend when I saw Tiger win, and saw how tennis player Roger Federer wrecking-balled his way through the Australian Open, demolishing Andy Roddick along the way. That match was otherworldly, with Federer playing like some descending racket-wielding angel, not like someone who knew that the spread of excellence in professional sports meant that outrageously dominant people like him should not really, you know, exist.

But Federer exists, and so does Woods, as does the latter’s staggering 25% career win ratio. Compare that figure to the same for his counterparts, and you see Phil Mickelson with a career 8.5% mark, former #1 Vijay Singh at 8.4%, and so on. Tiger is so far out ahead in win rate as to be freakish,, although it still puts a mere 1-in-14,000 likelihood on his current winning streak. (Mind you, the likelihood is an even more remote 1-in-33-million for Phil and Vijay.)

One way of alibiing Woods, Federer, and even bicyclist Lance Armstrong for that matter (he won seven straight Tour de France in an age when cycling was supposed to be post-patron), is to simply say that reduced deviation in performance doesn’t mean no deviation, and it also means that when you find someone who is a real outlier he or she stands out even more than usual.

Other explanations? I’m open to ideas, but I still find it fascinating how a Woods, a Federer, or an Armstrong emerge and is distinctly superior in an age of known training methods and when professional scientific training rules. Excellence continues to spread through the “full house” of diversity that Gould described, but it seemingly leaves room for some real performance surprises.

Further reading:

[Update] A few people are misconstruing at least part of my argument. In that part it’s not about whether Tiger (or Federer) is an outlier, because of course he is. The real issue is the puzzling fixity in the standard deviation of professional golfers’ scores over the last few decades. Why aren’t pro golfers getting better? Amateurs I understand, and their poor performance is well documented, but the non-improvement among pros is something else.


  1. Along these same lines, you can add Barry Bonds to the list. The recent controversy and home runs record have somewhat obscured it, but Bonds 2001-2004 baseball seasons were, from a statistical point of view, ridiculous. He went from being merely the best player in the game up to that point to being an extreme outlier.
    For example, in 2004, his on-base percentage was .609 compared to the runner-up at .469, and his slugging percentage was .812 to the next at .657. I haven’t broken it down, but I think the spread between him and the second best guy, in standard deviations, is unrivalled in baseball history (including Ruth), and certainly hasn’t been approached in the past 80 years.
    How did this happen? The performance-enhancing drugs issue doesn’t really explain it because, like in cycling, most of the competitors have that same edge.

  2. Drugs?

  3. Peter Clark says:

    Fascinating stuff – sounds like the genesis of some lucky person’s PhD thesis.
    I tend to think the biggest differences are mental, not physical. Look at Tiger on Sunday afternoon (not just last Sunday afternoon, but most Sunday afternoons!) … his two closest competitors both put up double-bogies within minutes of Tiger posting a birdie, and it was game over.
    Are these champions somehow mentally prepared early in life in a way that no subsequent physical training can overcome? Perhaps the mental standard deviation is not compressing as much as the physical one. Tiger is an outlier in not letting the frustrations of the game get to him.

  4. simple, there will always be black swans (nassim talib)

  5. The experiment isn’t pure. Pro sports isn’t an objective test of who can most successfully hit a ball with a golf club: it’s a form of entertainment. It’s a business which relies on people wanting to watch it.
    So the question become “is it more entertaining (and therefore, incidentally, profitable) for golf/tennis/baseball to have one – or any other statistically unlikely number of – outright leader(s)?”
    I’d speculate that it probably is. Most popular sports are very badly designed from the point of view of game theory. Look at soccer – victory conditions are very often met by one striker in a handful of seconds “on the break” rather than being a cumulative result of consistently better performance by the whole team over a whole ninety minutes. And it’s (one of the?) most popular game(s) in the world. People seem to like that approach: there’s a big disconnect between what makes a well-designed game and what makes a game that’s fun to watch or follow.
    If so, one reasonable expectation for these statistically unlikely spikes would be for a lot of the people involved in any given sport to be – however unconsciously – working towards that outcome. The rules of sports change all the time. Often these are explained away as making the game faster or fairer or more open. What if the constant adjustments that are forever being made by sporting bodies actually have the net effect of accentuating the performance of one (etc) leading athlete? For example, what if the new “Tiger-proof” courses are actually really Tiger-friendly? What if the Tour de France people spent seven tournaments in a sincere effort to be fair to all the riders but nonetheless following their impulse to make cycling as thrilling as possible, and knew that meant another Armstrong victory?
    That doesn’t require an active or malicious conspiracy anywhere along the line. It just requires many of the people involved to understand on some level that what makes for a great spectacle and an audience that comes back every week isn’t necessarily the levellest playing-field. We watch this stuff vicariously. We vest in the success of particular teams and individuals. Perhaps the rewards for the spectator are just a lot higher when the winner doesn’t change about all that often.

