St. Louis Rams $100K Giveaway

It was announced today that the St. Louis Rams are offering $100,000 to anybody who correctly predicts their 2014 schedule. The 16 opponents are known, so you must guess which opponent the Rams play each week, along with their bye week.  To make things more difficult, you must also predict if the game is played on Sun (which most are), Monday (typically 1 game each week), or Thursday (typically 1 game each week).

I did a quick back-of-the-envelope calculation to determine the approximate odds of winning such a contest and came up with 1 in 45,193,226,156,719,200 which is about "45 followed by 15 zeros".  Here's how I got this number:

First, let's choose the bye week.  Last year no teams had a bye in weeks 1-3 or 13-17. This leaves 9 choices for the bye week.

Next, we can place the 16 opponents among the remaining 16 weeks. This can be done 16! ways (reminder: 16! = 16 * 15 * 14 * ... * 2 * 1).  That's a lot of choices. However, the Rams play the 3 teams in their division twice each, and we can assume that they will not play the same team in consecutive weeks. Accounting for the bye week, this removes about 15 * 14 * 3 = 630 possibilities (although there is some double counting that I'm ignoring).

Finally, we need to select the day of the game.  On average, each team plays one Sunday night game and one Thursday night game. For simplicity, we will assume that the Rams will play exactly 1 Thurs. night and one Mon. night game.  Ignoring the bye week, this leaves 16 * 15 = 240 possibilities. (In reality, games that are thought to be "better" are on Monday night and games that are thought to be less interesting are played on Thursday. Therefore, the odds are probably slightly different).

To get the final number of possibilities, we need to multiply the different possibilities together: 9 * (16! - 630) * 240 = 45,193,226,156,719,200.  Although this is slim chances, I still took 5 minutes to fill out the schedule. So here's to hoping I'm $100,000 richer when I write my next post!

P.S. - I'm sure I made some silly mistake, so please comment if you notice one and I'll get it fixed.

Winter Olympics Medal Predictions Gone Wrong

I recently came across an article about an analytics company, MicroStrategy, that used their dashboard to predict the number of medals that each country will win at the 2014 Winter Olympics. They predicted that Canada will win the most medals (35), followed by Germany (31), with the US in 7th place (16 medals). They explain the results in their blog post. I think the company was just trying to do a simple, light-hearted analysis to show off the types of analyses that their product can do. Unfortunately for the company, there are several flaws in their model/analysis.  Two minor flaws have to do with the data itself:

• In their post, they state "Keep in mind that the algorithm is based on historical data, and doesn’t necessarily reflect more current information such as emerging stars, recent funding boosts, and an unexpectedly large addition of new events to the program."
• On a related note, they fail to explain how they handled the dissolution of old countries to form new countries. For example, are the medals from past Olympics won by the USSR now contributed to Russia? What about newer countries, such as Ukraine, that used to be a part of USSR?

The biggest problem is over-fitting of the model. Over-fitting occurs when you design a complex model using many variables that is more likely to describe random noise than the true signal. Because the model is describing the noise and not true signal of the historical data, it often results in inaccurate predictions (in this case, inaccurate medal predictions). If you are interested in performing predictions based on a model, one simple way to determine if a model is over-fit is by leaving out a subset of the data, fitting a model, then using that model to predict the data that you left out. Since you know the "truth" of these predicted data, you can assess the prediction accuracy. For example, MicroStrategy could have used all data prior to 2010, fit the model using that data, then predicted medal counts for 2010. We would be able to determine the accuracy by comparing to the true 2010 medal counts. 

The 2014 Winter Olympics are only half way over, but let's compare their predictions to current medal counts for selected countries:

	Predicted Medal Count	Actual Medal Count (as of 2/16)
Canada	35	14
Germany	31	12
Russia	18	16
USA	16	16
Netherlands	7	17

While it is possible that Canada and Germany can still reach their predicted medal counts, it looks like Russia, USA, and the Netherlands will all greatly surpass their predicted medal count.

Again, I realize that the company was doing this for fun and to generate some press. I just hope that customers don't look at this analysis, see how bad these predictions are, and ultimately decide to not buy the product. This goes to show how a little statistical knowledge can go a long way!

