2011 U.S. Open

[jamo]

This article lists the most dominant major performances ever based on comparing the winner's score to the mean score of the field - ranking Tiger at Pebble as the most dominant performance by a wide margin since 1960, and Rory's as the 17th most dominant.

http://espn.go.com/espn/grantland/story/_/id/6680477/relative-dominance

It seems like a decent method of analysis to me.  It could be even better if the strength of field were taken into consideration, since a Masters field for instance is typically weaker than other fields because of special exemptions and things like that.

The thing I like the most about that list is that both Tom and Jack form the 1977 British are on there.

[ghalfaire]

I like it because it is an attempt to take "human bias" out of the performance consideration by "quantifying" it.  I can't think of a better way than using the statistics of the tournament field's scoring to evaluate the performance of the individual players in that tournament.

Originally Posted by laxbballgolf

This article lists the most dominant major performances ever based on comparing the winner's score to the mean score of the field - ranking Tiger at Pebble as the most dominant performance by a wide margin since 1960, and Rory's as the 17th most dominant.

http://espn.go.com/espn/grantland/story/_/id/6680477/relative-dominance

It seems like a decent method of analysis to me.  It could be even better if the strength of field were taken into consideration, since a Masters field for instance is typically weaker than other fields because of special exemptions and things like that.

[zeg]

Cool, that's exactly what I had in mind.  Nice that someone's already done the work!

Edit:

Also, to get a sense for the magnitude of the outlier, if we assume the scores are normally distributed, Woods' 2000 z-score of -4.12 (or better) would be expected by chance about once in 26,000 player-tournaments, while McIlroy's z-score of -3.07 (or better) would be about once in 500.

They looked at 50 years of Majors, so something like 200 tournaments (maybe fewer, I don't know for certain how they counted).  There are what, about 70 players to make the cut, so that is a total of 70x200=14,000 player-tournaments.  We'd therefore expect to have seen less than one (about 0.5) performances like Woods' 2000 US Open and about 30 McIlroy performances.  That's not great agreement, but it's roughly (within a factor of 2) accurate---there are about 20 rounds in the < -2.99 z-score range and 1 in the < -4 range.

There are two conclusions I'd draw.  First, the scores can't be normally distributed---this means the z-score they're calculating is somewhat bogus because the standard deviation and mean alone don't measure the distribution very well.  That's ok, they're good enough for ballpark.  It also means that, while both Woods and McIlroy had phenomenal performances, neither is unexpectedly good.  Given the number of rounds we've seen in the Majors, purely by chance one guy should have had as good a Major as Woods did in 2000.  We should perhaps be surprised we haven't seen as many Rory-like performances.

By the way, don't misinterpret the "purely by chance" comment---it isn't suggesting that Woods just got lucky or that we shouldn't be surprised if an amateur had been the one to shoot that score.  The score distribution reflects golfers of different abilities, so we would obviously expect Woods (or some other highest-caliber golfer) to be the one to shoot the super-low score.  It just means that the numbers suggest that it's not so surprising that some elite golfer managed to shoot a round that far outside the norm.

Note also that the cut actually makes a bit of a statistical problem because you're cutting off the high-score tail of the distribution by not letting the worst-scoring players finish the tournament.  That biases the average score to be better and might lead to under-estimating the true z-scores, but it's probably a small effect.  It may contribute to why we don't get as many McIlroy-like performance as we do --- those low scores should all be a bit less likely than the z-scores suggest.

[deasy55]

I wonder are all the figures correct though. They also said Els won his first major at 28 (was 24), that Rory has played in 9 majors (actually 11) and had 2 top 3 finishes in majors already (actually 3). If they can make errors like that in the simple bits I have my doubts about the tricky bits (although it does look fairly correct)

Quote:

Cool, that's exactly what I had in mind.  Nice that someone's already done the work!

[zeg]

Originally Posted by deasy55

I wonder are all the figures correct though. They also said Els won his first major at 28 (was 24), that Rory has played in 9 majors (actually 11) and had 2 top 3 finishes in majors already (actually 3). If they can make errors like that in the simple bits I have my doubts about the tricky bits (although it does look fairly correct)

It's ok, I'd rather have inaccurate work done for me than do it right myself!

(btw, I added quite a bit more to my post in an edit while you were posting this)

[deasy55]

I noticed. You obviously have your homework done on this kind of stuff. (Stuff like this comes up in my college course also so it's nice to see it done by others )

Originally Posted by zeg

It's ok, I'd rather have inaccurate work done for me than do it right myself!

