3Blue1Brown has a great video explainer here on the exponential growth of epidemics that simplifies the spread of Coronavirus down into two basic factors: 

1. how many people someone sick is exposed to

2. the probability of each exposure in spreading the infection

So really there's only two things that everybody can do to slow down and (hopefully) stop the spread of Coronavirus:

1. Lower as much as possible the number of exposures you come into contact with by avoiding crowds, staying away from others in public, and touching as few things as possible
2. Lower as much as possible your probability of spread by coughing/sneezing into your elbow, wash/disinfect your hands often, and try not to touch your face

The higher each factor is, the more you should work to lower the other; if you're sick you should limit the number of exposures to 0 by staying home and isolating yourself, and vice versa.

Even what my seem like a small lowering of the growth rate (from say 15% to 5% assuming 21,000 initial infected population) over the course of two months makes a huge difference in total number of infected people

Coronavirus is an extremely complex issue facing the world right now and countries are responding in different ways. I believe the main difference between nations that are limiting the virus' growth and those that aren't is how they view the spread of the disease: is it more of a math or people problem?

Those that view it primarily as a math problem were quick to institute measures that go against social and cultural norms (lockdowns, quick testing and quarantining, etc.) - they risked overreacting because they understood with exponential growth things could get bad quick. They understood fat tails. Those that view it as a people problem were quick to ease fears or cast blame and slow to push back against normal everyday life - they risked underreacting because they didn't want to disturb life or economic markets.

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Here are updated charts from yesterday's post (through 3/14/20) showing the different exponential trendline growth rates of countries (steeper trendline means more growth). While the accuracy of the numbers may be off, their growth rates relative to each other will still be important.

For the last month in my Algebra 2 classes we've been discussing the inverse relationship between exponential growth and logarithms. Whenever we want to solve for an exponent "x", we convert the equation into a logarithmic equation and solve for "x". Well a virus spreading throughout a population is the perfect time to try to solve for an exponent, since we want to find the growth rate "r" in the exponential growth equation below.

I wondered if I could create a trendline based on the confirmed cases data for Coronavirus. Moreover, if I made this trendline exponential on a log graph, the trendline would be linear (since they're inverses, and an inverse is just a reflection over the line y = x, an exponential graph of a log function will just be a line). Taking the data from Our World in Data and graphing it in Google Sheets, I was able to create the exponential trendline and find the fit (R-squared) and growth rate.

Semi-related: this great video about exponential growth 

I created the above chart to show the semester start and end dates for the state flagship universities in America (not included: Oregon's trimester and Washington's quarter schedules). The start date is the date which classes began, and the end date is the last possible date of finals that semester.

As you can see, they're all pretty similar except Spring semester at the University of Delaware, which has an insanely late February 11 start date and June 1 end date! The average Fall semester start date is August 24 and its end date average is December 15 (113 days), and for Spring they're January 15 and May 10 (115 days) respectively.

It was interesting trying to put all of their calendars all together in a chart to visually compare them, and I learned a new Google Sheets trick along the way, the SPARKLINE function! But I wasn't initially interested in just comparing their calendars, I started out thinking about something completely else. I started out thinking about a Twitter bot.

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One of the accounts I follow is @year_progress, a bot that simply Tweets a status bar increasing 1% every 3.65 days throughout the year. It's just long enough in between posts that I'm mildly surprised each time I see the percentage increase and just a fun little reminder. 

On a soon-to-be-related note, something I've been slightly obsessed with for a while is the Golden Ratio (0.618 : 1 : 1.618). I'm paraphrasing here but it's basically just a balanced system with the smaller section proportionate to the bigger section as the bigger one is to the whole. Something about this special balance is beautiful to us humans; for thousands of years we have created art and built structures specifically to this ratio. There's a natural beauty as well to it, as evidenced in its fractal symmetry found everywhere in nature. In sum the Golden Ratio just feels right, with everything in balance.

