"I am unsure how buybacks affect future returns. Is there an equation that shows the long term expected value of buying back shares?

A buyback done at fair value does not change the value of the continuing shares at all.
Any buyback done above fair value reduces the value of a continuing share.
Any buyback done below fair value increases the value of a continuing share.
So much, so obvious: it's the same with buying any other stock. Bad if you overpay, good if you underpay."

Jim, question for you..... In the case where a company pays a dividend do buybacks also have the added value of saving the company money because you are not paying the dividend on retired shares? Now obviously Berkshire doesn't pay a dividend but Warren has said it is highly likely we eventually will so do you think this could also be part of the reason for continuous buybacks at a fair price? Considering Berkshire shareholders tend not to sell our shares perhaps he is making it easier in the future to pay a dividend while reducing the cost by retiring shares now? Or am I overthinking this which is also entirely possible? :-)
:-)