Possible Solutions to 2015 AP Statistics Exam questions, draft 1

Hi Colleagues! 


Well, here’s my first draft of possible solutions. 

You can access the questions here at AP Central.

Disclaimer: I construct these as a service for both students and teachers to start discussions. There is nothing “official” about these solutions. I certainly can’t even guarantee that they are correct. They probably have typos and errors. If you catch some, let me know! But if they generate discussion and help others, then I’ve succeeded.

The link to my solutions is here: Possible Solutions 2015 AP FRQ

Thoughts about the questions:

#1. Part a was straightforward. Part b  will require students to construct a pretty sophisticated criterion for preferring either company. It will be interesting to see how “convincing” students’ arguments need to be.

#2. A great, simple question that will require precise communication of how confidence intervals work.  I like how students must explain  why a lack of evidence for  claim does not imply evidence that its negation is true.

#3.  This should, hopefully, be a slam dunk for kids. This is a good indicator of whether your students are understanding the formulas you use, or simply mimicking things that were done in previous problems.

#4. A straight up inference test for the difference in two population proportions.  I anticipate students not being specific enough in stating that volunteers were randomly assigned to treatments. 

#5.  Again a great litmus test to see if students understand the tools they use. This seems almost too simple for  #5.

#6. I think that this was a great, challenging problem. It’s a great problem to use in teaching sampling distributions in the future. It requires students to consider the distribution of a population, the distribution from a sample from that population, and  the distribution of the sampling distribution of the sample means.  I especially like how the oft-ignored requirement of simple random sampling comes to the surface here.  I worry that too many students will overlook the questions posed and write something that is simplistic and irrelevant.

Posted in Uncategorized | 11 Comments

2015 AP Statistics questions released! Stay Tuned.

Hi colleagues,  The questions were just released. You can get them here!

Upon first glance, many of them seem very simple, but I can see that students will need a high level or precision in their language to give convincing, thorough responses.  #6 was accessible, but takes a lot of thinking about what you are seeing. I can see why some students might think it was “really easy.”  I worry that they may have read those questions too superficially.   But if the questions force students to read, write and think, it’s a good thing.  See you soon!

Posted in Uncategorized | Leave a comment

Stay Tuned: My attempts at 2015 AP Statistics Free Response solutions coming soon!

Hi Colleagues,

It’s time to dust off this blog!  It’s been a VERY busy year, and most of my work / correspondence has happened off-site.  But I am looking forward to reviving my blog this summer.

To get me off to a good start, I will continue my annual tradition. I will “walk the plank” and submit a set of responses to the free response section of the 2015 AP Statistics Test.

You can see what I did in previous years: here in 2014  and here in 2013 .

A few comments:

1.  I am NOT, in any way, claiming that these solutions are exemplary. or “what the college board expects.”  I am a teacher of AP Statistcs since 1997, and these are my version of “good ” solutions.

2.  My solutions will go up about 24 hours AFTER the College board officially releases the Free Respsonse questions to the public at AP Central’s Statistics Exam Page. 

3. Please ask questions, critique, make corrections, or suggest different, better, or more interesting responses. This is intended to start dialogue.

See you soon!

Posted in Uncategorized | 4 Comments

2014 FR questions, AP Statsitics Exam. MY REVISED first attempt at solutions.

Hi all: I just worked through the 2014 AP Statistics Free response questions, which are publicly available here. 

My attempts at solutions can be found here .  

Possible Free response solutions 2014 frq,  Second Draft!

Those were my first attempt.  Thanks to Corey Andreasen, Pat Humphrey and others who caught some errors!

Again, these are simply attempts at solutions, and they probably still have errors… so tear them apart! I invite corrections, critiques, questions, and commentary.

I look forward to the dialogue.

If they provide a starting point for further dialogue about the questions, then I have succeeded.

UPDATE: Thanks to Corey Andreasen for his on-point comments.

I agree with his critiques, but I also want to think more about 4a:  Is there more to a complete solution than simply “means are pulled up by unusually high incomes, and medians aren’t?”

Posted in Uncategorized | Tagged | 25 Comments

Stay Tuned: attempts at solutions, 2014 AP Statistics Free Response coming soon !

Hi all!

this Friday, about 180,000 students will take the AP Statistics exam.  Typically,  the College Board releases Free Response questions to the public 48 hours after the administration of the exam.  As soon as I can access the questions and work through the problems, I will post a first attempt at solutions for people to read, discuss, and critique.

Best of luck to your students, if you’re an AP Stats teacher!  Best of luck if you are taking the exam!

Posted in Uncategorized | Tagged , | 5 Comments

SSAC 14: What does it take to call a strike?