  6. I’d go along with Brian — and Nassim — and say there are always black swans. In other words, deviation isn’t always standard :-)

  7. True, but the comments about black swans duck the core issue. I acknowledge that shrinking deviation doesn’t mean no deviation, and that there will always be outliers.
    But that’s tangential to my broader point, because the trouble with golf is that the standard deviation of scores hasn’t shrunk in the last 25 years. That likely means one (or both) of two things: Golfers aren’t getting better, or courses are getting harder. If it’s the former, that’s really interesting, in that it puts golfers up against the right wall of performance, like male 100m sprinters.

  8. An interesting related question is that maybe golf scores are the wrong measure, in that perhaps a kind of homeostasis exists wherein course designers intentionally keep pro scores averaging around 70.
    So, another measure, and one I haven’t looked at in detail, is win rates. Tiger’s current 25% win rate is much better than his current competitors, but how does it compare to historical figures? And, more importantly, how does the average win (or place, or show) rate, and its standard deviation, across all pros compare to the same figure 20, 30, or 50 years ago?

  9. Sean Roach says:

    Jack’s total career PGA win rate is 12.5% (73 wins in 586 events). If you stop at 1986, the last year he won an event, it increases to 15.9% (73 wins in 460 events). Not sure about those of Snead, Hogan, etc.
    An interesting number to look at would be the average handicap of a professional golfers today vs those of 25 years ago as handicap factors in course “difficulty” via slope and course ratings. With the scoring having remained the same if the handicaps are lower you could reasonably attribute the difference to the courses.

  10. Of course golf is more difficult than in the past – just watch an old tournament on the Golf Channel – the greens were soft and slow, the fairways wide, the yardages much less.
    New golf course design and tournament conditions balance out the equipment, ball and player fitness improvements with the result being: essentially the same scoring averages.

  11. The spread of excellence works best in a large population base. For most of the last century, there were fewer golfers in proportion to the populations of other sports. Golf was one of the last sports to drop the color barrier; many golf clubs were white-only, either explicitly or implicitly, well into the 1960s. This implies a relatively smaller population base of players. Like tennis and pro cycling, golf also targets a smaller, higher-income demographic than many other sports, which further restricted the population of players.
    I don’t know if there are any high-income, white-only sports left today — lacrosse, maybe? — but if and when these barriers fall away, we should expect a spread of excellence to follow 25+ years further on.

  12. Pro golf scores haven’t gone down because the courses have gotten much more difficult over time.
    My family belongs to a club that has hosted 6 major championships over the last 50 years. Before each tournament, changes have been made to make the course longer and more difficult. It’s an arms race between the equipment designers and the course architects. So far it seems to be a draw.

  13. I think the choice of sports is unappropriate and as somebody also mentioned, the score per course not a good variable for comparison. As a matter of fact, there are too many variables in golf, tennis and route cycling.
    A golf ball with a minimum variation in spin on a course with a minimum variation in the grass played under weather with a minimum variation in the wind speed or direction can mean the difference between winning and losing. You can say that Tiger Woods (and Michael Jordan for that matter) are cooler than the rest under pressure, but how do you measure “coolness”?
    When Roger Federer plays, he does so against human beings and he tends to outsmart them, outplay them, make less mistakes or simply score more points than the rest. How do you measure that?
    Even Lance Armstrong, in a supposed race against time, also had to weave through traffic and coexist with his team and the rest of the teams. That also takes wit, besides his unique physical conditions.
    Maybe the deviations study will work better with olympic swimming, where the conditions are more controlled, the styles more similar and one swimmer has little influence over the rest (you can only see the swimmer next to you but can’t slow him down). There it would be hard to explain the existence of a twenty-first century Mark Spitz.

  14. I think the the number of .400 hitters in baseball during the live ball era is too small a sample set to draw any conclusions. Maybe ten with a cluster of five or six in the twenties?