All of the below theory must be laced with probability and statistics, especially expected scores for batsman and expected strike rate for bowlers. I'm not good at probability, so if you are gonna whine, take the list and improve it and cite me.
Swing bowling is applied physics, particularly fluid dynamics.
Spin bowling is applied psychology. : )
(Yes, I used to bowl leg-spin.)
Pace bowling is just simple geometry.
You need many skills for the Captaincy, most of which are NP hard problems. However, one easy one is field placement (reactionary), which is basically applying the pigeonhole principle. Anything else is tougher. Field placement (strategic) is a graph coverage problem, while bowling and batting orders are either combinatorial setups or versions of the secretary hiring problem. Finally, the twin issues of declaring the innings or imposing the follow-on are types of knapsack problems. (Are they really? Bite me.)
Wicket-keeping is an extrapolation problem. Get to where the ball will be. In fact you could say that for most fielding roles, but the time scales for wicket-keeping are harshly small. Probably only the first slip, silly point and short leg compare.
Batting! Oh the variations. Timing is resonance: if you've ever done it right then you know what I mean. Feels like silk. Figuring out what delivery is next is pattern recognition: look at tons of videos of Murli and see if you can pick the doosra (I can't, at least not from the TV perspective). The angle of the shot and the direction are geometry plus sampling the field.
Chasing: Deciding when to be aggressive or not is the knapsack problem. Setting: Deciding when to be aggressive or not is a expected run total maximization. Running between wickets is actually really hard. Coordination, extrapolation, tons of ACKs sent back and forth. The systems folk can handle this.
Umpiring is just a look-up table and therefore will be automated soon (pitched inside? hit inside? going onto the stumps?). Physios are the only bio folk in this mess.
And commentators? No theory there: just a black art.