Really influence is a commodity which can and is bought and sold (see enorsements) and money may be used to purchase it but the two aren't identical. You can't just compare budgets and pick a winner unless both have comparable strategies and influence.

It brings to mind a quixotic approach of trying to value influence quantitatively. Like trying to figure out how much value could be extracted from a celebrity endorsement.

Money, and the threat of money are both factors. There are bigger fish than Bloomberg.

Because Bloomberg is not the only one with a lot of money trying to get the presidency.