Super Bowl Squares Strategy

With the Super Bowl just a day away, I am hearing a lot of talk about Super Bowl Squares, the game of chance that only gets played one day out of the year.  With most variations of the game, people sign up for squares, then once all squares have been taken, the numbers are randomly assigned to the rows and columns, thus making this purely a game of chance (I guess the football game also plays a role too).

But suppose that these numbers were not randomly assigned: you get to choose the numbers that you want.  Which pair of numbers gives you the best chance of winning?  I have seen a few articles online trying to answer this question, but all the ones that I have come across look at the score after each quarter of all previous Super Bowl games.  While I see the point of only looking at Super Bowls, some of these games were played over 40 years ago and the game has clearly evolved since then.  For example, I have to believe that field goals are much more common now then they were 40 years ago, as kickers are now able to routinely make 50+ yard field goals (I don't have data to back this up, so let me know if I'm wrong).  Therefore, I have decided to look at all football games from this past season, including the playoffs.  If my counting is correct, this covers 266 games.  I should probably look at the score after each quarter of every game, but this would cover 1064 quarters, and I just don't have the time (or really care to) do this.  So I have decided to only analyze the final scores of the 266 games.  I also ignored whether the winning team was home or away, so to me, Team A winning by a score of 17-13 (making square 7,3 the winner) is equivalent to Team A losing 13-17.  That is, I treated squares (7,3) and (3,7) as the same.

Let's first look at the most common point totals, with respect to the last digit.  As expected the least likely point totals end in 5 (3.8% of all final scores) , 2 (4.3%) and 9 (5.1%).  The most common point totals end in 3 (16.4%), 4 (16.0%), 7 (14.8%), and 0 (13.5%).

Now let's look at pairs of numbers.  If you played over the full 2012 season, 3 squares would have never won (when only looking at final scores): (1,2), (2,9) and (5,6).  This isn't too surprising because, as shown earlier, it is difficult to score total points ending in 2, 5 or 9.  The most likely pairs this past season were (3,6) and (3,7)*, which each occurred 16 times this season.  Combined, these 2 pairs would have won over 12% of the games.  Additional pairs that would have won over 10 times this past season include (0,3), (0,4), (0,7), (0,8), (1,4) and (3,4).

In conclusion, if numbers were not randomly assigned in Super Bowl Squares, it would easily be possible to win in the long run.

* SI writer Peter King picked the Ravens to beat the 49ers 27-23, so he's playing the odds with his final score prediction.

UPDATE (2/4/2013). The score after each quarter (with the Ravens always leading) was 7-3, 21-6, 28-23 and 34-31.  This means that the winning squares were (3,7), (1,6), (3,8) and (1,4).  Did anyone follow my advice and bet on (3,7) or (1,4)?

Wimbledon 2012 wrap-up

Sorry for the long delay in posting - I'm still alive, but have been extremely busy with the new job.  I have also decided to spend more time on "novel" posts where I analyze the data myself to answer new questions, as these seem to get a much better response from readers.  But these posts take more time to write, so I will not be posting as often.  I am finishing up a new analysis with some data from Wimbledon, and I hope to blog about this soon.  For now, I want to give a quick update on my Wimbledon picks (you can read about my picks here).

First the good news: I correctly picked Serena Williams.  The bad news: I picked Novak Djokovic, but he lost to eventual champion Roger Federer.  So I went 1/2, or 3/4 when combining my 2 correct French Open Picks.  When looking at the ESPN expert picks over these past 2 grand slams, only Chris Evert has correctly picked all 4 champions.

Let's hope I can keep up the steam going into the US Open in August/September.

Wimbledon Picks 2012 (Explanation)

With the first week of Wimbledon now a thing of the past, I figured I should actually give my reasoning for my Wimbledon picks.

First, I went with my gut (over data because I didn't have the time) when picking the men's and women's sleepers - players outside the top 10 to go the furthest.  I picked John Isner and Venus Williams who both lost first round.  Guess I shouldn't listen to my gut feeling when making picks anymore.

