The top ten teams who have hit the woodwork were all in the top eleven in terms of both success (counted as points per game) and total goals scored. The one exception is Blackburn Rovers, who hold tenth place in both, with 927 goals in the Premier League era, which is only ten more than West am in 11th place.
This is proof that more successful teams have more shots, and are therefore more likely to hit the woodwork more often.
There are some trends – a few of the sides are clearly unluckier, such as Liverpool who do indeed have a higher ratio of hitting the woodwork compared to goals, an average of 7 goals per hit of the woodwork. West Ham. But Manchester United, Aston Villa and Newcastle cannot count themselves unlucky with an average of 11-12 goals for every shot hitting the woodwork.
It would be great if further research could be done on the number of total shots, and other general attacking statistics since the start of the Premier League. Another factor which also must be considered is the number of seasons which have been played in the Premier League. A team such as Blackpool, who have only been in the Premier League for one year would never be considered an unlcuky team. In fact, the sides which make it have all been in the Premier League for the most seasons.