(btw, I added quite a bit more to my post in an edit while you were posting this)

[ghalfaire]

Your point that the distributions are not Normal (Gaussian) is well taken.  Anytime your are dealing with finite data sets density and distribution functions are approximations of the real data distributions.    I assume what the author did was take 200 data sets and calculate the data mean and standard variation of each set (each tournament).    Then they calculated the z number of each player (probably just the winner in most cases).  The individual z number is the measure of how many standard deviations a player is from the data mean.  I suspect since there are more than 70 data in each set that the Student T tests would say that a Gaussian assumption is OK (But I've been retired for awhile so maybe not).  So I like the analysis and think it is significant (not in the probability sense but English language sense) i.e. Tiger's performance was much better than Rory's.  So I don't share your thoughts that the z score is bogus if by that you mean it does't represent how uncommon the relative performances were.

To determine  whether or not we should be surprised by Rory or Tiger's performance I believe would require we sort the data differently.  You would need to develop a data set on Tiger's and Rory's scoring ability (e.g. record Tiger's scores for many tournaments and then do the calculations for Tiger to see how likely it is  he would repeat his 2000 US Open performance).

Anyway I didn't mean to bore everyone to death but just to that Statistics is not an exact science like Probability Theory is but rather an application of that exact science to finite data sets so answers are not as precise and care in interpreting the answers is always advisable.

Originally Posted by zeg

Cool, that's exactly what I had in mind.  Nice that someone's already done the work!

Edit:

There are two conclusions I'd draw.  First, the scores can't be normally distributed---this means the z-score they're calculating is somewhat bogus because the standard deviation and mean alone don't measure the distribution very well.  That's ok, they're good enough for ballpark.  It also means that, while both Woods and McIlroy had phenomenal performances, neither is unexpectedly good.  Given the number of rounds we've seen in the Majors, purely by chance one guy should have had as good a Major as Woods did in 2000.  We should perhaps be surprised we haven't seen as many Rory-like performances.

[bplewis24]

(kidding) :)

[zeg]

Originally Posted by ghalfaire

So I like the analysis and think it is significant (not in the probability sense but English language sense) i.e. Tiger's performance was much better than Rory's.  So I don't share your thoughts that the z score is bogus if by that you mean it does't represent how uncommon the relative performances were.

No, I think we agree on this point.  By "bogus," I just mean that the detailed analysis I did (computing how many 4-sigma events are expected) should be taken with a grain of salt.  I think it is plausibly correct at about the order of magnitude level --- putting Tiger's about an order of magnitude rarer than Rory's --- but not much better than that.  For example, I'm not bothered that we've only had ~ 20 events when the numbers say we should have 30.  That's all I mean.

One could do the more sophisticated per-player analysis you're talking about, but I think it's interesting that ignoring that and treating the whole fields as a single population of scores works as well as it does for predicting the numbers of outliers.  It actually raises an interesting question: are there more outliers during, say, Tiger's era than there were before?  Is he actively pushing the statistics, or is he really just a fluctuation?

But, I think I'm starting to agree with Brandon...

[Frank-0-Sport]

Greetings ...

Some thoughts about the 2011 U.S. Open

Final Scores -- http://www.majorschampionships.com/usopen/2011/scoring/

First thing to point out -- there was nothing at all wrong with the Congressional Country Club Blue Course. It was just the combination of the weather and other factors (like maybe tee and pin assignments) that contributed in large part to the low scoring.

In the case of the winner, young Mr. McIlroy, it was his talent and his inner resolve, along with the prevailing conditions, that contributed to his remarkable mastery of the golf course.

If Mr. McIlroy had been out of the competitive equation, then runner-up  Jason Day and company would have been dealing with that classic US Open pressure to the max, and perhaps would not have ultimately finished as low as they actually did.  280 strokes for 72 holes has always been "par" to me, regardless of the actual course par. Only a small handful of players finished at 280 or better. They did so not only because of the overall playing conditions but also because Rory McIlroy took a certain amount of pressure out of the competitive equation.

In sum, this year's US Open at Congressional was a very fair, very challenging and very competitive event - the end result was that one very determined young competitor flat out performed worlds better than any of the other 155 participants.

Thanx-A-Lot and Congrats to Rory,
Frank-0-Sport

[bplewis24]

Originally Posted by Frank-0-Sport

If Mr. McIlroy had been out of the competitive equation, then runner-up  Jason Day and company would have been dealing with that classic US Open pressure to the max, and perhaps would not have ultimately finished as low as they actually did.  280 strokes for 72 holes has always been "par" to me, regardless of the actual course par. Only a small handful of players finished at 280 or better. They did so not only because of the overall playing conditions but also because Rory McIlroy took a certain amount of pressure out of the competitive equation.

By that rationale, the competitors at the 2000 US Open should have at least broken par.

Brandon