Another Golf Graph

Steve Sailer notes that even Charles Murray is opining on the Woods v Nicklaus controversy. Murray reproduces a chart from his terrifically fun book Human Accomplishment showing the distribution of career major wins by number of golfers. Here's Murray's chart:
Since I've got this data already stored in a handy manner, I thought I'd update it thru today. It looks very much the same, except that the numbers are even more skewed towards the lower number of winners (or is it the other way around? I always seem get the term "skewed" backwards) - and of course his chart is the product of a professional graphics editor. I'll have to work on that.
Do read both links.

Another No-Name Wins a Major

OK so S. African Louis Oooooooslkdhzzn has won the British Open. It seems that the major winners these days, particularly with Woods in a distracted state, are often not exactly household names. But even when Woods was on fire he wasn't winning every major, yet no other big guns ever seemed ready to really take on the champion's role (other than Mickelson, with limited success).

I've felt that Woods has benefited from there being a less than gutsy pack of challengers, compared with Nicklaus. Jack had to contend with Arnie and Player when he started, then he had to battle the likes of Trevino and Watson in his thirties. Tiger's competitors just seemed to wilt away. While one might attribute that to his intimidating play in tournaments, that doesn't explain what happens in those tournaments where he didn't dominate.

So has the game become less dominated by elite players, or is it just my the-older-days-had-more-heroes prejudice? Here's a chart that shows the combined number of career major wins for each major winner by year. The way this works is if four players with 3 career major wins won the four majors one year, that would count for 12. If all four winners had only one career win, then that would be 4. It's intended to measure how much the game is dominated in one year by accomplished players.

There is a slight downward slope, but pretty much it's all over the place with an insignificant correlation. But these are dominated by two super-outliers - Woods and Nicklaus. So let's look at it by excluding Woods and Nicklaus (which is what we're really trying to get to, anyway - the prevalence of tour studs other than those two). To avoid undercounting the years in which Nicklaus or Woods won, I substituted the average # of career major wins, 2, for their totals (18 and 14) in each of their winning majors. Here we see a clearer trend:
Here the r-squared is a more robust 0.26, suggesting a definite trend in the sport of less dominance by by a cadre of elite players. It also supports the notion that Woods has had less of a challenging field during his run of dominance than Nicklaus had in his heyday. Put another way, Nicklaus seems to have faced much gutsier challengers than has Tiger.

These are relative comparisons, of course - golfers on the whole are no doubt superior today - bigger, better-conditioned, better-equipped - so the trend of less dominance by a few top players is probably an expected result of more, better players entering the field. Looked at that way, you could make the argument that Woods's dominance is all the more remarkable given the generally higher standard of overall play. Still, there just seems to be an element of toughness missing in the game today.

UPDATE: Steve Sailer has some interesting comments below, as well as on iSteve.

Here's the basic data in spreadsheet form if you'd like to play with it yourself.

UPDATE: It occurred to me that this analysis is potentially flawed: there is built-in bias against later tournament winners as they haven't had time to build up wins. For example, when Watson beat Nicklaus in 1975, that was his first tournament. Perhaps Graeme McDonald will go on to win a whole bunch more tournaments before all is said and done.

So to address this, I compared Woods and Nicklaus at similar points in their careers. There have been 55 majors starting with Woods's victory at Augusta in 1997. So I've compared them to the 55 majors for Nicklaus beginning with his U.S. Open victory in 1962, again counting only 2 for the majors where Jack or Tiger won. I've also limited the # of career wins from the Nicklaus eras to those won prior to 1976. That means, for example, that Tom Watson and Ray Floyd are only credited with 1 career major. These results still suggest stiffer competition for Nicklaus - other major winners had a combined 135 career major wins by 1975, while Tiger's only had 79. By the way, through this period The Golden Bear had 14 major wins - the same as Woods.

Just Walk Away, Renee

The Times has an entertaining article on how the rich are walking away from their homes at a much faster pace than the middle class. It displays a Capra-esque disdain for the moralss of the wealthy in contrast to the more ethically-sound middle class.

Whether it is their residence, a second home or a house bought as an investment, the rich have stopped paying the mortgage at a rate that greatly exceeds the rest of the population. By contrast, homeowners with less lavish housing are much more likely to keep writing checks to their lender. About one in 12 mortgages below the million-dollar mark is delinquent.

The reporter does not shy away from inferring the underlying motive:

Though it is hard to prove, the CoreLogic data suggest that many of the well-to-do are purposely dumping their financially draining properties, just as they would any sour investment. “The rich are different: they are more ruthless,” said Sam Khater, CoreLogic’s senior economist...

The CoreLogic data suggest that the rich do not seem to have concerns about the civic good uppermost in their mind, especially when it comes to investment and second homes. Nor do they appear to be particularly worried about being sued by their lender or frozen out of future loans by Fannie Mae, possible consequences of default.

