Plot of the Week 1

Today is the first installment of Plot of the Week.  I am planning on posting a sports-related plot every week.  Some weeks I will interpret the plot; other weeks I hope that you will help post what you find interesting about the plot.

This is a scatterplot of athletes' win percentage in Majors vs. win percentage at other non-Major tournaments.  

• I have plotted male golfers (Tiger Woods pre-scandal, current Tiger Woods, Phil Mickelson, Jack Nicklaus) and female golfers (Yani Tseng, Annika Sorenstam) in black and male tennis players (Pete Sampras, Roger Federer, Rafael Nadal, Novak Djokovic) and female tennis players (Venus and Serena Williams, Martina Navratilova, Chris Evert, Steffi Graf) in red.
• Annika Sorenstam and Novak Djokovic are tough to read due to overplotting in the middle of the plot.
• The solid line represents the 45-degree line (y = x) and the dashed line is the least squares regression line.

Here are the most interesting features in this graph (to me, at least):

• Phil Michelson does not win tournaments (Majors and non-Majors) as frequently as the other athletes.
• Graf won much more often than anyone else - over 50% of non-Major tournaments and 40% of Major tournaments.  From this view, it seems that Graf is clearly the best female tennis player, with Evert and Navratilova not too far behind.
• Athletes close to the solid line win Majors at the same frequency as non-Majors.  This seems to represent the set of athletes who are not intimidated by the pressure at the Majors.
• Yani Tseng is the only athlete much farther above the line - she seems to over-preform at the Majors.  It is still very early in her career, so I would not be surprised if she moves closer to the diagonal line as her career progresses.
• The athletes below the line tend to under-perform at the Majors compared to other tournaments. But this set contains some of the best athletes ever, so this is not quite a fair assessment (Venus has 7 majors and Evert and Navratilova 18 each). Maybe it is more fair to say that they over-perform at non-Majors.
• Federer and Nadal have very similar winning percentages.  Since Federer is 5 years older than  Nadal, it will be interesting to see if Nadal can keep this same pace for the next 5 years to catch up to Federer in terms of tournaments won.

Do you notice anything else interesting that I missed?

Tiger's Winless Streak

With the Master's just played last weekend and Tiger winning his first tournament in 30 months a few weeks ago, I thought I would dedicate a post to golf.

When Tiger won the Arnold Palmer Invitational, he ended a drought of 923 days without a win on the PGA tour.  Looking at his previous stats here and here, Tiger had won 71 of 237 tournaments played (30.0%) before his winless streak began at the end of 2009.  Before his recent win, Tiger lost 27 consecutive tournaments (well, he didn't win, but his tournament earnings were still over $2 million during this time - I'd be happy with that).  Let's assume that the probability he wins a tournament is 0.30 and that each tournament performance is independent (probably not the case, but he has won at so many different courses that it should be relatively true).  Since the probability that he wins is 30%, the probability that he loses is 70%.*  The probability that he would lose 27 consecutive tournaments before winning the 28th is:

Prob of losing 27 * Prob of winning one = (0.70)²⁷ * (0.30) = 1.97 x 10^-5

which is equal to 1 out of 50,000.  In other words, it is highly unlikely that this streak would happen if Tiger's game did not significantly suffer after the "incident".

Let's now look at his Major winless streak (now at 11 straight after not winning the Masters).  As a professional, Tiger won 14 of 46 Majors played (30.4%) before his losing streak began.  Notice that this is very similar to his regular tournament win percentage.  The probability that Tiger would go 11 Majors without winning is:

(0.696)¹¹ = 0.018

This is still a small probability, but not completely unreasonable.  I looked back at his stats, and Tiger previously had a Major winless streak of 10 (2002-2004).  So I wouldn't write Tiger off just yet, especially if the "old" Tiger is back.

UPDATE:
* This needs to be pointed out because I originally switched the 0.3 and 0.7.  Oh, the mistakes I can make when I don't have a class of undergrads correcting me. Thanks to Matt for pointing this out.