Back to my story, I wondered one day what the Golden Ratio date would be for the year, similar to @year_progress: turns out that 61.8% of the way through the year is August 15. As a lifelong student this date instantly stuck out to me as right around when we normally started the school year.

Wait a sec... could it be that our school year started around then because that date "felt right"? I had always heard that the school year was when it was because of farming back in the day, but a quick search showed that it really had to do with wealthy people wanting to avoid the heat in cities during the summer and a need for standardization. But why were we still using these dates? Just because of the inertia of current processes or because of some other unexplained reason?

Ok then, for my theory of a "right balanced" school year length to be correct, there should be some significance to when we end school too. For it to adhere, the end of the year should be around the other significant percentage of the Golden Ratio, 38.2% (which is 100% - 61.8% OR CONVENIENTLY THE SAME AS 61.8% of 61.8% or 0.618 times 0.618). Well 38.2% of the way through the year is May 19...right around when college normally ends!

So that led me to begin painstakingly collecting all the semester start and end dates from state's flagship universities. Turns out that the average start date for those 48 universities (August 24) is 9 days after the Golden Ratio start date (August 15) and the average end date (May 10) is 9 days before the Golden Ratio end date (May 19). Symmetry is cool.

In the end my theory was close but wrong by a little over a week in both directions. Maybe if I averaged ALL universities in the U.S. instead of just the flagships it'd be closer to my prediction, but ain't nobody got time to do all that. However a new coincidence emerged when looking these date ratios; that I'll dive more into below.

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To reiterate, I originally hypothesized there was some significance in our school year calendar in regards to the Golden Ratio, with us starting the year around when we were about 62% of the way through the year (with the ratio of what was left in the year to what had already passed the same as what had passed to the whole year) and ending around 38% of the way through the next year. This turned out to be close but not exactly correct for flagships.

But in looking at their calendars, I began to wonder if there was any significance to a date within each semester, for the "just right" date feeling to show self-similarity like the Golden Ratio does with fractals in nature. So I began wondering, "What event in a semester signifies that we're as much of the way through a semester as the semester start date does to the year?" I settled on when students can begin registering for the next semester's classes, as that usually signals enough time has passed in the current semester that we should start thinking about the next.

Well guess the fuck what? The average day in Fall 2018 that students could begin registering for the Spring 2019 semester's classes is November 1, or 61% of the way through the Fall semester! The average first registration day in Spring 2019 for Fall 2019 classes is April 1, which is 66% through the Spring semester. Fall's registration is closer to the Golden Ratio than Spring's but the general theory is still relevant.

While each college's academic calendar is different than that of other colleges as well as different from its own year to year, on average our college schedules revolve around dates that "feel right" and are relatively in balance with the Golden Ratio.

1. Fall semester starts about 0.618 of the way through the year --> Aug 15 : Dec 31 :: 0.618 : 1
2. Spring semester ends about 0.618 of the way to the Fall start date --> May 19 : Aug 15 :: 0.382 : 0.618
3. Registration for the next semester starts about 0.618 of the way through that current semester
4. The total number of days (228) college students could be "in school" for the year (113 on avg for Fall and 115 for Spring) is about 0.618 of the year's 365 days [228/365 = 0.624]. Consequently, the average number of days (114) in each half school year -- a semester --  is about 0.618 of the number of days in each half year

Admittedly, I'm showing confirmation bias plus other biases by picking and choosing these similarities but I think the relative nature of the length of time ratios is fascinating. There's a lot that we currently do that we can't really explain why, but I believe we subconsciously set our school calendars relative to dates that "feel right". It's an interesting thought but that's probably as far as it will ever go.

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Here's the flagship date info for anyone interested, I'm sure there are errors in collecting and interpreting these dates from the college's individual websites but some were very easy to find and other registration dates and such were hard to find:

In an ideal world, every NFL team would pick the next best player on their draft board to maximize the expected talent on their roster, but we all know that teams put needs and prospects they become infatuated with ahead of the best available player. 

