Everton and Crystal Palace have scored 40 and 36 goals respectively. Man United, Liverpool and Chelsea have scored a total of 204 goals or an average of 68.
Despite this - Palace alone, have got as many penalties (9) as United, Liverpool and Chelsea combined. While Everton have got 8 penalties.
So a bottom club and a mid-table club who can't score goals - get roughly 1 penalty every 4 games. While 3 of the best clubs in the country - who probably spend a lot more time in the opponents penalty area - get one penalty every 12 games.
I know statistics rarely tell the true story - but I always find it a bit strange when the topclubs are far behind other clubs in penalties awarded
I feel a reason for this is that referees know that if they wrongly award a top club a penalty, or wrongly miss a call for a team playing against a top team it is blown up a lot more in the media than the opposite cases. A good example of this is when we didn't get a penalty against West Brom, and it was hardly mentioned, compared to when Bournemouth didn't get a penalty against us, and it was the main talking point after the match.
You are just trying to build a story when there is none. The thing is the number of penalties awarded is so few that you cannot draw any significant statistical conclusion from that. For e.g., the average number of penalties awarded is between 4 to 5. there are number of clubs who have been awarded just below average, like 3 penalties. Over the course of season, there could easily be 1 or 2 one off situations/decisions that might comfortably lead these same below average club to above average (in terms of penalties awarded). I remember discussing this topic in Talking Reds in 2013/14 season where Liverpool, Chelsea and City were awarded highest number of penalties closely followed by Spurs and United.
If we want to see if there is a trend in penalties, then we need to analyze good number of years. You can make a weak case for few expected trends but its not consistent enough. For e.g., a team who spends lot of time in opponents box being awarded more penalties - Man City in last few years. A tricky player earning more penalties like Zaha for Crystal Palace. A team that is good in counterattack being awarded more - like Leicester in last few years. A team that plays with high line conceding more - like Arsenal conceded some 10 penalties in 13/14 I think.
Referres are trained not to be biased towards bigger club, and at the same time, not do the opposite and punish them. They seem to make some wrong calls, some for and some against big clubs, so over the season it will be normalized.
Only trend that is significant in penalties is Home teams are awarded more penalties (around 60%) than away teams (around 40%).