The report that the total earnings of directors of FTSE 100 companies has risen by 49 per cent in the past year has caused a huge outcry. Certainly, when set against the experience of the average salary-earner, this increase appears hard to justify. Nobody, indeed, seems to have tried very hard.

There are, however, several points that can be made. First, the survey by Income Data Services does not show huge increases in basic salaries. These have grown by a relatively modest 3.2 per cent in the past year.

Where the big gains have been made is in bonuses earned during the year, and in gains in value of long-term incentive plans made on share options exercisable  during the year.

This is important because membership if the FTSE 100 depends upon the value of the shares of a company in issue. Each year there is a big turnover of companies entering and leaving the index. In the past 12 months entrants have included IMI, Resolution, Tomkins, Weir, Wood Group, ITV, Hargreaves Lansdowne, Tate & Lyle, Ashmore Group and Bunzl.

These companies have ousted others because their total value has grown, which means that their share price has increased. Incentive plans are often based on share performance, so directors of the new FTSE entrants are likely to have done well, certainly better than those of companies that have fallen out of the index. They have gained either real or paper increases on the same share price rises that put them in the FTSE 100 in the first place.

Comparing rewards of FTSE 100 directors year to year is not, therefore, comparing like with like. If you examined the rewards of the directors of the the companies that made up the FTSE a year ago with the same 100 companies today, the figures would be very different. An index that rewards size,  combined with incentive schemes that are targeted at achieving growth, almost guarantees increases in the rewards paid to directors.

Finally, there is a huge difference between mean and median figures for the increases. The mean – and the figure that generated the fury – is 49 per cent, but the median is 16 per cent. The ratio between these two is a measure of how skewed the distribution of increases is.

When a median is only a third of a mean, it tells us that a very large proportion of the increased rewards is going to a very small proportion of the directors. It means, roughly, that a third of the increases in rewards is going to about 1 per cent of directors, and that two thirds is accounted for by about 10 per cent.  

Close examination of company annual reports could identify who these people are. Some are likely to be entrepreneurs who started their own company, grew it successfully until it achieved FSTE 100 status, and are now cashing in. Indeed, since IDS  counts unexercised share options as part of the rewards, paper gains are included, so it is not even necessary to cash in. Comparing them with the directors of companies that have shrunk in relative terms and disappeared from the index does not tell us very much.

None of this is to argue that remuneration committees may not have been overgenerous. But companies have been encouraged for years to motivate their directors by tying rewards to share price performance, since that also benefits the investors they are there to serve.

Nobody should expect salary earners who have no such options at their disposal to find this very consoling. The gap between boardroom pay and that of employees is huge. But it’s important not to be driven to fury, or to unwise legislation, by headlines that fail to represent accurately what’s going on.

The Institute of Directors today released its annual pay survey, which questioned 1,500 directors of large unlisted companies or small and medium sized enterprises. This showed that 46 per cent had had either a pay freeze or pay reduction in cash terms in 2010, while the other 54 per cent had had increases averaging 2.5 per cent.

The survey also found that the average basic pay of a managing director in a small company (turnover up to £5m a year) was £70,000; in a medium sized company (turnover up to £50m a year) it was £100,000; and in a large company with a turnover up to £500m a year it was £128,000.