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.

Analyzing Pro Athletes' Physiological Dashboard

I recently came across an article about the "sports science" changes that Chip Kelly has implemented since becoming head coach of the Philadelphia Eagles.  Basically, the Eagles spent more than $1 million investing in new technology that measures physiological details (heart rate, amount of time spent running during practice, 3d views of how players are lifting weights, etc) in the hopes of creating a "physiological dashboard" for each player.  They want to monitor the performance of each player during practice to increase training efficiency, such as ending practice early for players reaching their endurance limits or ensuring that players receive the correct amount of hydration based on what was lost during practice.  A large portion of the article is dedicated to describing the Eagles sports-science coordinator, who has previously served as a strength coach and nutritionist for colleges and the Navy SEALs.

Here are some interesting quotes:

• "The result is a data driven approach to training"
• "Players can log into their personal computers to check their own fitness profiles"
• "Last season Catapult helped on of its NFL clients compare practice data ... in weeks when the team won compared to those when it lost.  A trend emerged: during Thursday practices before losses, offensive skill players were running a lot but not very quickly."

OK, so NFL teams are beginning to collect all of this data about their players.  But who exactly is mining all of this data to find useful information?  I can't believe that its the sports-science coordinator (he doesn't have a statistics degree).  Plus, who can actually monitor and interpret all of this data in real-time (i.e. during practice)?  It seems that Catapult, an IT consulting company focused on interpreting data, is doing some work after the season is over, but do any of these teams have the capacity to perform analysis in-house?  Here are a few things to think about:

1. I'm sure most of the companies selling the equipment have guidelines or suggestions for how to interpret the data.  So maybe a bell goes off when a player's heart rate gets too high.  But how accurate are these baselines, especially when the same guidelines are applied to 180lb running backs and 350lb linemen?
2. What is the goal of collecting all of this data?  Making real-time decisions about players' health during practice?  Drawing team-wide conclusions about what does/doesn't work at the end of the season?  These are 2 very different questions that could influence the most effective way to collect data.
3. How much are teams investing into analyzing this data (either in-house or through ouside companies)?  For current genomic sequencing projects, more money is spent on the analysis than the sequencing experiment itself.  So are the Eagles planning to spend an additional $1 million on interpreting all of this data?  Or will this data just go to waste?

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)?

NFL Pop Quiz

As a new resident of St. Louis, I've enjoyed having a local NFL team to cheer for (although maybe not for much longer if they move to LA).  Rookie punter Greg Zuerlein had some incredible special plays this year and completed 3 of 3 pass attempts for 42 yards and 1 touchdown.  Can you guess which high-profile (and highly paid) quarterback threw for fewer yards?  Find out here.

Why the NFL is supporting the wrong cancer research

Unless you live at the bottom of the ocean, you have probably noticed that the NFL is showing support for breast cancer research by having the players and officials wear pink accessories (sounds a little girly when I say it like that).  As a cancer researcher, I think its great that the league with the most exposure in the USA is joining the American Cancer Society in its fight to end cancer.  However, the NFL is making a huge mistake by choosing to support breast cancer research over prostate cancer.  Here are a few statistics from the American Cancer Society that may surprise most people:

1. Approximately 1 out of every 6 men will develop prostate cancer in his lifetime.  In contrast, 1 out of every 8 women and less than 1 out of every 1,000 men will develop breast cancer in her/his lifetime.  

2. There will be an estimated 241,740 patients diagnosed with prostate cancer in 2012, compred to 229,060 new cases of breast cancer (<1% of those cases ocuring in males).

3. Treatments are not as effective for breast cancer as prostate cancer, and this is reflected in the 5 year survival rates: 99% of prostate cancer patients will survive 5 years, compared to only 89% for breast cancer.  However, until the 1990s, males with prostate cancer had a higher 5-year mortality rate than females with breast cancer.

4. It is estimated that 39,510 women and 410 men will die of breast cancer in 2012.  An estimated 28,170 men will die of prostate cancer this year.  That is, over 65 times more men will die of prostate cancer than breast cancer.

5. Prostate cancer is the second most deadly cancer type for males, behind only lung cancer.

6. African American males are 1.6 times more likely to develop prostate cancer and 2.5 times more likely to die from it than white males.   

Do these numbers surprise you?  While breast cancer is a more deadly disease than prostate cancer, all of the support for breast cancer month and "wearing pink" makes it seem like the disparity between the two diseases is much larger.  Considering that there is not a single female player in the NFL, the league is going out of its way to promote research for a cancer that its players are 150 times less likely to develop than prostate cancer (supporting evidence: allowing players to wear pink shoes and towels but fining them $5,000 for wearing a red undershirt).  Additionally, with the NFL consisting of a large proportion of African Americans males, you would think it would support research for a disease with significant racial disparities.

If you happen to meet Roger Goodell on the street and point these facts out to him, he will mention that the NFL is committed to promoting prostate health, and he is technically correct. However, I don't see the NFL encouraging players to wear blue during September.  A bit hypocritical, don't you think?