Modelling the money

Inspired by the ‘h-index‘ – which measures the productivity and impact of the published work of scientists IRL Industry and Outreach Fellow Professor Shaun Hendy wants to present the TIN100 data in a new way.

Scientists have the h-index, which is so easy to generate, and I thought that the t-index would be just as catchy,” says Hendy.

The h-index is based on the set of a scientist s most cited papers and the number of citations that they have received in other publications.

Similarly, the t-index uses the fact that the distribution of TIN100 company revenues follows a power law. So if the TIN100 are ranked in descending order by revenue, the t-index is calculated by counting down the list until the revenue in millions of dollars is equal to, or just greater than, the rank.

It s very easy to scale it up or down, says Hendy. So you can, for example, work out the figure needed to catch up with Australia.”

Crunching the numbers, Hendy has determined that the 2011 t-index is 39, the same as for 2010. That means that 39 technology companies have had annual revenues greater than $39 million this year.

“To match Australia’s GDP per capita today, New Zealand would need to have 78 companies with annual revenues of more than $78 million that is we would need a t-index of 78,” says Hendy.

Power laws are also found in the natural environment, says Hendy, for example if you compare the biomass of plants versus their density in the bush.

“People have been using the term ‘innovation ecosystem’. I really hated it, but started using it myself. It wasn't until I saw it mathematically, that the TIN100 power law is just like the power law in a forest ecosystem, with big players and small players in the innovation chain, that I felt comfortable using the term,” says Hendy.