Many Premier League sides made some big purchases this summer. However, some paid more than they should have.

With the summer transfer window closed, many have begun analyzing the moves made by England's biggest clubs.

It was a record-breaking season for the 20 teams in English football's top flight, with an estimated spending of £850 million, more than has been ever spent in any transfer market to date.

England's "Big 5", namely the quintet of Arsenal, Chelsea, Liverpool, Manchester City, and Manchester United were all quite busy, with each making at least one notable signing over the past three months.

However, now that the dust from the market's frenzy has settled, some interesting facts have come out regarding some of the clubs' purchases.

As per the CIES football observatory, Manchester United, who set a new transfer record by signing Angel Di Maria for £59.7 million, actually were on the losing end as they paid over £20 million more than the 26-year-old's true value of £35.8 million.

Meanwhile, Liverpool, according to reports, not only paid too much for the bulk of their new players--save for Mario Balotelli--could have also gotten more money for their talismanic striker Luis Suarez.

And, the overspending isn't just limited to the Premier League, as can be seen in this graphic below:

Manchester United, PSG, and Real Madrid among the sides who paid too much for their new players:

And the club that did the best during this summer? Chelsea. Their two big signings--Diego Costa and Cesc Fabregas--were gotten for cheaper than the players' values, as was Loic Remy. And, to top it off, they successfully transferred defender David Luiz to PSG for a mind-boggling £50 million.

Come May, it will indeed be interesting to see how these clubs' investments pay dividends in terms of clinching the league title--and perhaps other silverware--by the end of the season.