I have forgotten some of the rules. You might suppose the ‘bot needs to continously accelerate and decelerate for the length of a match. Say 4m/s^2. Take the mass of the ‘bot, and solve for the energy needed. Add in the energy needed for electronics, and any safety factor (x2). After you get how many Joules you need, and a minimum voltage for your motors (or more likely electronics) Shop for a battery that meets the requirements with the minimum weight.
For a 2-minute run, I get 807kJ
Divide Energy (joules) by volts (J/Coloumb) to get Amp-seconds. Divide A-s by 3,600 to get A *hours*, which is a standard rating (curves) for larger cells.