Baseball_Cases

I was approached one day by a client who requested a particular Baseball simulation. The objective was to acquire a distribution of "game states" via Monte Carlo-ish simulation with N number of runs.

It turns out that there are particular "game states" in Baseball. An example of a "game state" is having one player on first base and nobody on second or third with two outs total (kudos for making "Who's On First" jokes as you read this). There are a finite number of game states that can emerge after the pitcher throws the ball (IMPORTANT: this does NOT include stealing bases or pitching balls yet). I'll enumerate the possibilities explicitly below:

• 1. Batter gets a strike.
• 2. Batter goes to first, first goes to second.
• 3. Batter goes to second, first goes to third.
• 4. Batter goes to third, first goes home (1 point).
• 5. Batter hits a home run, first goes home (2 points).
• 6. Batter goes to first, first goes to third.
• 7. Batter goes to first, first goes home (1 point).
• 8. Batter goes to second, first goes home (1 point).

After one of the above valid events (valid for the explicit example aforementioned) occurs, another game state emerges. In other words, these games states are emergent in the game of Baseball.

The question then is to figure out which game state is the most common. One way to answer this question is by using Monte Carlo simulations. My client gave me a list of all the game states labeled with a number from 1-25 (where state 1 is 0 outs and empty bases and state 25 is 3 outs without regard to the bases). Included in this list was all the possible game states one could travel to from the given game state. For example, all the possible accessible game states from state 1 are 2 (batter goes to first), 9 (strike out), 3 (batter goes to second), and 1 again. (You might've noticed that there is no way to access the "batter goes to third" game state. That's correct. Again, this is what the client provided to me.)

The approach was to simply construct a DataFrame using Pandas and traverse it, incrementing a counter every time a particular cell was reached. That was easy enough to set up as it only requires turning a CSV file into a Pandas DF. The rest of the iteration can be understood from the code.

I ended up sending these results to my client:

	2	3	4	5	6	7	8	9	10	11	12
1	29069	58213	87050	115615	144968	173948	144954	116058	86528	58248	29023
2	8346	16606	24827	32967	41537	49304	41103	33053	24751	16333	8359
3	1702	3504	5317	6995	8750	10454	8634	7130	5301	3512	1804
4	0	0	0	0	0	0	0	0	0	0	0
5	1915	3773	5771	7676	9427	11346	9458	7589	5731	3792	1918
6	1262	2592	3798	5168	6369	7667	6406	5185	3822	2562	1224
7	632	1401	2023	2654	3343	3909	3271	2717	2017	1343	694
8	629	1319	1961	2545	3418	4024	3343	2621	1904	1317	652
9	19668	39523	58488	79019	98449	118159	97899	78800	59069	39545	19687
10	10465	21272	31404	42193	52659	63372	52918	42215	31561	21379	10605
11	2529	5133	7641	10023	12509	15104	12607	10059	7547	5038	2510
12	0	0	0	0	0	0	0	0	0	0	0
13	3730	7337	11074	14708	18657	22283	18302	14759	11154	7344	3585
14	2430	4909	7554	10100	12445	15024	12385	10069	7223	5069	2489
15	1391	2602	4133	5365	6841	8178	6707	5553	4119	2696	1385
16	1547	3266	4990	6581	7935	9822	8115	6522	4943	3249	1510
17	13808	27441	41645	55164	68954	82748	68887	55591	41243	27673	13971
18	11209	22635	33653	44979	55936	67110	55721	44273	33557	22180	11039
19	2800	5573	8450	11456	14148	16942	14250	11462	8604	5740	2864
20	208	428	639	844	1094	1291	1096	853	643	430	206
21	5065	10258	15123	20115	25128	30449	25156	20252	15352	10187	5196
22	3490	6886	10540	13841	17265	20770	17157	13726	10347	6950	3461
23	1918	3805	5826	7697	9713	11392	9555	7613	5755	3855	1924
24	2509	5135	7926	10406	13080	15742	13090	10402	7897	5219	2652