NYT Crossword Difficulty’s Non-Linear (For Me in 2007, At Least)

As a Christmas giftee, I’m no enigma. Really, there are only three things that I make sure someone gets me each December: A bottle of Bombay Sapphire gin, a bottle of 18-year old Jameson Irish Whiskey and the upcoming year’s New York Times (NYT) Crossword Calendar. (Apparently, drinking and wordplay are my base desires.)

Alcohol aside, I’ve always been a big fan of puzzles. When I was a kid, my dad used to take me on his weekend journeys to the brick-and-mortar newsstands around Miami, and my reward for a six-hour date with paper was a haul of various puzzle books that ran the gamut of nerddom: invisible ink quizzes, logic problems, brain teasers, word searches, mazes…and crosswords.

Fast forwarding from 1986 to 2006, one day I happened upon the movie Wordplay, a documentary about, in part, the world of competitive crosswording. Given my aforementioned puzzle-solving proclivity as a child, it should come as no surprise that I frequently daydreamed about winning a ton of money on Wheel of FortuneThe Price is Right, $25,000 Pyramid (R.I.P.), Classic Concentration (R.I.P.), and Scrabble (R.I.P.), the last of which was a Chuck Woolery-hosted show that, although based on a vocabulary game, was actually a crossword game. So, when I saw Worplay, I immediately thought, “People actually compete at this? For money?”

Ostensibly, Wordplay‘s main character is longtime NYT crossword editor Will Shortz, but the real star of the movie — its emotional compass, if you will  — is the American Crossword Puzzle Tournament, where entrants try to solve crosswords as quickly and accurately as they can.1 Inspired, I got my first NYT crossword calendar in 2007. Since then, my morning routine has consisted of making breakfast, brewing coffee, and timing how long it takes me to solve the next crossword challenge that the calendar has to offer. Amazingly, I’ve kept all of these results to this day.

So, I’m sitting on daily crossword data from 2007 to 2013, and I have my own site now.2 Methinks I should do some statistical analyses and publish it as a part of Random Rounding! What follows are a couple of interesting observations I made based on my overall results in 2007.

Solution Times by Day

In 2001, Will Shortz wrote

The perfect level of difficulty, of course, differs from person to person. This is why, as editor, I vary the weekday Times crossword difficulty from easy-medium on Monday up to what the actor and puzzle aficionado Paul Sorvino calls “the bitch mother of all crosswords” on Saturday. (He said this as a compliment.)

Shortz doesn’t explicitly make a claim that there’s a linear progression of difficulty from Monday to Saturday (e.g., Tuesday puzzles are 2x as difficult as Monday puzzles, Wednesdays are 3x as difficult as Mondays, Thursdays are 4x as difficult as Mondays, and so on), so it seems worthy — or at least a bit of fun — to test the question, “Based on my solution times in 2007, is NYT crossword difficulty linear?”

Crossword Times By Day (2007)

Well, shit, that’s not linear at all. In fact, given the R2 of 99.5%, I’m confident in saying that the impact of day on solution time — at least based on my brain in 2007 — is exponential. If a linear difficulty trend prevailed, I would have finished Mondays in an average time of 56 seconds, Tuesdays in 11:33, Wednesdays in 22:10, Thursdays in 32:47, Fridays in 43:23, and Saturdays in 54:01.3 Instead, I averaged 7:15 on Mondays, 10:02 on Tuesdays, 16:58 on Wednesdays, 28:26 on Thursdays, 42:11 on Fridays, and 59:59 on Saturdays.

In terms of how my average solution time for each day varied around its average, there was a distinct shift on Wednesday. Specifically, whereas the coefficient of variation (CV) for Mondays and Tuesdays were 22.3% and 34.9%, respectively, the CVs from Wednesday through Saturday were all between 45.3% and 46.3%.

Solution Times by Date

Knowing about the progression of NYT crossword difficulty is one thing; knowing about the progression of my crossword skill is quite another. Ericcson et al. (1993) found that it takes about 10,000 hours of practice to become an expert at something. In total, I honed my crosswording skills for 143 hours in 2007. Taking Erricson et al. (1993) literally, that amount of time spent translates to climbing 1.43% of the way up the expertise ladder. So did I make the grade?

Crossword Times By Date (2007)

By most any account in this graph, yes, yes I did.

Over the full course of the year, I reduced my average weekly time by about 7% (aka more than 1.43%), from 30 minutes to 28 minutes. From January to October, my average weekly time decreased from 30 minutes to 20 minutes, which represents about 33% improvement. And from March to October, my solution times dropped by about 46%, from 37 minutes to 20 minutes. I may not have gotten a beep from Kim, but 2007 was a good year.

That bit of self-aggrandizement said, sitting here in 2015, I have no clue why (or how) my brain went soft during the holiday season of 2007. I imagine that, when it comes time to provide a Random Rounding report on 2008, the answer will reveal itself. If not, then I’d hazard a guess that there were characteristics of the November and December puzzles that were particularly powerful in their ability to make me take a long-ass time to find a solution.

What characteristics might those be? Sorry, you’re going to have to wait for that payoff months down the road.

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  1. Incidentally, the speed-accuracy trade-off is a big deal in sport psychology research, which I’ll be writing about on Wisdom Wednesday

  2. Everyone assumed someone else was getting me the 2014 calendar, and, as I detailed on this week’s Three Cone Drill Podcast, I wasn’t in a mood to give many shits about gifting failures in 2014. 

  3. Even NYT crossword constructor Merl Reagle’s on-camera best for a Monday puzzle was just over two minutes in  Wordplay

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