The Infinite Monkey Theorem and VC Pay

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There is an idea that people should be paid to perform and that if you perform better you should be paid better, particularly if you are in a high level executive position. In academia, at least in the UK, for the most part executive pay looks random.

What do I mean? If you take the table of Vice Chancellor pay data from the THE and make a histogram, you get something that roughly resembles a normal distribution. The histogram can be approximated by a Gaussian distribution in which the average pay for a VC is £244,000 ($370,000) and the standard deviation is £64,000. No it is not perfect, but it is close enough to be remarkable.

There is some tendency for top executive pay to follow university ranking within the UK, but, like the US, it is not as strong as one might like. For example, only 3 of the top 10 paid VCs (2011/12)  lead universities appearing in the top 10 of the 2013 Guardian University Guide. They are: Oxford, Bath, and Exeter. There are also 2 that are unranked. Of the top 10 universities, 2 have VCs paid in the bottom half of the distribution (Durham and Lancaster). While these data indicate some tendency for the VCs of highly ranked universities to be paid better, the stronger trend is randomness.

The other point is that the highest paid university VC in the UK is getting about 4.5 times LESS than the highest publicly funded University President in the US. This too is remarkable.

Conclusions: 

1)  While there is some weak tendency for highly ranked universities to have well paid executives, the stronger tendency is for randomly distributed salaries about an average. Further, I suspect at every university there are pay review committees who have all kinds of tick boxes, incentive schemes, and salary reviews and I am sure they take their roles quite seriously. However, for the most part they could be replaced with a monkey and a Gaussian random number generator. This is a little like the proverbial monkey with a typewriter writing Shakespeare.

2)  Like many of us, VCs do not seem to be paid to perform, they are paid.

3)  Publicly funded University executive pay in the US at the high end is a bit outlandish. 

General comments on the data set: 

Please see the THE document for details on the data and its limitations. This data will be limited by cases of missing data. For the purposes of this exercise where there was an indication of “not stated”,  I have entered a 0. This is similar for what THE has done for the total excluding pension. For the overall I have summed salary, other benefits, and pension.

Selection of the Guardian league table was arbitrary. I have my issues with league tables, but they can provide an index for trends which may be better than nothing.

Pay for performance? It is a myth.

With discussions in the news about CEO pay and its rise relative to average worker pay, I thought it might be interesting to look at Universities in a similar way. There is useful data on HE executive salaries here (for the UK) and here (for the US). The US data is for public universities.

In a reasonable world you might expect a VC at a top 100 university to earn more than one in the same city that is not ranked at all. You might be wrong. League tables are fraught but they are an index and hence useful. Much as I hate seeing long discussions about whether Cal Tech or Cambridge is better and by how much, I accept that there is a difference between an unranked university and a global top 100. 

So, I spent some time trying to align some of this data with data from league table rankings (QS and THE). I haven’t had a lot of time yet so only got through the first page or so of the US data. There is some relationship between base pay and ranking it is weak (explains about 24% of the variance). However, there is a really no relationship between total pay (including incentives) and ranking.

Note: unranked universities appear as 1000. 

There are 5 US universities in the top 20 for highest paid executives which are not ranked in either league table. I do not see how this makes sense. The graph is puzzling.