Statistics, Sports and School (SSS): “The Choke”

It’s time for the designing process for “SSS” to begin.

I’ve been both excited and scared to start constructing a course in “sports research”  since it got approved about six months ago.  Since then, I’ve been attending conferences on undergraduate research, teaching statistical reasoning through activities, learning a lot about the sports analytics / sports medicine industry, and promoting the course to colleagues and sports professionals.  Now the grunt work begins.

Big Task 1: Select tasks to achieve the following goals for students:
1. Feel more comfortable and rewarded for asking questions, wondering, and suspecting without “knowing”  or “telling,”
2. Recognize the power of designing probability  simulations to to answer some questions in sports.
3. Better understand how to design a plan to answer a question analytically.

My main resource for the statistics part of the course will be Josh Tabor’s and Chris Franklin’s wonderful book, Statistical Reasoning in Sports.  The book prefaces each new statistical technique with a very plausible question a student could ask. Here’s their first question:  Did LeBron James choke in the 2008 NBA Playoffs?  In other words, did LeBron James short-term performance in the 2008 NBA playoffs provide convincing evidence that his ability to make three pointers actually went down in the playoffs?

Here are the facts:
1.  In the regular season,  former NBA Cleveland Cavalier LeBron James made 113 of 359 three pointers. This gives a good estimate of his ability to make three pointers during the regular season: about 31.5% .

2.  In the playoffs, his three-pointer performance was worse. He made only 18 of 70 three-point shots (25.7% made). Not great for LeBron.

What caused it?  two possible explanations:

1. LeBron’s ability to shoot 3s in the playoffs be the same as it was in the regular season, and this weaker performance fell within the plausible range of “bad luck” performances?
2. LeBron’s ability to shoot 3s was indeed lower (for some reason: not necessarily a lack of mental resilience). His weaker than average performance shows this.

Note: The careful and intentional use of ability and performance is being taken from Josh Tabor’s, who thoughtfully followed the example of stats education pioneer Jim Albert. 

Can we determine a way to rule out explanation #1?  

(PS – after LeBron’s performance in the 2013 NBA playoffs, this question seems positively disrespectful.  But more on that later).

A few questions I would prepare before investigating: 
1.  Suppose LeBron’s ability hasn’t changed. How many three pointers  out of 70 would we expect him to make? (Answer:  (0.315)(70) = about 22 out of 70.
2.  Would he get 22 out of 70 every time? Why not?
3. How about 21? 20? 19? 18? What’s “too low to get” by chance?

PS – This final  question is a surprisingly tough one for some students of statistical reasoning: Once they acknowledge that the average won’t necessarily happen, they then sometimes default to “anything can, and will happen.”  The binary yes-no logic form mathematics  is a bit too simplistic  to be useful in this context.  The interesting stuff is happening between these two extremes, the in between: What do your insides tell you?  What seems “too far off” in your own gut? 

The plan:  Run a simulation of 70 three-pointers, assuming LeBron’s ability was the same is in the regular season (His three-point percentage is 31.5%).  The Statistics Program Fathom is a wonderful tool for executing a simulation, but so are note cards, random number generators, spinners, and a variety of other low-tech, inexpensive tools.

If you don’t know about KeyPress’s statistics learning program called Fathom, then climb out from under your rock and get a copy.

Back to the task: Suppose I wanted to assume LeBron’s three pointer ability didn’t go down in the playoffs.  How could I see what possible performances (of 70 free throws) are plausible by sheer luck?

Questions I would prepare:  
1. How would I create a simulation of 70 free throw attempts?  What tools would I use:  Dice?  Coins?  Random numbers?  What “program,”  or “recipe”  would I need to follow in order to fairly simulate LeBron shooting 70 free throws?  Let’s make one up.
2. What would we look for at the end of the simulation?
3.  So how would we decide whether Lebron’s performance (18 out of 70)  is a “choke-worthy” performance?

lebron threes

Results of a simulation of 70 three pointers, assuming LeBron was as good at shooting 3s in the 2008 playoffs as he was in the 2008 regular season.

After the simulation was over,  I’d love for them to raise critical questions about the analysis. Some that came to my mind:

1.  Is it fair to assume that players should be performing in the playoffs as they did in the regular season? Aren’t playoff opponents, by design, better than the average team the Cavaliers played against in the regular season?
2.  Is it reasonable to assume that Lebron’s role on the team (whether he shoots 3s, plays closer to the boards, etc) is the same was it was during the regular season?

2. Does this lead to other questions/ claims to analyze? 

So that would be an in-class task.  The hope/ goal for my students is to find a similar question/wonder they could ask where they could run a similar simulation, but:

1. they come up with the idea in their own.
2. It benefits themselves, their curiosity, or the school in some way.

That’s the first day of work.  Of course this led me to about a thousand other pathways to pursue. I hope I can maintain my focus and stay on my “road map”  for the rest of the summer.   More about that road map very soon.

About roughlynormal

I have been a math/statistics teacher for 25 years. I currently teach at an independent school in southern California. I also coach teaching fellows for Math for America - Los Angeles chapter. I love my career, my colleagues, and my friends & family.
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