Probability Calculation
Last updated
Last updated
Using a approach to simulate 1,000,000+ games with the given probabilities for singles, doubles, triples, homeruns and outs, the expected score after 3 outs is approximately 4.65 runs.
To calculate the expected score we built a model that considers the complexity of baseball's scoring rules, including advancing runners' states and the effect of different hits on scoring opportunities. In addition to extensive simulations, we tested manually to achieve the same results included in detail below.
An overview of the approach:
Singles (33.5%) allow the batter to get to first base, potentially advancing any runners already on base.
Doubles (16.75%) allow the batter to get to second base, advancing runners on base potentially to home, depending on their starting position.
Triples (10.0%) allow the batter to get to third base, typically scoring any runners that were on base.
Home Runs (6.70%) score the batter and any runners on base.
Outs (33.0%) move the inning closer to its end without directly contributing to the score.
Normal baseball scoring has somewhat complex logic, but given the straightforward probabilities & limited amount of actions in Basedball🎩⚾️, determining outcomes becomes a relatively simple scenario to simulate. Upon simulating a large number of games (1M+, varying ranges) with the given probabilities our model consistently provided ~4.65 to be the expected score per game.
In addition to simulation testing we've manually tested thousands of games and were met with a nearly identical average result of 4.68. Below we've included the logs of a random set of an actual 100 games individually played, set to 100 $degen games.
This all leads us to believe 4.65 runs per game is a reasonable estimation.
1
13
260
2
9
180
3
0
0
4
7
140
5
9
180
6
2
40
7
0
0
8
4
80
9
0
2
10
3
60
11
6
120
12
0
0
13
4
80
14
4
80
15
11
220
16
5
100
17
3
60
18
4
80
19
3
60
20
4
80
21
0
0
22
6
120
23
4
80
24
10
200
25
2
40
26
7
140
27
2
40
28
7
140
29
4
80
30
0
0
31
1
20
32
18
360
33
8
160
34
12
240
35
0
0
36
2
40
37
1
20
38
0
0
39
8
160
40
9
180
41
6
120
42
3
60
43
2
40
44
8
160
45
8
160
46
2
40
47
0
0
48
10
200
49
0
0
50
0
0
51
6
120
52
4
80
53
0
0
54
4
80
55
2
40
56
1
20
57
4
80
58
4
80
59
4
80
60
24
480
61
7
140
62
7
140
63
3
60
64
6
120
65
5
100
66
5
100
67
1
20
68
3
60
69
2
40
70
3
60
71
9
180
72
0
0
73
0
0
74
10
200
75
0
0
76
6
120
77
24
480
78
1
20
79
4
80
80
0
0
81
2
40
82
0
0
83
11
220
84
3
60
85
11
220
86
3
60
87
0
0
88
1
20
89
11
220
90
5
100
91
3
60
92
3
60
93
1
20
94
5
100
95
0
0
96
3
60
97
6
120
98
8
160
99
5
100
100
7
140