TLDR: Should You Invest In Universities—YES

In Rogue Tower damage investments via gold increases not just the individual HD, AD or SD but also the Base Damage making this damage increase a Geometric Progression (damage goes up faster). This is one of the reasons we place towers on higher elevation not just because it increases the range but also the base damage. (Example: a ballista with a base damage of 10 and a SD of 13 has a total of 130 but if you increase the tower to level 2 using SD it now has a base damage of 11 and a SD of 14 for a total of 154)

Universities on the other hand DO NOT increase your base damage but only the HD, AD and SD making it an Arithmetic Progression (damage goes up slower). (Example: a ballista with a base damage of 10 and a SD of 13 has a total of 130 but if your university increases the SD by 1 it still has base damage of 10 and a new SD of 14 for a total of 140)

Universities are EXPENSIVE. On my low run of 8 universities (raising them 9 levels each) it cost 11,200 gold. On my high of 24 universities, it cost a staggering 33,600 gold. Yet it is not just the cost in gold but in the opportunity cost of the upgrade cards (base university card, the first upgrade card adding three research points, the second card adding two research points and the last card adding one research point per university per damage class (HD, AD and SD). On my runs I used all cards available with a low of 2, a high of 4, with an average of 3.4 for all runs.

Universities are very RNG. I upgraded all universities at the same rate for each damage class but would have one class that received significantly more damage for that class than the other classes; the highest differential was 11 and the lowest differential was 3 with an average of 7.6 for all runs.

When looking at return on investment (on my average of all runs), I took the damage of each type 17.8 HD, 19.4 AD and 21.2 SD for an average damage of 20.3 across all types. This is because the university is only applying one type of damage per tower per attack. Taking the average investment of 19,600 gold for the run it comes to 964.7 gold per damage unit.

This might seem like an extravagant expense but if you are applying it to 50 towers it is around 20 per tower and if you have 150 Ballistas it is under 7 gold per tower.

Remember that this damage unit is multiplied by the base damage (for a level 10 Ballista we are now talking less than one gold per damage unit). For the value returned, universities are quite efficient.

The return is not just in increased damage but in the potential 5% critical chance upgrades that apply to all tower types.

Always strengthen the damage of new towers in the later game by at least five levels as it greatly increases the base damage (since the universities are only increasing the individual damage type HD, AD and SD).

Use universities to offset the weaknesses in your tower types for achievement runs. Poison Sprayers are strong on SD but weaker on AD so focus more of your universities on AD. Flame Throwers on the other hand are strong on AD but weaker on SD so focus more of your universities on SD. You get the point.

You do not need universities to win. I have completed encampment only (no ballistas, universities or haunted houses) runs successfully. HOWEVER, the use of universities will make Rogue Tower much easier.

I currently have over 200 hours of game time and will continue to track my results to see if patches or updates radically alter these results.

Special recognition to SeemannTheAssamite and Ohm is Futile for their outstanding guides.