Five years ago, I did some exploratory draft analysis and wrote a blog post looking at the number of team visits by position. I decided to re-do that for the 2019 draft. I'll reiterate the caveats: these visits were pulled from Walter Football (as of 4/9/19) and it's likely that they don't cover even half of the visits some teams and prospects have had. But it's still useful info (and put together in a format that I haven't seen yet).

To begin with, here are the number of players each team has met with, by position:

Insights:

• NY Giants, Washington, and Denver have met with the most QBs, then Miami and LA Chargers
• Chicago and NY Jets have met with the most RBs
• Tampa Bay has met with the most WRs BY FAR (and the most visits total by team) then Washington
• Detroit and Denver need a TE apparently
• Minnesota, NY Giants, Tampa Bay, and Carolina need an OT
• Buffalo needs a G and Baltimore a C
• Philadelphia wants a DT
• Tampa Bay, Miami, Kansas City, NY Giants, and Tennessee need EDGE rushers
• Tampa Bay and Denver need more OLB while SF needs an ILB
• Kansas City, Houston, and Denver need CBs
• Kansas City and Tampa Bay need Safeties
• Chicago needs a K and Philadelphia needs a P

Next let's look at the 25 prospects that have been the busiest (or have the best promoting agents). Multiple visits with the same team are counted, so Jaylon Ferguson hasn't visited 18 teams, but is on record for 18 visits total:

Finally, I awarded points per type of visit (1 pt for a meeting at the Senior Bowl, 2 pts for a meeting at the Combine or that prospects Pro Day, and 3 pts for a private visit or workout), and you can see what prospects have been thoroughly vetted by teams:

Insights:

• QB fits are fleshing out: Haskins with Oakland (at #4 likely), Jones with NY Giants (at #6 or #17), and Will Grier with Washington (at #15)
• New Orleans doesn't have a first rounder, but is likely targeting Blake Cashman with their second rounder
• Denver is likely targeting Isaiah Johnson with their second rounder and Houston with Brandon Hitner (don't know what round but probably earlier than I expect)
• Buffalo likes Caleb McGary and I'd bet they go with him at #9

With all of that info, I tried my hand at a second attempt of a mock draft, with emphasis on what players have visited which teams or positions the teams have focused on:

I had the opportunity to attend my first academic conference, put on by the Association of Education Finance and Policy (AEFP) in Kansas City, MO. Since I live in KC, had the time to attend all three days, and am very interested in policy regarding college access -- it all worked out really well. 

I went into the conference as a first-time observer with the goal of learning how paper presentations work and how a college counselor could help improve both a student's college choice and their persistence through graduation. Some things that I took away from the sessions I attended include: 

(if something shouldn't be discussed email me at cdjarrell [at] gmail and I'll remove it)

• Online instruction helps more students graduate high school, which is good, but doesn't help enough to get them to enroll in college
• Charter schools help students to enroll in slightly higher quality (less bad) colleges
• Higher quality colleges help minorities more, in regards to graduation
• When looking at quality of college, helpful to look at (in no order): their selectivity, graduation rates, spending on faculty/resources, test scores, and the amount of undergrad faculty

• Gloria Bernal had a very informative flow chart of how the study was set up that really helped me
• more academic study presentations should include this to help people quickly understand how the experiments were run
• The most relevant factors to Columbian (country) students college decisions: the amount of scholarship money and the quality of the college
• Most college-going interventions take a behavioral view: they try to simplify the information and reduce its complexity through reminders, steps, etc.
• The College Board did a massive study with 700,000+ students basically replicating a lot of the popular interventions through sending personalized college info through mailers and emails and, unfortunately, found little impact at that scale. They didn't affect college attendance, the quality of colleges attended, or the expected cost of said colleges. Students also generally didn't apply to the recommended colleges that were suggested
• Although I would've loved to see large positive impacts, I don't think this closes the door on low-touch, personalized interventions at scale. Maybe they don't come via mail or email?
• HS Seniors have their college lists in mind by senior year, so behavioral nudges to better quality and/or cheaper colleges should happen before then. And if they are nudged senior year, it's normally because of sudden changes in test scores/financial aid awards
• A large percentage of HS students still don't know much about FAFSA verification or what their next steps are in the summer before they enroll or even if they got and accepted a financial aid award or not
• We need to communicate these things much clearer

