The following is a list of sponsors and their line of business for each English Premier League club at the start of the 2008-09 season. The title is sponsored by Barclays.
Arsenal -- Emirates (airline)
Aston Villa -- Acorns (charity)
Blackburn Rovers -- Crown (paints)
Bolton Wanderers -- Reebok (sportswear)
Chelsea -- Samsung (electronics)
Everton -- Chang (beer)
Fulham -- LG (consumer products)
Hull City -- Karoo (communications)
Liverpool -- Carlsberg (beer)
Manchester City -- Thomas Cook (travel)
Manchester United -- AIG (insurance)
Middlesbrough -- Garmin (navigation equipment)
Newcastle United -- Northern Rock (bank)
Portsmouth -- Oki (printers)
Stoke City -- Britannia (building society)
Sunderland -- Boyle (bookmaker)
Spurs -- Mansion (casinos)
West Bromwich Albion -- T-mobile (telecom)
West Ham -- -- XL* (travel)
Wigan -- JJB (sportswear)
So from the list we have one club beginning the season with a sponsor since gone bankrupt, one now owned by the US government, and one now owned by the UK government. There's almost enough there for a correlation. And that's before one notices that there is still some awkward sectoral exposure for other clubs.
*sponsorship cancelled with bankruptcy of XL.