Wordfeud and you (and me)

I know that many of you play a lot of games on your phones and tablets and facebooks and GameBoys (I swear I know people who still use this as a blanket term for handheld electronics).  I don't play many - I tend to prefer a console or PC experience for my gaming - but do play a few. 

I tend to play DrawSomething at the pace of about a turn a month, and Wordfeud a little more frequently (the mobile app, not the facebook app, though I guess they work cross-platform). 

Wordfeud, for those of you who don't play it, is basically Scrabble.  By basically, I mean almost exactly.  The placement of double and triple word and letter squares on the board are a little different (and you can play a board where they're laid down randomly), but that's about it.  Makes for some subtle but interesting differences.

The cool thing is that a few months ago Wordfeud started recording stats within the app against all the other people you play against.  I generally have a few games going on at a time, so I figured at some point I'd take a look at the stats that I've accumulated. 

Now, there's not a whole lot I can tell from these stats on their own (we'll talk about the problems), but I thought it would be interesting to discuss exactly I'd need to be able to know more.

Basic stats are given about each of your opponents, in terms of win-tie-loss.  I'm not going to call out my friends individually, so we'll just list them anonymously.

	Win	Draw	Loss
A	2	1	5
B	4	0	1
C	2	0	4
D	7	0	1
E	7	0	1
F	3	0	6
G	4	0	2
H	4	0	2
I	3	0	1

Now, like I said, this doesn't tell us that much.  I could be playing against preschoolers, and I could be playing against Nobel Laureates (presumably winning their Nobel prizes in Scrabble).

We can get a range of the people I'm playing against by ranking them a bit in terms of difficulty (or at least the difficulty I seem to be having with them).  We'll do this with simple win percentage (FYI, we'll treat that single tie as not a win or a loss, but simply as not a game. 

That gives us another table.

	Win Percent
A	28.57%
B	33.33%
C	33.33%
D	66.67%
E	66.67%
F	75.00%
G	80.00%
H	87.50%
I	87.50%

Which we can change into a rudimentary chart.

You can see that there are a few problems with this chart.  The x-axis is both arbitrarily scaled and ranked.  It's done with the best information I have available at the moment.  Ideally, I'd have some stats on the people I'm playing against in terms of their overall win percent.  This would allow me to rank them in terms of all the games they've played, not just all the games that they've played against me. 

It would also allow for them to be scaled to that win percentage, rather than simply all spaced the same distance apart.  There are two pairs of individuals who I have the same record with.  They're certainly not identical in skill, so more information would help to differentiate their actual ability. 

What we can tell from the graph is that I'm not playing a bunch of people who are all better or all worse than me, but a good mix of people across a good range.  That, or the results of games are just random noise...

Overall, more data is the best way to tell.  Interested in seeing how you measure up?  Play me a game (or 20) - my username is 'paul_28'.  Don't miss the underscore, unless you want to just play against some random guy (which I might actually be to some of you).  I will mine your data.