Does Firaxis know how to do math?

A car driving 40 mph will cover 40 miles in 60 minutes.
A car driving 50 mph (25% faster) will cover 40 miles in 48 minutes.
48 minutes is 80% of 60 minutes. So a car driving 25% faster (a 25% bonus to speed, you could say) gets to the destination in 20% less time.

The 25% faster car would not make it in 45 minutes, as your math would imply.

The Glory of Rome gives, as a special ability, "25% production towards any buildings that already exist in the capital".

The building costs 100 hammers on turn X. The building is completed in Rome at the end of that turn. On turn X+1, the building should get a "25% production". 25% of 100 is, to me, 25 hammers.

The ability does not say "gets built in a shorter time". It says "gets 25% production". 25% production of 100 cost is 25, not 20.
 
The Glory of Rome gives, as a special ability, "25% production towards any buildings that already exist in the capital".

The building costs 100 hammers on turn X. The building is completed in Rome at the end of that turn. On turn X+1, the building should get a "25% production". 25% of 100 is, to me, 25 hammers.

The ability does not say "gets built in a shorter time". It says "gets 25% production". 25% production of 100 cost is 25, not 20.

In your 'Glory of Rome' example, the hammers required to build the building is irrelevant. It is the hammers produced in the city building the building that is rlevant.

So, if your city produces 80 hammers, a 25% bonus would be 20 hammers. the 20 hammers contributed 20% of the total cost, but you got a 25% bonus.

Consider a more realistic city with production of 20 hammers... you would now build the building in four turns of 25, rather than 5 turns at 20. You still got the same 20% of total, contribution, and a 20% savings on the total time. (1 out of 5 turns saved)
 
The same problem crops up elsewhere. As Rome, if you've got a building in your capital, you get a 25% bonus towards its construction in other cities. So, turn X, my Granary was 1 turn from completion in Rome. It was a cost of exactly 100 in one of my other cities. I didn't start building yet because I wanted that bonus. Next turn, Rome was finished and I turned to the other city. The new cost for a Granary? 80 hammers. Last time I checked, 25% of 100 was 25, not 20.

They do the math as 100/1.25 = 80 hammers.
 
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