https://twitter.com/NateSilver538/status/965704157754810369

presidential-birthdays.js

const _ = require('lodash');
const moment = require('moment');

const birthdays = [
  'February 22',   // Washington
  'October 30',    // Adams
  'April 13',      // Jefferson
  'March 16',      // Madison
  'April 28th',    // Monroe
  'July 11',       // Quincy Adams
  'March 15',      // Jackson
  'December 5',    // Van Buren
  'February 9',    // Harrison
  'March 29',      // Tyler
  'November 2',    // Polk
  'November 24',   // Taylor
  'January 7',     // Fillmore
  'November 23',   // Pierce
  'April 23',      // Buchanan
  'February 12',   // Lincoln
  'December 29',   // Johnson
  'April 27',      // Grant
  'October 4',     // Hayes
  'November 19',   // Garfield
  'October 5',     // Arthur
  'March 18',      // Cleveland
  'August 20',     // Harrison
  'January 29',    // McKinley
  'October 27',    // Roosevelt
  'September 15',  // Taft
  'December 28',   // Wilson
  'November 2',    // Harding
  'July 4',        // Coolidge
  'August 10',     // Hoover
  'January 30',    // Roosevelt
  'May 8',         // Truman
  'October 14',    // Eisenhower
  'May 29',        // Kennedy
  'August 27',     // Johnson
  'January 9',     // Nixon
  'July 14',       // Ford
  'October 1',     // Carter
  'February 6',    // Reagan
  'June 12',       // Bush
  'August 19',     // Clinton
  'July 6',        // Bush
  'August 4',      // Obama
  'June 14',       // Trump
];

const momentBirthdays = _.map(birthdays, (birthday) => {
  return moment(birthday, 'MMMM D').startOf('day');
});

const linearAverage = () => {
  const daysOfYear = _.map(momentBirthdays, (momentBirthday) => {
    return momentBirthday.dayOfYear();
  });
  const averageDayOfYear = _.sum(daysOfYear) / _.size(daysOfYear);
  return moment().startOf('day').dayOfYear(averageDayOfYear).format('MMMM Do');
};

const polarAverage = () => {
  const vectors = _.map(momentBirthdays, (momentBirthday) => {
    const angle = 2 * Math.PI * (momentBirthday.dayOfYear() / 365);
    return [Math.cos(angle), Math.sin(angle)];
  });
  const sumOfCos = _.sumBy(vectors, (v) => { return v[0]; });
  const sumOfSin = _.sumBy(vectors, (v) => { return v[1]; });

  const averageAngle = Math.atan(sumOfSin / sumOfCos);
  const averageDayOfYear = 365 * 24 * averageAngle / (2 * Math.PI);
  return moment().startOf('year').add(averageDayOfYear, 'hours').format('MMMM Do');
};

console.log('linear average is ', linearAverage());
console.log(' polar average is ', polarAverage());

Results for me:

$ node presidential-birthdays.js
linear average is  July 4th
 polar average is  December 5th

@natesilver538 Did you use vector averaging method? How'd you arrive at November? 🤔