Political Calculations
Unexpectedly Intriguing!
October 2, 2015

Normally, we would expect to see the advocacy of the multitasking use of ordinary power tools for the purpose of food preparation put forward such people as Alton Brown. Or perhaps Red Green.

But YouTube's Handimania makes a really good case for the use of hand drills to peel fruit.

HT: Core77, where Rain Noe (a.k.a. Hipstomp) reflects on what is perhaps the most useful way to employ a spade bit:

Yes, I know it's totally silly. But I have to admit that if my girlfriend left me alone in the kitchen after one of her annual apple-picking trips, she'd probably return to find an enormous mess (and me holding a drill with a dead battery). And it might be worth getting yelled at for.

It totally would!

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October 1, 2015

In 2009, after five years of extraordinary growth in its enrollment, the Apollo Education Group (NASDAQ: APOL), the parent company of the University of Phoenix, recognized that the days of booming enrollment in the Associate's degree programs it had launched in September 2004 were about to reverse, in part because the Great Recession, which had helped boost the school's enrollment, was ending.

At the same time, the leadership of the private educational institution realized that far fewer students graduating from its Associate's degree programs were making the transition to the University of Phoenix's Batchelor's degree programs than they had been counting upon. Worse, a much higher than expected number of students enrolled in its Associate's degree programs were failing to complete the program and were dropping out because they were not able to pass its required classes in Algebra.

To address its situation, the Apollo Education Group adopted a two-part strategy. It would:

  1. Restructure its Associate's degree programs to be more closely integrated with its University of Phoenix division, which would help facilitate the transfer of students graduating from the Axia College division it established to launch its Associate's programs to the University of Phoenix' Batchelor's programs.
  2. Degrade its academic standards for passing its Associate's degree program's Algebra classes, which would enable a higher percentage of students enrolled in the program to pass.

The chart below, in which we've shown the enrollment figures for the University of Phoenix' Batchelor's and Associate's degree programs that we obtained from the Apollo Education Group's SEC filings, shows how that strategy played out.

Apollo Group (University of Phoenix and Associated Institutions) Total Quarterly Enrollment by Degree Type, 2004Q1-2015Q1

In this chart, we see that the changes that the Apollo Education Group implemented in September 2009 succeeded on both counts. We first see that enrollment levels in the University of Phoenix' Batchelor degree programs increased in the year after its Associate's degree programs were integrated into the University of Phoenix division.

At the same time, we observe that enrollment levels in the University of Phoenix' Associate's degree programs, instead of beginning to fall as the U.S. economy exited from the worst part of the Great Recession, were able to be sustained near their peak levels for a year as the degradation of the school's academic standards allowed more students to remain in the program without dropping out.

Unfortunately for the Apollo Education Group and its investors, those changes were not sufficient to permanently sustain the enrollment levels of the University of Phoenix' Associate's degree programs, whose enrollment began to plummet shortly after an intense marketing effort during 2010 led enrollment to peak at its all time high in September 2010. Shortly afterward, in response to increasing criticism, the Apollo Education Group implemented reforms in its recruiting practices, which limited its ability to acquire and retain new students.

As for how the University of Phoenix degraded its academic standards, we have obtained copies of four documents that describe changes in student evaluation practices that would enable students to pass its Algebra classes with lower levels of proficiency.

PHD Comics - Grade Inflation - http://www.phdcomics.com/comics/archive/phd012014s.gif

That's possible because a student's performance in a math class, unlike nearly all other academic disciplines, may be fully evaluated according to objective standards, rather than by subjective ones, where a student's grade is based in part upon an instructor's opinion of how well they've learned the subject. In math classes, like Algebra, how well a student has learned the material covered in the class may be directly assessed by counting the number of assigned math problems that they correctly solve, where correct solutions are obtained by a rigorous application of logic that is fully independent of any opinions the instructor might have.

In a traditional math class, 100% of a student's level of proficiency is directly determined by the percentage of assigned math problems that they correctly solve. A student's grade for a class is then determined by that percentage, where a student correctly solving 94% or more problems might earn a letter grade of A, between 90% and 94% would earn an A-, and so on down the line, where a student correctly solving fewer than 60% of all the problems assigned during the class would fail, as they would not have demonstrated sufficient proficiency in solving math problems to be allowed to advance.

