## Wednesday, February 18, 2009

### TunkRank Scoring Improvement

Recently Daniel Tunkelang blogged about an influence rank for Twitter. Jason Adams took up the implementation challenge and coined it TunkRank.

$Influence(X) = \sum_{Y\in Followers(X)} 1 + \frac{p*Influcence(Y))}{ \left \|Following(Y) \right \| \right}$

After some poking at it, I'm suggesting a scoring improvement. At the moment the primary rank is percetile in the UI, however the raw score is given as well. I checked a few users and put together the table below, and it feels wrong. It saturates @ 100 too quickly and there is not enough differentiation between people with healthy versus massive influence.

Why 'feel'? Human interpretable numbers need a tactile sense to them in my opinion. One critique of the metric system is that the English system just feels more human compatible, an inch is not too small, a foot is reasonable, a mile is a long way and 100 miles per hour is darn fast.

I'm proposing two new scoring possibilities. Both are based upon logarithms and span from 1-100. The slight difference between them is how 'linear' the resulting rank feels across the accounts I compared.
1. LEAST(100,ROUND(POWER(LN( tunkrank-raw-score +1);1.82)))

$TunkRank(X) = ln(Influence(X) + 1)^{1.82}$

1. LEAST(100,ROUND(LN( tunkrank-raw-score+1)/LN(3.5) * 10))

$TunkRank(X) = 10 * ln(Influence(X) + 1)/ln(3.5)$

What are the constants? They are magic numbers to map Barak Obama to a TunkRank of 100 as well as provide an interesting spread between the test accounts below. Comments welcome! Which is my choice? I can't decide.. #1 is smells more accurate, #2 tastes more natural.

Yes this is an inexact science.

Possible Tunkrank Bug? Check out dewitt's rank.. looks off given his number of followers and that he's an influential guy from Google.

NAME       PERCENTILE RAW SCORE  NEW SCORE #1 NEW SCORE #2BarackObama        100     277770        100        100wilw               100      79118         82         90guykawasaki        100      62543         79         88JasonCalaca        100      59075         78         88THErealDVOR        100      43207         74         85anamariecox        100      38177         73         84WilliamShat        100      13932         61         76fredwilson         100      13340         60         76abdur              100       1351         36         58johnhcook           99        407         26         48johndcook           94         61         13         33gutelius            84         20          8         24nealrichter         81         16          7         23ealdent             80         16          7         23dtunkelang          79         15          6         22dewitt               1          2          1          9