Thursday, 1 March 2012

Finals preview (series 4): Letters, Numbers, Conundrums

Some of the finalists will be better at the letters, and some at the numbers.  My feeling is that someone who is reliably better at the letters will beat someone who is reliably better at numbers, but it is a bit more finely balanced than I first thought.  In any case, I thought it would be interesting to take a look at how the contestants have performed in the various categories, and what their strengths or weaknesses seem to be.

First up, here are the average points scored by contestants in each of the appropriate rounds (not games), assuming no competition.  (i.e., solo scores.)  Naturally we would expect the letters to have a smoother distribution than the numbers, which would be much smoother than the conundrum.  (The conundrum results are particularly unreliable since the other contestant sometimes solved it first.)


This does show some interesting results, in particular the large gap in numbers performance between the top five and the lower three.

How might this translate into results?  Consider a game between Sam and Alan.  Alan's average letters result is 0.2 better than Sam's, or an average of 1 better over the course of a game.  That could mean finding an eight to Sam's seven, and an eight point gain overall.  Similarly, the average numbers advantage is 1 to Sam, or 3 over the course of a game; that could translate to 10 vs. 7, or ten points to Sam.  And the conundrum results are even, but only one contestant can score.

So the above results could be taken to suggest that a Sam vs. Alan match would have Sam leading by 2 points going into the conundrum, and a tossup as to who actually wins.  (And yes, I know this is so far from being statistically valid that it is silly; I'm just playing around, really.)

Of course, as I mentioned in the previous post, solo scores do not take into account how difficult the rounds were (whether in terms of best possible result, or how feasible it was to find it).  They also don't reflect well the nature of the scoring, where a single point difference in the letters could mean as much as an eighteen point difference in the scores.

The following doesn't adequately reflect that well on it either, but it's the datapoint that I have.  Here are the average points won or lost by each contestant against me.  This time it is average per game, rather than per round.


This reflects some larger differences.  If we apply the results of this to that matchup between Sam and Alan, then we see about 3 points of difference in the letters, but a massive 16 points in the numbers -- that's a 19 point lead to Sam going into the conundrum, and a safe win even if Alan solves it.

Can we conclude much of anything from this?  Not really, particularly as all of us are moving targets, ability-wise, and the game is too short to properly shake out variance.  Fortunately tonight we will get some real data.


Sam Gaffney said...

Great stats, Geoff, but what about conundrum speed?! Like Ricky Bobby says: if you ain't first, you're last!

Good luck playing from home in the finals (except against me).

Sam Gaffney said...

Also, give back my tiebreaker conundrum!