Just because I can and I kind of get bored and want to see stats of things. I decided to turn off use of Alacrity potions (both normal and pet) when I was at zero and started a new shubbie. Then see how many casts I would gain between fresh level 0 shubbie right up to first split (level 32).
3070 Effects of Pet Alacrity(Speed Cast).
1390 Effects of Alacrity(cast speed boosted)
*results may vary due to randomness*