Fernando Torres scored 81 goals in 142 games for Liverpool FC. In 2011, he was sold to Chelsea for a rumoured £50 million and paid a reported £140,000 per week. For Chelsea, Torres has scored 32 goals in 125 games, a loss of form that has become the subject of many terrace songs.

What has this got to do with investing? Well, there’s the relentless wage inflation among players and the concurrent impoverishment of clubs and fans, for one. The parallels with banking – where star traders and top executives were paid millions in bonuses while dividends to shareholders were slashed – are obvious.

Then there’s the “Torres effect” in executive pay. My colleague Merryn Somerset Webb postulated last week that the ever-widening gulf between pay at the top and the pay of average workers is not only bad for social cohesion and the economy, it’s bad for investors too. This is because it encourages a focus on short-term performance metrics that trigger bumper payouts to managers.

The argument is a popular one, because it’s intuitively obvious. But is it quantitatively robust? And more importantly, is it investable? Can we pick shares based on boardroom pay levels? These aren’t easy questions to answer, partly because executive pay is hard to measure and because so many factors drive company and share price performance. Each option grant and long-term incentive plan is different from the next. And much of the research that links pay and performance is based on the US market.

But the annual Pay Dirt survey, from Glass Lewis, gives an idea. The corporate governance consultant has a complex model that compares all aspects of executive remuneration with company performance to come up with a list of overpaid and underpaid chief executives.

Their conclusion is stark: "Simply put, companies in the underpaid 25 lists maintain high financial performance while providing executive pay in the bottom percentile of their peers, while companies in the overpaid 25 lists award extravagant compensation packages despite marginal – or in many cases, distressingly poor – corporate performance." Top of the dogs list for 2012 was Hewlett-Packard. Citigroup came second. Abercrombie & Fitch and Lockheed Martin were among the repeat offenders. Overall, Glass Lewis found that among the "underpaid 25" of the S&P 500, the median earnings growth was 29.7 per cent and the median share price gain was 17.5 per cent. Among the "overpaid 25", those figures were minus 1.24 per cent and minus 12.3 per cent.

You can quibble with the methodology. Compensation packages can be distorted by big one-off awards. Earnings per share are easily manipulated. Chief executives don’t control the share price. A year is a short period over which to measure performance. But another study* I came across used a longer timeframe – 1994 to 2011 – and different measures of return.

Its conclusion was the same; those who paid their executives the most relative to their peers went on to earn “statistically significant abnormal returns” of between -4.67 per cent and -5.83 per cent in the following year. Over the following three years, the underperformance becomes even more marked.

The explanation the authors gave for the underperformance was not a myopic focus on key performance indicators. It was overconfidence. An overpaid chief executive starts to believe in his own infallibility and becomes prone to making grand value-destroying acquisitions or big strategic bets that go wrong. This finding corroborates another US study which found that companies run by chief executives who’d won major business awards tended to underperform in the subsequent two years.

I can't claim to know a great deal about the companies in the Glass Lewis "overpaid 25" list. However, the company used a simplified version of its US model to look at UK firms. Among its "notable pay-for-performance disconnects" – based on 2012 remuneration reports – were RSA and Aviva (both subsequently cut dividends), WPP (where performance has been good, but pay has been stratospheric) and Barclays (based on the lavish awards to former chief Bob Diamond).

Glass Lewis also looked at bank chief executives' pay and performance; top of the disconnect list was Citigroup's Vikram Pandit, who presided over a 90 per cent share price decline but still left substantially enriched.

The message seems clear. Star chief executives on lavish packages don't guarantee share price outperformance any more than star strikers guarantee goals and trophies. And when it comes to picking your investment dream team, it's best to avoid the Torres of the world, and look instead for the Bentekes and Michus (total cost £9 million and 43 goals between them this season). – Copyright The Financial Times Limited 2013

* Performance for Pay? The relation between CEO incentive compensation and future stock price performance (Michael Cooper, Huseyin Gulen, Raghavendra Rau, March 2010)