So let's get to the picks that I actually put some thought into.  I only looked at one stat when choosing my women's champion.  Here are the results of the Williams sisters (both singles and doubles) at Wimbledon since 2000.

Williams Sisters Wimbledon Results 

Year	Doubles Result	Venus Singles	Serena Singles
2000	WON	WON	SF
2001	3RD	WON	QF
2002	WON	RUP	WON
2003	3RD	RUP	WON
2004	-	2RD	RUP
2005	-	WON	3RD
2006	-	3RD	-
2007	2RD	WON	QF
2008	WON	WON	RUP
2009	WON	RUP	WON
2010	QF	QF	WON
2011	-	4RD	4RD

Since 2000, every year that the Williams sisters have played doubles at Wimbledon (highlighted), one of them also wins the singles title (8/8, with both Williams reaching the Final 4 times).  Notice that it doesn't matter how they perform in the doubles, as long as they are playing.  The 4 years that the Williams did not play doubles, often due to one sister being injured, only once did one of them win the singles title (Venus in 2005).  

Serena and Venus entered to play doubles this year (they are currently in the 2nd round).  Looking at past results, the probability that a Williams wins the single title given they play doubles is 1.  So all I had to do was choose between Serena or Venus winning.  I went with Serena because she is the higher ranked and Venus is coming back from injuries.  As of this post, Serena has won her first 3 singles matches and is still alive.

For the men's, I looked at the winner's seed and previous year's performance since 2003 (Federer's first Wimbledon win).

Men's Wimbledon Champions 

Year	Winner	Seed	Previous Result
2003	Roger Federer	4	1st
2004	Roger Federer	1	WON
2005	Roger Federer	1	WON
2006	Roger Federer	1	WON
2007	Roger Federer	1	WON
2008	Rafael Nadal	2	RUP
2009	Roger Federer	2*	RUP
2010	Rafael Nadal	2	-
2011	Novak Djokovic	2	SF

* Federer was the 2 seed, but he was technically the top seed after Nadal withdrew as the number 1 seed with injury before the 2009 tournament began.

Because Federer, Nadal and Djokovic have won 28 of the last 29 major titles, I have eliminated the rest of the field.  I eliminated Federer because it has been one of the top 2 seeds to win every year since 2004.  I went with Djokovic over Nadal because the defending champion has won 6 of the last 9 years (if I consider Federer the defending champ in 2009 since Nadal withdrew and Nadal the defending champ in 2010 since he had not defended his title.**)  Also, Federer and Nadal each defended their first Wimbledon title by winning the following year that they played.  This gives me belief that Djokovic will continue this trend and win his second straight Wimbledon title.  

My men's pick is looking even better after Nadal lost in the second round.  (Still, I'll be cheering for Roger Federer to win the title as he is my favorite player.)

** Under this argument, both Federer and Nadal would have been considered defending champions in 2010, so you could change the fraction to 6/10 defending champs winning. 

Wimbledon 2012 predictions

Wimbledon starts on Monday and I wanted to announce my picks (I was 2/2 for the French Open).  

I am going to follow ESPN's format for their picks (which you can see here):

Men's winner: Novak Djokovic

Men's sleeper (someone outside of the top 10 to go the furthest): John Isner

Men's toughest road (top 10 player to lose earliest): Janko Tipsarevic

Women's winner: Serena Williams

Women's sleeper: Venus Williams

Women's toughest road: Samantha Stosur

Things are very busy for me, so I do not have the time to justify my picks right now - but I hope to later in the week.

French Open Picks: Follow Up

A few weeks ago, I made my picks for the 2012 French Open champions (Part 1 and Part 2).  Using my statistical wizardry (ok, more like logic and process of elimination), I correctly picked Rafael Nadal as the men's champion and Maria Sharapova as the women's.

Compare this to the ESPN expert picks: 11 of the 12 correctly picked Nadal, but only Chris Evert picked Sharapova.  Maybe if I keep this up for Wimbledon and the US Open, ESPN will start knocking on my door.

