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Bookmaker William Hill has warned that empty sports stadiums are hitting its profits by producing a string of unpredictable results at fixtures being played behind closed doors.

Bookies expect to be able to estimate the likely winners of sports fixtures, in order to set appropriate odds. But the fact that sport has been played without crowds and the psychological influence of fans on players, has given rise to some shock results.

In the Premier League, for instance, last season’s runaway champions, Liverpool, were thrashed 7-2 by Aston Villa, who spent much of the 2019-20 campaign battling relegation. William Hill said it expected the unpredictable results to continue.

“As a result, we continue to see volatile gross win margins, and we would expect this situation to continue,” it said.

The bookmaker, which is the subject of a £2.9bn takeover by the US casino company Caesars, said betting income was is gradually returning to pre-Covid levels, but still reported third-quarter revenues that were 9% lower than the same period last year.

The result was a significant improvement on the first six months of the year, when it took 32% less from punters than in the first half of 2019, due to the cancellation of live sport and the prolonged closure of high street shops.

William Hill began the year with 1,533 shops and was already shrinking its bricks-and-mortar estate as customers moved online, along with managing the impact of a government-imposed reduction in maximum stakes on lucrative fixed-odds betting terminals.

It operated 1,414 shops during the third quarter as it moved the majority of its estate back into action following lockdown restrictions and said like-for-like sales were just 2% below last year as punters returned.

But it said regional lockdowns such as those being imposed across the UK would hurt business.

A four-week lockdown of 100 shops would wipe £2m off operating profits, it said. At present, 10% of its retail estate – about 140 shops – is located in areas where the Covid alert level is classified as “very high”, signalling an ongoing drag on profits.