To the best of my understanding, a Markov Chain is a type of Monte Carlo simulation, which means it uses a (pseudo) random number distribution to simulate stochastic (meaning, non-deterministic) processes. The Markov distinction is that it requires a discrete chain of outcomes.

Baseball example:
A given hitter has a 50% chance of putting the ball in play, 20% chance taking a walk 30% chance of striking out. (3 discrete states)

Randomly generate a number, n, between 0 and 1: if n<.5, in play, .5<n<.7, walk, n>.7 K.

For the sake of this example our hitter will put the ball in play. For the super simple case we’ll just use his BABIP and do the same random number generating method above. You could also simulate to what field the ball is most likely to go to, but because the places a ball can land is continuous/non-discrete, I’m not sure you’d want to do that.

The result is either a base runner or an out.

Once the outcome of this hitter’s at bat is decided you can store this current state in a matrix and simulate what happens with the next batter. You now have to account for the batter and base runner (Pickoff’s, DP, steals, etc.). The matrix is just your bookkeeping.

You would repeat process for thousands or hundreds of thousands of games and see what the most likely outcomes are. You’ll want to store you’re final results in a separate matrix and then plot them as a histogram to figure out the frequency of certain events.

And boom goes the dynamite.