TL;DR

The labels on the mouseover of the upgrade buttons on the Provision House and Barracks are incorrect and should read:

Level 2: "Increases recruiting speed by 50%"
Level 3: "Increases recruiting speed by 66%" or "Increases recruiting speed by an additional 16%"
Level 4: "Increases recruiting speed by 75%" or "Increases recruiting speed by an additional 9%"
Level 5: "Increases recruiting speed by 80%" or "Increases recruiting speed by an additional 5%"

/TL;DR

If math gives you a headache, ignore this next part.

Basically, the current text is incredibly misleading and incorrectly states the percentage change between either Level 1 and the next Level or the current Level and the next Level. Either way one runs the math, the current numbers are not true percentage increases. They are, however, additive divisors. Which, frankly, is far too confusing for the average player and definitely misleading.

IE

An increase from Level 3 to Level 4 is supposed to be a 33% increase in speed. The only formula that uses that number is actually:

Base Speed ÷ (1 + 1.00) ÷ (1 + 0.50) ÷ (1 + 0.33) = New Speed

That's not a coherent percentage formula. It should just have been related to the players as:

Base Speed ÷ Level = New Speed