Summary
– Arsenal have been awarded more penalties than any other Premier League club in 3 of the last 8 seasons. City have been awarded more in 2 out of 8 seasons. United and Chelsea have been awarded more in 1 of the 8 seasons.

– Arsenal and City have conceded more penalties than any other Premier League club in 1 of the last 8 seasons.

– Arsenal have had the most penalties awarded for and against them in the last 8 seasons.

– Chelsea have had the fewest penalties awarded against them in the last 8 seasons.

– Over 8 seasons, there is a difference of 11 penalties awarded for between Arsenal and United, or 1.4 a season. There is a difference of 17 penalties awarded against between Arsenal and Chelsea, or 2.1 a season. Essentially, the difference is negligible so any argument suggesting the refs give preferential treatment to one club is pretty soft.

Disclaimer
– This table is just a comparison of these five clubs. The clubs which had the most penalties for and against have been included to give some perspective.

– How many penalties each club is awarded doesn’t prove anything as it is the quality of the decisions that would determine any preferential treatment.

– Attacking/dominating teams are going to spend more time in their opponent’s box than less successful teams. They are also less likely to have the opposition in their own box. This can have bearing on the opportunity for a penalty to be awarded for or against.