I agree that there's an exploration-exploitation tradeoff, but for what you specifically suggest wouldn't you presumably just normalize by sample size? You wouldn't allocate based off total conversions, but rather a percentage.
Or in the above scenario option B performs a lot better than option A but only with the sale going, otherwise option B performs worse.
We weren’t at the level of hacking our users, just looking at changes that affect response time and resource utilizations, and figuring out why a change actually seems to have made things worse instead of better. It’s easy for people to misread graphs. Especially if the graphs are using Lying with Statistics anti patterns.
The average base rate for the first variant is 5.3%, the second is 6.4%. Generally the favoured variant's average will shift faster because we are sampling it more.
While it's non-obvious this is the effect, anyone analyzing the results should be aware of it and should only compare weighted averages, or per distinct time periods.
And therein is the largest problem with A/B testing: it's mostly done by people not understanding the math subtleties, thus they will misinterpret results in either direction.