The Words With Friends (WWF) addiction is bittersweet for me. On one hand, it’s fun to play all your friends and discover new words. On the other, it’s sad to see Scrabble fall by the wayside because it is such a classic; sure, it needs a bit of updating on the tile distribution and point values, but at least it has a confirmed published dictionary. Well, actually, it has a few of them, but in the US we mostly use TWL06. The lack of a consistent WWF dictionary (it changes with updates) is just annoying. Learning the additional two-letter words was easy (there are currently only four: DA, DI, FI, and GI), but there is no way to learn the three letter words because there is no official list.

Recently, Zynga (the maker of WWF) has had a bit of financial trouble. They’ve started adding new features to WWF for ridiculous prices. One of the features is a stats summary that shows you your best word, scoring average, record against opponents, etc. I think I’ll keep my $4.99, but I was curious about how tournament-level players perform.

I used scores from the monthly tournaments on wordwithfriends.net over the past year to calculate a scoring distribution. Because better players (i.e., higher scorers) are more likely to advance in a tournament, I used only the first-round scores to ensure that I wouldn’t skew the data toward higher values. Also, scores below 100 were excluded due to the likelihood of early resigning - it’s pretty hard to score below 100! The final dataset included 11334 scores.

I’ve plotted the data both as a probability mass function (PMF) and a cumulative distribution function (CDF). Because the score is a discrete variable, the PMF and CDF are related via summation rather than a simple derivative, but I find it easier to conceptualize the relationship using calculus. A blue bar with a value of zero would correspond to a slope of zero (horizontal) for the yellow line. The taller the blue bar, the steeper the positive slope of the yellow line – if the PMF were continuous, it would be the derivative of the CDF.

I added some summary statistics to the graph so you can see how you measure up. The median is 387, which is lower than I expected. Even with removing the values below 100, the distribution still has a pronounced negative skew; only nine scores (less than 0.1%) were above 600.

Data source: http://wordswithfriends.net/?page_id=212