I tried applying the wisdom of crowds idea instead :D
https://twitter.com/SmittyW62858649/status/13589265825139957...
Not sure if taking a median is the best idea. I figure a gamma distribution might work better!
Not sure if taking a median is the best idea. I figure a gamma distribution might work better!
You were allowed X guesses per day, per account (so I roped a few friends in). Since the guesses were public, it seemed like a good opportunity to try the theory out. The closest guess would win. The strategy was pretty simple: use your guesses to bracket other people's answers. So if someone guesssed £100, you would guess £99.99 and £100.01. Of course someone might guess exactly, but I don't think that happened (or maybe it did?).
I wrote a script (I think in PHP of all things) to poll the hashtag and put all the entries into a database, with some code to figure out what ranges we needed to cover each day. There may also have been some heuristics to account for the fact that you couldn't possibly cover everyone's guesses, but you could try to maximise the range of values that you would win for. I think we also tried to weight the suggested guesses around the median value.
In the end it didn't win, but it was a fun exercise. I think the winning answer was very close to the median.
I am surprised the median was an accurate estimator in your case but I suppose it makes sense if you are not close to the bound of zero (I.e. it start approximating a normal distribution)
I would really like to use a z-score metric to remove the outliers and fit a gamma distribution, but unfortunately its a busy Monday!