Having established that basis for evaluating student performance, let's look at the University of Phoenix' academic standards, as described in the following documents we obtained, first describing the academic standards that applied in classes that began in the nine months prior to September 2009:

  • Axia College of University of Phoenix MAT117 Algebra 1B Course Syllabus, Version 5, 15 December 2007 (PDF Document)
  • University of Phoenix Faculty Handbook 2007 (PDF Document)

In these two documents, we find that, at most, 90% of a student's grade is based upon an objective assessment of their proficiency in correctly solving assigned math problems, with 10% begin determined by the instructor's subjective assessment of the students' responses to Discussion Questions and their overall level of Participation in online discussions during the class. We further find that faculty members are not permitted to alter the percentage weighting of these assignments in determining a student's overall letter grade for the class.

And now in classes that began in September 2009 and afterward:

  • University of Phoenix Axia College MAT117 Algebra 1B Course Syllabus, Version 6, 2009 (PDF Document)
  • University of Phoenix Faculty Handbook 2009-2010 (PDF Document)

In these two documents, we find that although there has been no change at all in the materials or assignments for its MAT117 Algebra 1B class, faculty members are now able to alter the percentage weightings of assignments within their classes, with the official guidance that they should set a weighting of 20% for their subjective assessment of student responses to Discussion Questions and their overall level of Participation in online discussions during the class. This change means that, at most, 80% of a student's grade is now based upon the objective assessment of their proficiency in correctly solving assigned math problems.

The chart below reveals how that degradation in academic standards would affect a student's grade, as compared to how their performance would be evaluated in both a traditional math class and also the University of Phoenix' previous academic standards.

Degradation of Academic Standards at the University of Phoenix, Before and After September 2009, Versus Traditional Math Class

In the chart above, we focused on the key major thresholds between the letter grade divisions, where in a traditional math class, correctly solving 90% of all assigned problems would result in a student earning a letter grade of A-, 80% for a B-, 70% for a C- and 60% for a D-.

We see that prior to September 2009, a student earning these same letter grades would only need to correctly solve 80.1% of all assigned math problems to earn an A-, 71.2% for a B-, 62.3% for a C- and 53.4% for a D-, provided they earned the maximum possible scores for their other, subjectively graded activities. Another way to describe the University of Phoenix' pre-September 2009 grading system for its math classes is that a letter grade earned at the University of Phoenix is the equivalent of one lower letter grade at universities with higher academic standards.

But in September 2009 and afterward, we see that a given letter grade in a University of Phoenix math class is even more greatly diminished with respect to its equivalent letter grade in a traditional math class. Now, to earn an A-, a student who maximizes their scores in other graded activities can get an A- on their transcript with only having the demonstrate the same proficiency in solving math problems that a student earning a C- in a traditional math class would.

The same degradation carries through the entire grading scale, until reaching the bottom, where a student who failed to correctly solve at least half of the problems they were assigned could obtain a passing letter grade of D-, where a similar academic performance at both a traditional math class and at the University of Phoenix prior to September 2009 would be considered a failing score, where the student would not be permitted to progress to more advanced classes.

Consequently, the University of Phoenix didn't just degrade its academic standards, it also diminished the value of the degrees earned by its students prior to September 2009, as the institution never so much as placed an asterisk on the diplomas that it subsequently issued. That, in turn, is something that might have significant class action liability risks for the Apollo Education Group, not just on behalf of students who earned their diplomas from the institution before it degraded its academic standards in September 2009, but also for those earning the institution's academically degraded diplomas thereafter, as they are unable to demonstrate that they achieved the same level of academic proficiency on their transcripts that all previous graduates with the same earned letter grades did.

The Apollo Education Group will be releasing their fourth quarter results next month. It occurs to us that a sharp analyst participating in the related earnings call might wish to raise this particular issue with the company's current management.

