Fielding percentage and its relationship to wins

There is a certain amount of debate in baseball about how important fielding is. Old school baseball people usually consider fielding to be the utmost importance, while many sabermatricians dismiss it all together (or at least dismiss stats like errors and fielding percentage). So I wanted to look at the past several years in the American League and see if there is any kind of correlation between fielding percentage and wins. In 2011 the rankings were:
1 Tampa Bay 91 wins 2 Chicago Sox 79 wins 3 LA Angels 86 wins 4 Boston  90 wins 5 Kansas City 71 wins 6 NY Yankees   97 wins 7 Detroit 95 wins 8 Toronto 81 wins 9 Cleveland 80 wins 10 Seattle 67 wins 11 Baltimore 69 wins 12 Texas 96 wins 13 Minnesota 63 wins 14 Oakland 74 wins
2010:
1 NY Yankees 95 wins 2 Minnesota 94 wins 3 Tampa Bay 96 wins 4 Toronto 85 wins 5 Oakland 81 wins 6 Chicago Sox 88 wins 7 Baltimore 66 wins 8 Texas 90 wins 9 Detroit 81 wins 10 Cleveland 69 wins 11 Seattle 61 wins 12 Boston 89 wins 13 LA Angels 80 wins 14 Kansas City 67 wins
2009: 1 Toronto 75 wins 2 Minnesota 87 wins 3 Boston 95 wins 4 LA Angels 97 wins 5 NY Yankees 103 wins 6 Detroit 86 wins 7 Baltimore 64 wins 8 Cleveland 65 wins 9 Tampa Bay 84 wins 10 Oakland 75 wins 11 Seattle 85 wins 12 Texas 87 wins 13 Chicago Sox 79 wins 14 Kansas City 65 wins
2008: 1 Toronto 86 wins 2 NY Yankees 89 wins 3 Boston 95 wins 4 LA Angels 100 wins 5 Tampa Bay 97 wins 6 Cleveland 81 wins 7 Kansas City 75 wins 8 Seattle 61 wins 9 Oakland 75 wins 10 Baltimore 68 wins 11 Chicago Sox 89 wins 12 Minnesota 88 wins 13 Detroit 74 wins 14 Texas 79 wins
2007: 1 Baltimore 69 wins 2 Boston 96 wins 3 NY Yankees 94 wins 4 Oakland 76 wins 5 Seattle 88 wins 6 Cleveland 97 wins 7 Minnesota  79 wins 8 Toronto 83 wins 9 Detroit 88 wins 10 LA Angels 94 wins 11 Kansas City 69 wins 12 Chicago Sox 72 wins 13 Tampa Bay 66 wins 14 Texas 75 wins
2006:
1 Boston 86 wins 2 Minnesota 96 wins 3 Oakland 93 wins 4 Seattle 78 wins 5 Chicago Sox 90 wins 6 Kansas City 62 wins 7 Texas 80 wins 8 Toronto 87 wins 9 Baltimore 70 wins 10 NY Yankees 97 wins 11 Detroit 95 wins 12 Tampa Bay 61 wins 13 Cleveland 78 wins 14 LA Angels 89 wins
2005:
1 Seattle 69 wins 2 LA Angels 95 wins 3 Oakland 88 wins 4 Chicago Sox 99 wins 5 NY Yankees 95 wins 6 Toronto 85 wins 7 Minnesota 83 wins 8 Cleveland 93 wins 9 Baltimore 74 wins 10 Texas 79 wins 11 Boston 95 wins 12 Detroit 71 wins 13 Tampa Bay 67 wins 14 Kansas City 56 wins
So is there any correlation? No team that had the worst fielding percentage in the American League had 90 wins in this time (although the Angels had 89 in 06). The '06 Angels were the only team in this period who had the worst fielding percentage and a winning record. However, 3 times the team with the best fielding percentage had a losing record. The team with the worst record in the league averaged being about 11th in fielding percentage and was never better than 7th. The team with the best record in the American League averaged being about 4th in fielding percentage, with no team leading in both fielding percentage and wins. If one looks at one case study, Tampa Bay, one notices that when they were a bad team 05-07, they were near the bottom of the league in fielding percentage. When they have been been good 08, '10-11, they have been around the top in the league (being the best in 2011). When they were mediocre in 2009, they were in the bottom half. A relatively similar story can be told about the Minnesota Twins, while the Yankees and Rangers seem to be exceptions. There does seem to be a correlation between fielding percentage and wins, but there are exceptions and it is not absolute. It does seem to be a general rule, at least recently in the American League, that the better fielding percentage usually leads to better win percentage.