Rare Entries Overall Scores

[Starkey7]

Neil old fruit, not a bad idea at all. Might I suggest that since within each quiz the scores are multiplied, you take the geometric average of the scores, rather than the arithmetic average? So if I get 1, 1, 1, 1, 1, and 1,000,000 for my scores, the average would be 10, rather than 100,001, which seems more reasonable.

[tubeguru]

How does one calculate the geometric average?

[Starkey7]

Let's say that there are five numbers. You simply multiply them all together and then take the fifth root.

It's really useful with very large numbers. For example, if you've got some stars whose distance from the earth are something like 10^12, 10^12, 10^15, 10^16 and 10^20 miles, then with the arithmetic average you'd get something like 2x10^19, which isn't very reflective of the data. With the geometric average, you'd get 10^15, which is a bit more accurate.

(To see how this relates to the "normal" arithmetic average, you could also take the logarithm of all of them, add the results together, divide the sum by five and then take the anti-logarithm.)

[tubeguru]

But will people understand what the geometric average actually means when looking at the table? Will they understand how it relates to their performance?

[Starkey7]

Yes, the higher the number the worse they've been.

[greatkingrat]

Yes, the geometric average would be fairer. Matt is a good example, he is currently bottom of the table because of his massive 46 million score in Round 17, although he has actually done pretty well in general.

[tubeguru]

Good point. I'll attend to it later today.

[tubeguru]

The next question is, should I make the average score that non-players get for not entering a particular round the geometric average too, or leave it as the mathematical average? It seems that leaving it as the MA means (no pun intended) we have two different average types, with one affecting the other.

[tubeguru]

OK, it's all sorted now.

Any non-playing player in each quiz is allocated the geometric average score for that quiz. Each player's overall score is then the geometric average of all of their individual scores.

As you can see, Sam still leads, but scrxisi has been catapulted upwards despite his huge score in Quiz XVII. Starkey's score is much larger than everyone else's because he tends to score highly in each quiz, and no amount of averaging can save him.

https://docs.google.com/spreadsheet/ccc ... zRUd3lXT3c

[tubeguru]

OK, the table has been updated with the scores from Round XIX (Disney). The table now has a "previous position" column, so you can see how your position has changed.

The geometric average for Round XIX was 1,109. All non-participating players score this amount, but Sam remains firmly in the lead with only Going Underground's Round XVI to come (if he ever writes it). Tubeguru falls down the rankings thanks to his stupid answers.

Once round XVI is completed (if at all), I can reset the scores and we can start again.