Difference between P(strike|S) and P(Strike|not S) for four different counts in baseball

Difference between P(strike|S) and P(Strike|not S) for four different counts in baseball

Have you ever thought that umpires are a bit too willing to call strikes when the count is 3-0?  Or, perhaps, you’ve noticed that umpires rarely call strikes when the count is 0-2?  In this very clear paper,  Etan Green and David Daniels  from Stanford University use Pitch f/x data to answer questions about how the  count (number of balls and strikes against a batter) help predict the chances that an umpire calls a ball/strike on the next pitch.

I was impressed with how the researchers wrote and presented so that everybody can understand their work.  This paper is easy to understand and share with students in high-school, in my opinion.  It simply takes a baseline understanding of the rules of baseball, basic probability ideas, and reading three-dimensional graphs.   

How are umpires biased?

  •  3 balls:   P(called strike) rises by about 10 per
    centage points above what happens overall.
  • 2 strikes:  P (called strike)  reduces by as much as 20 percentage points below what happens overall.
  • Last pitch called strike:  P (strike) reduced by  as much as 15 percentage points.

Is this isolated to a subset of umpires?  

Let’s look at the 50% contour line of calling

a strike overall, When looking at pitches after 2 strikes,  this contour contracts.  The area between these contours is called a “band of reversal:”  We found  a lack of bias emerging for pitches called after a ball.  But the ENTIRE distribution of strike thresholds is above zero for pitches after two strikes.  IN short, EVERY UMPIRE IS BIASED.


Every umpire shows bias for certain ball counts.

Posted in Uncategorized | Tagged , , , , , | Leave a comment

SSAc 2014: Baseball Analytics: The Next Frontier

I chose to attend this because it featured Nate Silver.  I am anxiously awaiting the new fivethiryeight.com, and hoped that some spoilers/ previews would leak out form the conversation: No dice.

This was one of the only sports panels I attended this year: not enough interesting information gets shared. It’s interesting to see high-profile people on the same stage together. It’s also cool to hear top players answer the same question from different viewpoints. But the content is rich on sound bytes and light on substance for my taste.

Here’s my rough account:

Moderator:   Brian Kenny, ESPN
Vince Gennaro, President, SABR
Jeff Luhnow, GM, Houston Astros
Rob Nyer, FoxSports.com
Bill Squadron, Bloomberg Sports,
Nate Silver, Statistician, Author, Founder of  fivethiryeight.com,

BK:  Vince, There seems to be a disconnect in the amount of info out there, and how much gets transferred into the field. Where are we?

VG;  There’s work to do.  Translating to the field has to do with the lack of organizational alignment, that is, the analysts are not considering all of the stakeholders. One opportunity:  vertical alignment for a team, getting all the parts working, is key.

BS:  Every club has embraced to some degree.  Consider the Bloomberg System, some are big on using it, others pieces, but a long way to go. Many are simply using Lotus Notes or Excel spreadsheets to gat answers.

BK:  It’s football lagging, according to you. Where is baseball?

NS:  There’s new types of data… so “who’s ahead” is a moving target.  I am more of an optimist: Pitch f/x data, visual tracking, etc. There’s  lots there to use and grow from.

RN:  The Pirates are a good example: They saved a lot of runs b/c of buy-in from coaching staff and maganers. The coaches and managers had to be convinced. That’s one example of what we’re talking about. People don’t realize that what we are sharing makes sense. It’s a matter of time when almost all of the teams are using analytics more.

JL:  Baseball is in great shape.  The analysts don’t recognize all the factors going into decisions on the field.  Even a well aligned club, in the best of situations runs into implementation challenges. sometimes the outcome is not what you want when the outcome is right. But you’re not playing 10,000 times. You’re dealing with humans. Sometimes analysts don’t consider all the factors that truly matter. It’s a challenge, but we’ve progressed.  TLV DATA, radar data, etc. There’s so much out there. It shows what we don’t know…

BK: Jeff, has your organizational structure changed?

JL: No;  we have a well intergrated structure. Our five analysts are in the clubhouse all the time.

BK:  what’s a competitive advantage out there to grab onto?

RN:  The batters hadn’t tried to take advantage of defensive shifting.  The game has become a power game (more HRs). On the pitching side for sure.  Can the hitters adjust? Can hitters do anything?  Maybe they could make adjustments, bunt against the defensive shifts?

BS:  If so, it’s about focus. Not a silver bullet.  We have more data coming in (defensive, biometric, etc.). You need a way to filter out the noise. If you don’t you’ll miss opportunities. I would say that really the advantages come form having the right focus and the people having fast efficient processes.

NS: I think that player health from game to game is an opportunity.  A healthy team is probably a wild card contender on that basis alone.  The reward for a healthy team is very high.  The notion of positional versatility is underdeveloped.  More ability to shift around  when people get hurt. The Indians and the A’s are great at this.

