You will save an expected number of animals

Is that "expected" in the mathematical sense? As in, probability of my actions having the consequence that N animals are saved, times N? How do you work out that the numbers work out in such a way that N equals the number of animals I would have eaten? That strikes me as an unlikely coincidence.

As a rough basis for back-of-the-envelope calculation, assume I eat 200g of meat per day. I estimate one cow provides about 250Kg of the type of cuts I eat. That means I have so far in my life eaten about 4 cows. (Simplifying assumptions: I eat only cow meat, have eaten the same amount constantly for 40 years. We could work this out in more detail but I'm interested in orders of magniture here.) Perhaps five to ten times as many hogs.

Cows don't seem to lead a particularly horrible life. True, this life is cut short at a fraction of their natural lifespan, but on the other hand cows don't seem to form explicit life plans or intense emotional attachments to other members of their species beyond rearing. I worry about the hogs a little more, but it's also the more affordable meat (the disutility of not eating them is larger).

So, we're talking about a major lifestyle change, traded for a reduction in animal suffering which is only probable, not certain, and which tops out at a small number of individual animals.