To celebrate Father’s Day in the United States (June 21 this year), I’m going to use this and my next column to honor my late dad by using a game he loved—golf—to teach some very basic statistics lessons. Some of these may have been lost on you previously, not through some fault of your own, but rather from trainers’ tendency to concentrate on a technique’s mechanics. Analysis of means (ANOM) might be new to many of you, but even if it’s a review, I hope you have as much fun reading this as I did writing it.
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The recent Masters tournament, in which 97 golfers participated, will provide the data. The Masters is the crème-de-la-crème of golf tournaments. One qualifies by winning a major tournament or by formal invitation. Past champions qualify automatically.
The first two rounds of any tournament are used to establish the “cut” to narrow the field for the last two rounds. Cut rule: Following the second round, the 50 golfers with the lowest scores, plus ties, plus any golfer within 10 strokes of the lead, advance to play the final two rounds. In this case, players with scores above 146 were cut, narrowing the field from 97 to 55.
Here’s the analysis of variance (ANOVA) for the first two rounds:
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Comments
Six Sigma Golf
I agree with Davis; much of any golfer's variability is common, not special cause.
Most golfers don't think about tracking their shots, but 80% of golf shots occur within 100 yards of the hole, yet were do most golfers spend their time? On the range, hitting their driver. This is why the short game and putting are so essential to scoring well. A good drive is important, but pros only hit driver on a maximum of 15 holes (the others are par 3s). Keeping the number of putts per round under 30 is key for scoring. Want to score better? Double your putting practice. Simply tracking whether you tend to putt long or short, left or right will dramatically reduce your score.
Pro golfers think about hitting a sprinkler head on the fairway; amateurs think about hitting the fairway. Pro golfers think about hitting the hole; amateurs think about hitting the green. Amateurs have a much higher variation because they're thinking about a bigger target. Want a better score? Shrink your target.
Years ago I wrote a 24 page booklet on <a href="http://www.qimacros.com/pdf/golf.pdf">Six Sigma Golf</a>. One reader didn't think you could apply Six Sigma to golf, so he tested it out and cut 10 strokes off his game. See how Six Sigma can improve your golf game.
Good insights, Jay
Insightful comments, as always, and, as usual, the elegant simplicity of your suggestions hit the nail right on the head.
Davis
Use of a run chart?
Thinking back to Tiger's golden years (e.g. 1995 to 2005 perhaps?), would a run chart of his combined 1st two round scores show he was consistently "different", i.e. better than the rest of the field? Perhaps his more recent scores would give a clear statistical signal of his powers waning?
I remember, come the final day, Nick Faldo was always in the reckoning for many years, perhaps his low-scores in the 1st 2 rounds would consistenly show him as an outstanding performer (in the 90s?).
Perhaps even Greg Norman, going back 15 to 20 years perhaps, would give a signal with his final round scores when he often went into the final round top of the leaderboard but failed to come away with the trophy due to a last round of perhaps 75 or 76? Was Norman's performance in these final rounds due to common cause or evidence of some potentially identifiable assignable cause affecting his game?
Here I'd be curious to see which technique/s you'd recommend if we included this year-by-year time element in the process as well.
thanks, scott.
I think you're onto something, Scott
Good comments and suggested analyses! The data are easily available should one wish to do it. I think I gave a good example with Jim Furyk's cut history and citing the recent performance of the 2003 champion. Isn't is amazing what simply plotting data over time can do?
Davis
graph headers
Not being a golfer, I don't know what your first table headers refer to. I haven't used statistics for a long time either.
DF
SS
MS
F
P
What do these represent?
It was perfectly clear to ME what I meant
Sorry for the confusion. That is a classic Analysis of Variance table. Your main concern should be the "p" at the very right. That is the probability that, if you declare an effect significant, you could be wrong (based on the current data). Classic statistics courses teach that one is willing to take a 5% risk of that, so you are looking to see whether p < 0.05.
Other terms: SS (sum of squares), df (degrees of freedom), MS (a factor's SS/df), F (a statistical test of significance of a factor using the common cause (Error MS): MS factor / MS Error. The "p" results from looking up the value of "F" in a statistical table, which good statistical packages now do automatically -- I remember the days when they didn't!)
I hope this helped. Thanks for reading.
Davis
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