VG: Nate is right: health is the next frontier.  We know so little about helping players perform at maximum capacity.  Not just injury prevention, but simple stuff like sleep and nutrition. How do we encourage players to get the rest they need while traveling?  Also, how do you take this and turn in into teaching tools for 16 year old in the Dominican Republic?  We evaluate to rank and forecast who will do well, but how do we turn a person around?   We’re seeing an increasing interest in data collection at all levels.  We’re trying to get into our system data from all levels, to help find potential.

Big Picture:  What’s next?

JL:   10 years ago, we had only 2% of the amount of data we have today.  Radar, video, hundreds of thousands of pitches thrown a year, 15 measures on each pitch. It’s so critical to ask the right strategic questions.

BS:  Best tools are always important.  With any new technology, it takes time to develop. Good decisions about structuring organization. More info coming out of tracking systems to analyze a player’s defensive skills.  So two big ares: HEALTH, and DEFENSE metrics.

BK:  Jeff: The Cardinals have a roster with a bunch of line-drive hitters…  not an accident?  Is that where we’re at?

BS:  We’re not putting run expectancies on vectors of hits. Player evaluation components are pretty advanced. Doppler Radar to measure the spin axis of a ball.  Going into DivI and Minors probably pitch f/x in every NCAA-D1 place in the country.

JL  We can now develop an individual park factor for every player in baseball.  The way they play can be customized.

NS:  Pitching has caught up to hitting. As an observer, it seems now that the clubs have pulled pretty far ahead and recruited lots of the stat geeks. I think that outsiders still needed to help all teams grow and improve.

RN:  Reaction data to balls now has objective measurements. That’s new.  There’s still a long way to go.

BK:  Is it now very proprietary?  Who is able to use this and not tell anyone?

JL:  you bet. we want a proprietary edge, but we rely on the outsiders that write/ analyze for all 30 clubs.  Some club not so much because hiring them and integrating the analysts in takes time and work.

BS:  You can build an entire system within, but the moving targets  – best to work with those who do this professionally. 27 of 30 MLB teams use our system.

BK:  Red Sox:  trying to find guys with good chemistry.

??: no clear correlation between being nice and being a good teammate.  Porter’s synergistic chemistry lab. “you know it when you see it.”  Creating it is hard.  Leaders must evolve , followers must follow.  Leadership is organic. To engineer chemistry? That’s difficult.

JL : It’s palpable and tangible and understanding it:  It’s a huge thing to study.

RN:  I remember how volatile chemistry is: so dependent on winning and losing.  The A’s and Yankees were constantly fighting in the clubhouse, but winning pennants. Putting a finger on it is tough. “sure it’s important.” But dying to pick guys based on that?  The Red Sox has great chemistry, but will they win 97 games?

BS:  Yep, important and difficult to put a finger on.  If we create a workflow to finish tasks more quickly,  that’s a good thing for chemistry.

NS:  Sure yeah.  I think less in baseball than in football, but hard to measure.  a randomized controlled trial?  But chemistry can also excuse some shitty decisions, poor ways to analyze the value of a player in my view.

BK:  A rise in 3-2 outcomes. More strikeouts. Boring. A problem?

RN:  SO’s exciting when a star is on the plate. For a more humdrum starter, I’m not sure it’s interesting.  Trying to separate my aesthetic reaction. The variety of experiences is what makes it outcomes. But runs and walk not changing. SO’s are rising steadily. Ruled would need to be changed, this means players need to be consulted – they are conservative.  There is a feeling that the pace should quicken.

JL:   Pitching today is extraordinary.  5-6 guys throwing 95 MPH.  People love pitchers’ duels.

BS:  Something about place of play:  I do think that fans are digging deeper into the game, getting into the data/ analytics side more. we’re able to project in real time  how P(on-base) in THIS situation is changing ptch by pitch.  I’d hesitate to change some of those core things. More to bring out via visualization.  Rule change,s not so much.

NS;  Yeah-  tings revert to the mean.  Lots of power pitching. Maybe some hitters can exploit this?  Innovation can probably lead to a change.  It’s a tangibly duller pace of play than, say, football.

BK:  You are incentivized to moves that lead to the 3-2 outcome.

JL:  There will be someone who breaks out on the hitting side with a very low SO rate.

BK: Player projections:  Where are we?  Nate?

NS:  PECOTA, 11 years ago. Now, I’d start from scratch with all the new data and enough years to see what is predictive. Now we can more directly measure skills, not proxies of skills.  A half year to innovate well to use everything we have now.  Projections are improving, but smart quants getting hired by teams.  Not as much on the public side.

BS:  We see the fantasy side increase – our predictive formulas are great.  It’s a lot of fun, the fun part of what we do.

VG:  More focus on batted ball performance,  incorporating the ball park.

RN: I haven’t seen anyone to consistently beat the over/unders.

JL:  We’re trying to win games. We have a great projection system.  They are giving us really valuable info and blending it in with out projection system to improve the system.  Using the scouts helps, The fundamentals there, but with the new data, a whole new ballgame.

Posted in Uncategorized | Tagged , , , | Leave a comment