Wednesday, January 14, 2009

Crucimetrics

I started solving the New York Times crossword in a casual way late last year, helped by my American wife Magdalen. We make a pretty good team, as she "gets" most of the US-specific references (names of cars, sports players, TV shows etc) and I know a lot of obscure words and the cryptic ways they can be clued.

We hadn't been solving very long before noticing that some compilers make an effort to produce unusual grids: either visually interesting, with "stacks" of 15 letter across answers; or by including lots of the rarer letters in English - the ones like J, Q, X and Z that have high Scrabble points.

Magdalen coined the term "crucimetrics" for my analyses of grids. Crucimetrics attempts to do for crosswords what Sabermetrics do for baseball. The analysis is divided into these sections:

Grid
The grid dimensions and number of black squares (and their percentage of the whole).

Conventionally no more than 1/6th (or 16.6%) of the squares are black.
Answers
The number of answers and their average length. The maximum number of answers in a 15x15 grid is usually 78.

The average answer length is a useful measure of the connectedness of a grid. A grid with longer words is harder to fill, but tends to be more satisfying to solve - there are fewer clichéd answers and getting one answer is more likely to help with other ones.

The average answer length typically ranges from around 4.5 to around 6.
Scrabble Points
The sum of the Scrabble point values for every letter in the grid. This indicates the effort made to include low frequency letters, since the Scrabble point system is based on how often letters occur in English: the most common letters (E, T, A, etc) score 1, while the least common letters (Q and Z) score 10. The higher the Scrabble points, the more unusual letters there are.

The Scrabble points are also given as an average and this typically ranges from around 1.4 to around 1.9.
Letters Used
This shows which letters are used at least once in the puzzle (the used letters are in black type, while unused ones are in light gray type).

This identifies pangrammatic or lipogrammatic grids, which are given special mention in the next section.
Feature
This section describes any special features of the grid not inherent in the theme.

For example, a pangrammatic grid includes every letter of the alphabet at least once. You can even have dipangrammatic and tripangrammatic grids - each letter being used at least twice or three times.

Lipogrammatic grids deliberately suppress one or more common letters.
Grid Colors
The solution grids are all generated with Sympathy Crossword Construction and use cell coloring to show the Scrabble point values of the letters, as in the following chart.



Scrabble is a trademark of Hasbro, Inc. in the United States and Canada, and of Mattel elsewhere.

6 comments:

Anonymous said...

Excellent site! Just recently graduated to the dreaded NY Times Crossword Puzzles: early attempts averaged in the seventy percentiles; currently plugging along in the higher eighties, occasionally a low nineties. Said rare events encourage me to greater verticals (and horizontals). Thank you, Brit friend, and Spouse as well.

Crossword Man said...

Thanks Anon. I don't quite understand the stuff about the percentiles, but you're improving and that's the main thing!

joe said...

This site is fantastic! I've been plugging away at the NYT Crossword for a few years and have steadily increased my successes. Having found this site, my grasp on 'Shortzian' word play has definitly improved. Many thanks! I used to pride myself on not using any help but I recommend your site to crossword rookies all the time. Cheers!

Crossword Man said...

Thanks Joe, I hadn't heard the term 'Shortzian' before! You might find Pavlov's Guide to Crosswords particularly useful.

Anonymous said...

In the Nov. 14 crossword, perhaps your British background explains why you aren't familiar with the low-slung plastic tricycle brand-named "Big Wheel," ubiquitous in America. See: http://www.coolest-toys.com/200810/classic-toys-%E2%80%93-big-wheels.htm

This puzzle must not have been too hard--I'm not usually able to solve them without looking at some references (i.e., cheating)!

Crossword Man said...

Thanks Anon ... I've acknowledge my ignorance of the Big Wheel in a comment to the November 14, 2010 post.