The article concentrates on Silicon Valley, but also points to Chicago.

The sheriff in Cook County, Ill., is increasingly in demand to evict foreclosed owners in the upscale suburbs to the north and west of Chicago — like Wilmette, La Grange and Glencoe...“I’ve never seen the wealthy hit like this before,” Mr. Lowman said. “They made their plans based on the best of all possible scenarios — that their incomes would continue to grow, that real estate would never drop. Not many had a plan B.”“I’ve never seen the wealthy hit like this before,” Mr. Lowman said. “They made their plans based on the best of all possible scenarios — that their incomes would continue to grow, that real estate would never drop. Not many had a plan B.”

Which reminds me of Steve Sailer's description of Obama's financial plan:

1. Borrow against home equity and consume.
2.
3. Get rich!

Of course for the Obama's it all worked out - he got himself appointed to a State Senate committe overseeing hospitals followed by Michele's $200k promotion from the hospital she worked for, and then of course he got a big advance on his book.

But all that aside, this is one big reason why any upward growth in housing prices needs to be taken with a grain of salt - as more-and-more high priced homes are the targets of distressed sales, the average sale price will go up, even though the overall health of the real-estate market is not improving.

Our Future Elites

High schoolers scoring above 750 on the Math SAT are good candidates to be out in the forefront of newer or at least dominant technologies and driving growth in our "Information Age". On the other hand, we are a race-obsessed society, believing that this elite must - surely must - reflect our wonderful diversity - that this elite should "look like America." Surely, as we all know from watching the most popular shows on T.V. (House, Grey's Anatomy), a large proportion of doctors in elite hospitals - indeed, the more brilliant among them - are African-American. But what can we glean about these future leaders from the published SAT's?

The College Board doesn't publish numbers of students by race at each 50-point scoring cohort -- they only do that for male/female overall (and even now they're only showing results at 100-point cohorts beginning in 2009). But we can estimate how many there should be based on the mean and standard deviation for each group. In the post below, I compared estimated to actual for males/females overall, and the results were right in line. So here are estimates for 2009:

Race	Mean	Std. Dev.	Total	Est 750+	Est 800
Asian	587	125	158757	15259	7016
Black	426	97	187136	78	11
Latino	461	106	103937	333	72
Mexican	463	99	79766	149	26
Native Am	501	128	66448	1719	648
Other	514	119	51215	1212	416
Pacific Isl	450	104	22881	45	9
White	536	103	851014	16059	4414

What's immediately notable is that there are nearly as many Asians expected to score at this level as there are whites, despite the great disparity in overall numbers of test takers - and significantly more Asians than whites are expected to score 800. Next you'll note the very low numbers of minorities who can be expected to score at this level. And the math test is pretty straightforward - nothing fancy, just math a high-schooler should know. It's hard to argue that there are any significant numbers of hidden math geniuses who can't score high on the SAT-M. So the prospects of an innovative elite looking like the rest of the country are pretty dim.

NOTE: It's not unlikely that the actual numbers of minorities, particularly blacks, who scored 750+ was significantly higher than these numbers as there is a strong incentive for high-achieving minorities to take the SAT even in non-SAT regions due to the lure of Ivy League affirmative-action admissions.

The Gender/Math Gap

An item mentioned over in Discover GNXP on the Male-Female Math Gap got me looking a little more closely at SAT scores. The gap in high-level achievement in math has been narrowing, at least as measured by the SAT's. But there's reason to suspect that the narrowing may not be quite as straight-forward a trend as it may appear.

The SAT's - until last year - have published the number of male and female test takers by 50-point score ranges for the Verbal and Math tests. Thus we can compare the number of male vs. female students who have scored at 750 and above on the Math test to see how the gap has been fairing.

The SAT also publishes average test scores by sex along with their respective standard deviations. Thus we can also calculate the expected number of each sex who should score above 750 each year. The chart below compares the actual achievement gap vs. the predicted.

The actual/expected stayed within fairly tight bounds, but in 2007 and 2008 there was a noticeable shift where the actuals have dropped significantly below expected. The SAT is not universally taken. While in most states it's considered mandatory, it's certainly plausible that in traditional ACT states high-achieving girls have made a concerted effort to take the SAT in recent years, thus pumping up the 750+ scores over what would be expected based on the distribution of the scores generally.

Here's the same chart with expected male-female ratios for those scoring 800. Again it does not suggest quite the narrowing that has actually occurred in the 750+ scores.


Looking at the actual numbers of SAT test takers by sex who scored 750 and above compared to the expected number based on their means and standard deviations, it would appear that there is indeed a tendency for more high achievers to be more likely to take the SAT in recent years - and the female effect looks larger.

(Note the shamlessly sexist color scheme.)