I think you need to take a step back and add some context here. Even though I think this whole penalties conspiracy theories is a crock of shit, comparing Liverpool’s number of penalties to West Ham’s over the last 20 years or so is a bit strange. Even if they have been in the league the same amount of time, that doesn’t mean anything. I would naturally expect the bigger teams to have more penalties than the lesser teams simply because they will statistically attack more, have more touches in the opponents area and therefore invite more fouls. I highly doubt West Ham’s attacking statistics are anywhere near Liverpools in that period.
Crock of shit? Obviously a bit strange? Without the bias, whats left isn't anything but a conspiracy it's reality. They haven't won the Premier League more than one time. One time! Just recently. They have attacked a bit more than West Ham maybe, and in that context, as I pointed out what about Babel? The guy mysteriously disappeared after getting a lot of penalties, I even remember Scousers proclaiming his talent to be bigger than Ronaldo's at one point. So why the sudden change, why leave so abruptly if something wasn't going on at that time?
Sure, they have probably attacked more than West Ham overall, but why haven't West Ham more penalties then when Andy Carrol also played for Liverpool who has a lot of penalties. Andy Carrol was Liverpool's biggest signing at the time, yet when West Ham bought him they got him for half the price, and what do you know, they also got half the penalties. Coincidence? No.
Also, They have had some legendary players that has not been getting the credit they deserve for diving their way into first place of the PL penalty league throughout the years, like Gerrard. He is probably responsible for cheating 60% of the 86 undeserved penalties and gotten away with it because of his standing in the England national team ahead of class acts like Scholes and Lampard. Now, would you be willing to hazard a guess as to why he was picked ahead of superior midfielders on countless occasions for the national team? One word, non penalties don't win world cups.