French Open 2012 - Part 1

It's already the middle of May, which means that the French Open is right around the corner.  In this week's posts, I will make my predictions for the men's and women's 2012 French Open Champions.  I will be looking at the results since 2000 to determine the player who I think is most likely to win.  Let's start by looking at the seed for the winner:

French Open Champions

Year	Men's	Seed	Women's	Seed
2000	Gustavo Kuerten	5	Mary Pierce	6
2001	Gustavo Kuerten	1	Jennifer Capriati	3
2002	Albert Costa	22	Serena Williams	3
2003	Juan Carlos Ferrero	3	Justine Henin	4
2004	Gaston Gaudio	44	Anastasia Myskina	6
2005	Rafael Nadal	5	Justine Henin	10
2006	Rafael Nadal	2	Justine Henin	5
2007	Rafael Nadal	2	Justine Henin	1
2008	Rafael Nadal	2	Ana Ivanovic	2
2009	Roger Federer	2	Svetlana Kuznetsova	7
2010	Rafael Nadal	2	Francesca Schiavone	17
2011	Rafael Nadal	1	Li Na	6

10 of the past 12 men's champions have been seeded 5 or higher.  Using this as our cutoff, this leaves the following players as possible winners this year (by current world ranking):

1. Novak Djokovic
2. Roger Federer
3. Rafael Nadal
4. Andy Murray
5. Jo-Wilfried Tsonga

Djokovic, Federer, and Nadal have won 27 of the past 28 Grand Slam tournaments (Del Porto won the 2009 US Open), but we won't eliminate Murray and Tsonga quite yet.

11 of the past 12 women's champions were seeded in the top 10.  Using the current world rankings, this leaves the following players:

1. Victoria Azarenka
2. Maria Sharapova
3. Agnieszka Radwanska
4. Petra Kvitova
5. Samantha Stosur
6. Serena Williams
7. Marion Bartoli
8. Carolina Wozniacki
9. Li Na
10. Vera Zvonareva

Also note that Kuerten, Nadal, and Henin are the only players since 2000 to have won the French Open as the number 1 seed.  Each time, they were the defending champion.  Since it looks like Djokovic and Azarenka will receive the number 1 seeds and neither won the French Open last year, we will eliminate them from out list.

Now let's look at each champion's performance in that year's Australian Open (the most recent Grand Slam).

French Open Champions

Year	Men's	AO Result	Women's	AO Result
2000	Gustavo Kuerten	1R	Mary Pierce	4R
2001	Gustavo Kuerten	2R	Jennifer Capriati	Win
2002	Albert Costa	4R	Serena Williams	DNP
2003	Juan Carlos Ferrero	QF	Justine Henin	SF
2004	Gaston Gaudio	2R	Anastasia Myskina	QF
2005	Rafael Nadal	4R	Justine Henin	DNP
2006	Rafael Nadal	DNP	Justine Henin	F
2007	Rafael Nadal	QF	Justine Henin	DNP
2008	Rafael Nadal	SF	Ana Ivanovic	F
2009	Roger Federer	F	Svetlana Kuznetsova	QF
2010	Rafael Nadal	QF	Francesca Schiavone	4R
2011	Rafael Nadal	QF	Li Na	F

None of the past 12 men's champions had won the Australian Open in the same year.  Assuming this same pattern holds, this eliminates the 2012 Australian Open Champion, Novak Djokovic (who we had already eliminated). Our updated men's list looks like:

1. Novak Djokovic (#1 seed but not defending champ, AO Winner)
2. Roger Federer
3. Rafael Nadal
4. Andy Murray
5. Jo-Wilfried Tsonga

Each of the past 12 women's champions either did not play (DNP, ocurred 3 times in the past 10 years) or reached at least the 4th round if they did play.  This leaves us with the following women:

1. Victoria Azarenka (#1 seed but not defending champ)
2. Maria Sharapova
3. Agnieszka Radwanska
4. Petra Kvitova
5. Samantha Stosur (1R)
6. Serena Williams
7. Marion Bartoli (3R)
8. Carolina Wozniacki
9. Li Na
10. Vera Zvonareva (3R)

The next post will look at how important previously winning a Grand Slam or winning a clay court warm-up tournament is.