Previously on Political Calculations

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September 30, 2015

In 2013, poor Americans received the equivalent of $412 billion worth of welfare benefits from the U.S. government, which it raised through a combination of taxes, fees and borrowing. The chart below details how that breaks down among the federal government's various welfare programs.

Major Federal Welfare Programs, Fiscal Year 2013

To visualize that data, we experimented with the tools available at IBM's Watson Analytics site, the successor to our old favorite ManyEyes. Here's the treemap we generated:

U.S. Welfare Spending by Program Treemap, FY 2013

If that $412 billion were equally divided among the 86.6 million Americans whose incomes are equal to or less than 138% of the official federal poverty level, they would each receive $4,758.

If we just focus on the top four welfare programs, Medicaid, Supplemental Nutrition Assistance Program (SNAP, or perhaps best known as "food stamps"), Temporary Aid for Needy Families (TANF) and Section 8 Housing Choice Vouchers, a national average of $4,018 is spent to benefit poor Americans, representing 84% of all major welfare program spending.

Data Source

Furchtgott-Roth, Diana. Welfare in America, 1998-2013. Figure 1. Major Federal Welfare Programs, Fiscal Year 2013. Manhattan Institute: Economic Policies for the 21st Century, e21 Issue Brief, No. 3. [PDF Document]. January 2015.


September 29, 2015

In several major U.S. cities, police are beginning to use math originally developed to predict earthquakes to fight crime. Or more specifically, the kinds of crime that occur in either series or sprees that tends to be concentrated within a defined region, such as burglaries or gang-related violence.

If you live in Los Angeles there are two things you might feel particularly worried about: earthquakes and crime. It's nice to know, then, that mathematics can help to keep you safe from both. A software system called PredPol, that has been developed by the mathematician George Mohler, the anthropologist Jeff Brantingham, and others, is now being rolled out across multiple jurisdictions of the Los Angeles Police Department and in other cities too. Officers on the ground use it every day.

PredPol stands for "predictive policing". It works by calculating the probability that crimes will be committed in a particular area on a particular day, based on real-time data from the previous couple of days. Police officers are then given prediction maps telling them where the probability is high, so they can put in place extra patrols and hopefully prevent at least some of those crimes from happening.

The initial results of using the math-based approach to directing police activity would appear to have some promise. After being introduced in the Los Angeles Police Department's Foothill Division in 2011, after having seen its violent crime rates rise significantly in 2010 as the city reduced its budget for policing the area, the incidence of crimes fell by 13% in the first four months after the division implemented the PredPol software, while crime elsewhere in the city rose by 0.4%. That reduction came as the city further reduced its policing budget in 2011.

More recently, the LAPD Foothill Division saw a 20% reduction in the level of predicted crimes in the year from January 2013 to January 2014. According to PredPol's marketing, other cities where the predictive crime software has been introduced have reported similar experiences.

+Plus Magazine's Marianne Freiberger describes how the math behind the software works.

To get a feel for how this works, let's concentrate on something that's rife in LA and other big cities too: gang crime. Fierce battles over territory are central to gang violence, and whatever one gang does to another, retaliation is sure to follow. That latter point is what makes gang violence similar to earthquakes: acts of violence come with follow-ups, just as earthquakes come with aftershocks.

Earthquakes can be described mathematically as self-exciting processes. They are events that happen over time as a result of all sorts of complex factors we don’t really understand. So we might as well treat them as random processes. What we do know, however, is that once an earthquake has happened, the chance of another one (an aftershock) goes up, at least in the immediate future. That’s the self-exciting part.

There’s a mathematical technique for dealing with self-exciting sequences of events, called a Hawkes process, which you can also apply to the rivalry between two gangs. The idea is to treat acts of violence between the gangs (it doesn’t matter which way around) as a sequence of events in time. What you are after is a rate function r(t), which essentially measures the chance that a crime happens at time t, with that chance depending on what happened previously (because the process is self-exciting). We usually think of a rate as the number of events over a given time interval, for example the number of crimes we expect to happen per day. In this case, however, the time interval is made infinitesimally small. So you can think of the rate function r(t) as the instantaneous rate at which we expect crimes to happen at time t.

