Heavy plow pay-off table.

Since the Burgundians came out I figured I would demonstrate how heavy plow actually pays off. You can make this analysis more specific/accurate but the general pattern will remain. That is to say the numbers would change but the resource/time-equivalent difference between each column along each row would be very similar.

Imagine some civs: each researches heavy plow 8 farms sooner than the next. Assume villagers gather from the farm at a net rate of 22f/min. For ease of display I will group them by 1/3rd the reseed time of a heavy plow farm because it makes the reseed times line up nicely. Ignore reseed build time. This assumes you need the same food income rate (because I'm ignoring the heavy plow +1carry) in each column.

The following table shows the wood accumulated (+125 food which is lumped in for the tech) at each time step relative to the civ which researched heavy plow at some time, normalized to t=0.

There are two key patterns to notice, before and after the alternative civs research the tech. The before research is pretty straightforward. It's a back and forth of +250/-230/-480 every ~5.5min or so for a bit depending on when the enemy upgrades. Moral of the story here is unless your build can accommodate at least 8 farms after you spend the 250 to upgrade but before you would get it in castle age normally, probably not the best idea.

The key pattern to notice after everyone has researched is how many times -480 appears in each column. You'll notice in the first delay column it appears every 1 of 3 rows, in the second delay column every 2 of 3 rows, and in the 3rd delay column it appears every row. How you interpret this is that your opponent will be perpetually reseeding their farms before you. This means every 17min you get a resource advantage of 480 wood for 5.75 / 11.25 / 17 min.

Averaging that out nets you a 480 * 5.75/17 = 162 , 480 * 11.25/17 = 318 or a 480 perpetual wood bonus.

Note that in-game people aren't going to put off heavy-plow for like 22.5min, so columns 2 and 3 don't matter much except to make the pattern explicit. So generally each upgraded farm you plant before the opponent researches heavy plow will give you a 60 wood bonus in 11.25 min and this occurs for 5.75min every 17min perpetually. This averages out to 20 wood per farm.

Random Note: I've seen SOTL's video on horse-collar which did a similar analysis to this but IMO he messed up big time by hand-waving away the temporary nature of the payoffs. The bonus for this line of eco upgrades is inherently temporary and surges/wanes with cycles of the farms. At the very least you have to average out the bonus to give a proper representation of the effect.