Helpers help most in photo finishes

Caveat up front: I'm focused here on marginal value of donations / helping out, and ignoring many important political effects like "everyone joins together to create a big change."

Last year, K and I donated a lot more than usual to political campaigns. A lot of it was focused on trying to help the Democrats take the US Congress. I had pretty high hopes, going off predictions like 538's.

When the first set of results came in, Democrats had done worse in Congress than I had hoped. This made me wonder: had I misunderstood the situation, and donated to something that was actually pretty unlikely to work? The models hadn't predicted the presidential election being as close as it was either, which didn't help. I felt a little burned, like maybe I'd overvalued donating -- it was still an honorable thing to do, but looking kind of bad from the "help people with $" perspective.

After Democrats took the Georgia runoffs and won control of Congress, I felt waaaay better -- we won! Donating was an incredible idea!

...

Uhhh, flipping back and forth like this can't be right -- what's going on here?

This situation almost seems artificially set up to illustrate this lesson, which I think is basically right:

If you're contributing a little to a win-or-lose group outcome X, your help was most valuable when X is either just barely achieved, or just barely not achieved.

How helpful you were is independent of whether X is achieved or not -- it all comes down to how close the call was. 

In other words: if the Democrats are set up to win by a lot, helping them win by a little more isn't very valuable. Likewise if they are set up to lose by a lot, and you help them lose by a little less -- not very valuable. But when it's really close, it means your contribution has a better chance of pushing them over the finish line.

Right after those first Congressional results came out, when I thought I had been overoptimistic and Democrats would probably lose Congress, I drew exactly the wrong lesson! I should have said "wow, my help was even more valuable than I thought -- look how close it was! Thank goodness I donated."

Democrats "losing" the first round of the Congressional election is weak-to-moderate evidence that the models I was using were too optimistic about their chances, and I should take that into account in future predictions. But counterintuitively, my models being too optimistic means I undervalued political donations, if anything. (An easier case to illustrate this principle: if your model of plane crashes is too optimistic, you will undervalue efforts to prevent them.)

...

Lessons:

1. *All else equal,* you maximize efficiency by aiming for your "marginal contributions to group outcomes" portfolio to have a 50% win rate -- if you're always contributing to things that (win / lose), you should swap them for things that are (less likely / more likely) to succeed in order to make a bigger difference with the same amount of marginal help. 
2. Be careful when reflecting on whether things were worthwhile -- there's some counterintuitive interplay between having been overly optimistic / pessimistic, and overvaluing / undervaluing marginal contributions.