The idea now is to express the rate function as a sum: the first term of the sum is the background rate of crime: that’s the rate at which unprovoked attacks between the two gangs happen, ignoring any retaliations. The other terms in the sum correspond to the amount by which any previous violation between them raises that background rate. These reflect the self-exciting part (the retaliations). The longer ago a particular attack happened, the smaller its contribution to the rate function at time t....

Once you have the parameters, you can use the rate function to simulate crimes between two gangs as sequences of events in time. The crimes happen randomly by chance, but that chance isn’t the same for all times t, rather it’s given by the rate function. By seeing how the simulated patterns of crimes compare to real data you can assess how well your model does at describing reality (there are standard statistical methods for making that comparison). And once you’re happy the model does reasonably well, you can use it to predict what will happen in the real world and, hopefully, intervene.

The same math works for property crimes like burglary as well, where criminal offenders will often case a defined region before their crime sprees to identify their targets of opportunity before working through them in a relatively short period of time.

On a final cautionary note, we can't help but think in reading through PredPol's success stories of when the software is introduced in some areas of a city but not others, which see crime fall where PredPol is directing police activity but also see general crime rates rise elsewhere, that the use of the software might in fact be partially responsible for those increases. Much like squeezing a water balloon in one spot causes it to expand everywhere else, as those seeking to conduct criminal activities moved away from where the police presence has been concentrated. In that sense, what the results suggest is that simply providing an effective police presence provides a deterrent to crime, which is something that doesn't require an investment in software.

But that's not the whole story. It is also important to recognize the budgetary environment in the city of Los Angeles during the period when the software was being introduced, where the money to fund policing activities across the whole city was being reduced. That crime in the area where resources were concentrated was reduced while only expanding rather modestly everywhere else suggests that the predictive crime software does provide a real benefit in making more efficient use of the city police department's limited resources.

That's a winning story in anybody's anti-crime playbook.


Freiberger, Marie. Crimes and earthquakes. +Plus Magazine. [Online Article]. 11 August 2015. Accessed 29 August 2015.

International Association of Crime Analysts. (2011). Crime pattern definitions for tactical analysis (White Paper 2011-01). Overland Park, KS. [PDF Document].

McNeely, Jim. Your Home Security - Never Before Revealed - How Burglars Case Homes. [Online Article]. 13 July 2011. Accessed 29 August 2015.

National Science Foundation: UC Mathematical and Simulation Modeling of Crime Project - https://www.nsf.gov/news/news_images.jsp?cntn_id=116357&org=NSF

Image Credit: National Science Foundation: UC Mathematical and Simulation Modeling of Crime Project.

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September 28, 2015

For the S&P 500, the week ending 25 September 2015 went pretty much as well expected, as the index' value remained well within the range we indicated it most likely be a week ago.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot on 25 September 2015

Really, the most interesting day of the week was Friday, 25 September 2015, when stock prices opened the day up thanks to Janet Yellen's speech the evening before, in which she indicated that the Fed would seek to raise interest rates before the end of 2015-Q4.

But then, something overrode that expectation after 2:08 PM that day, and the S&P actually closed lower for the fourth consecutive day, as whatever was plaguing health insurers and pharmaceutical companies throughout the day caught up to the bigger market-cap players in those industries.

Speaking of which, four consecutive down days is something that the market has only a 1.3% (or a 1 in 73) chance of doing.

And while the range we indicated left plenty of room for the market to have one or more up days, our model suggests things should be a little bit better through the end of the month. At least in the absence of a significant change in the expected future dividends that are the fundamental driver of stock prices or an outburst of market moving noise, where the worst outcome would be news that drove investors to focus upon 2016-Q1 for whatever reason.

Most likely, unless new information resolves the current split in the forward-looking focus of investors, the actual trajectory of stock prices will fall somewhere between the trajectories indicated for a strong focus on either 2015-Q4 or 2016-Q1. Janet Yellen tried her best, but alas, fell short.

And with that, we won't be discussing the S&P 500's actual trajectory during the next couple of weeks, as we'll be jumping ahead in time to check back in with the index after 2015-Q4's earnings season is officially underway, and also because we already have.

Tenses are difficult, aren't they?

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