There has been much analysis and discussion about when the best time to research Wheelbarrow is.
People have discussed this topic on Reddit, and there is a video from SOTL on the subject.
This technology is difficult to analyze because it improves all resource gathering rates, requires town center time to research, and increases speed for villagers, which can be hard to quantify.
To better understand this issue, I conducted an experiment that mimicked a real game situation.
I tested two scenarios: one where Wheelbarrow was researched just before Castle Age, and one where it was researched right after.
The experiment was conducted with three different strategies (Scouts into Knights, Archers into Crosbowmen, and Drush into Fast Castle) and the results showed that it was better to research Wheelbarrow before Castle Age for the first two strategies.
However, the Drush into Fast Castle strategy showed that it was better to research Wheelbarrow after Castle Age.
Additionally, I found that if the goal was to prioritize certain resources or buildings, it may be better to research Wheelbarrow after Castle Age.