• It's important for colleges to look at leading academic momentum indicators, which can be easily predicted at most colleges and community colleges via machine learning; can predict odds of graduation at close to 80%
• Causal and prediction questions are different but can be complementary. It's important to identify which you're looking for

• Most adults don't have strong opinions either for or against income share agreements, except for parents currently paying for college which oppose them
• Interesting thing about ISA's is that they reverse the inter-generational way of paying for college: instead of currently paying for future benefits (like social security), you're paying for current benefits in the future
• Simplified grant language, along with little messages of belonging and encouragement, raised the percentage of people that followed through and took advantage of them
• Previous study finding: Dynarski and Deming found that for every additional $1,000 in aid money, a college would see a 3-4% increase in chance of enrollment
• The timing of financial aid communications is extremely important and overlooked

• To have an impact with education online, the more personalized you make it the better. The impact is also not the same across all courses, as it varies greatly by type of subject and the instructor
• One way to scale online education quickly is to have a course shell that could then be adapted by instructors
• Minority students disproportionately struggle with college-going skills such as study skills and coping strategies
• First Year Experience (FYE) courses are common at colleges and have been shown to have positive impacts across the board
• One way to provide FYE mentoring is via small groups (3) in their first semester and then 1:1 mentoring in the spring
• Simple things such as providing virtual meeting software for group communications, utilizing texting with students, and encouraging faster response times to questions, even if it's just to say that you'll have an answer at the next meeting
• In community colleges, A LOT of students are underplaced in developmental courses, which could lead to less students graduating. A simple algorithm helped more properly place students at one CC and could be adopted easily elsewhere

• We should be careful to attribute more diversity at colleges to affirmative action plans, more so changing population demographics
• A socio-economic status based diversity plan can roughly replicate a race-based one
• I didn't know what "pair programming" was before but I like the switching of "driver" and "navigator" responsibilities that is encouraged in it
• I also didn't know that standardized admission tests first came about to help identify higher achieving, low-income students that were previously hidden. This was surprising because most of the coverage you hear now about SAT/ACT is how they hurt disadvantaged students. Also it was surprising to hear that the grad school standardized tests are better for minorities than whites, although it wasn't fully clear how
• The main differences in standardized test performance by race/SES are due to differences in test prep courses, personalized tutors, and an overall familiarity with the process
• Another surprising note: There's no evidence of test optional policies actually helping diversify colleges
• One thing colleges need to do a better job accounting for is local information for where that student is coming from

• Framing, reference points, and spatial choice architecture all have behavioral effects important to students
• Framing: showing students things such as expected salary earnings vs. showing them graduation rate or the cost of the college vs. the amount of aid given
• Reference points: setting estimated average costs by SES quintile
• Choice architecture: the sequence of info presented
• Good college counseling helps reduce the hassle of figuring out the college admissions process, it helps with setting proper defaults, assists with applying, and providing timely outreach
• Students surveyed in 2017 said they chose their college based primarily on the quality of the teaching and the availability of scholarships
• When the school name is hidden, people prefer the cost more. When the school name is shown, they prefer the perceived quality more
• It's interesting but not surprising that we act more rational when the school name is not shown
• In China, they have a much more centralized college admissions process based solely on your college entrance exam score and rank-order choice of college. A simple machine learning algorithm helps students quickly and accurately establish where they match academically

• Student loans are generally bad for borrowers intending to go to a 2-year college
• Setting a reference point of the max amount of loan possible reduced 2-year college borrowing whereas information about not having to borrow all of what was possible had no effect
• Students that are particularly loan-averse are Hispanics and those that are already risk-averse
• Creating an opt-out procedure for an academic grant increased the number of people that accepted the grant, not surprisingly
• The Bureau of Labor Statistics has 20 year projections of careers that students can use to determine if a college degree is needed or not