I can estimate the head-to-head
performance of two teams from their win percentages.
If a is the win percentage for Team A
and b is the win percentage for Team B, then the probability of Team
A beating Team B in one game can be estimated as a * (1 – b) / [ a
* (1 – b) + (1 – a) * b ] .
In my last post, I estimated the win
percentage for the 7 teams in the league based on the expected runs
for and against for each team.
I can now estimate the probability of
each team winning in head-to-head competition.
The table below shows these
calculations.
0.765 | 0.562 | 0.521 | 0.456 | 0.429 | 0.425 | 0.364 | ||
A | B | C | E | G | D | F | ||
0.765 | A | 0.500 | 0.717 | 0.749 | 0.795 | 0.812 | 0.815 | 0.851 |
0.562 | B | 0.283 | 0.500 | 0.541 | 0.605 | 0.631 | 0.634 | 0.692 |
0.521 | C | 0.251 | 0.459 | 0.500 | 0.565 | 0.592 | 0.596 | 0.656 |
0.456 | E | 0.205 | 0.395 | 0.435 | 0.500 | 0.527 | 0.531 | 0.595 |
0.429 | G | 0.188 | 0.369 | 0.408 | 0.473 | 0.500 | 0.504 | 0.568 |
0.425 | D | 0.185 | 0.366 | 0.404 | 0.469 | 0.496 | 0.500 | 0.564 |
0.364 | F | 0.149 | 0.308 | 0.344 | 0.405 | 0.432 | 0.436 | 0.500 |
Assuming a balanced 18 game schedule, the win-loss record for the 7 teams would be as follows
A | B | C | E | G | D | F | Wins | |
A | 0 | 2 | 2 | 2 | 2 | 2 | 3 | 14 |
B | 1 | 0 | 2 | 2 | 2 | 2 | 2 | 10 |
C | 1 | 1 | 0 | 2 | 2 | 2 | 2 | 9 |
E | 1 | 1 | 1 | 0 | 2 | 2 | 2 | 8 |
G | 1 | 1 | 1 | 1 | 0 | 2 | 2 | 8 |
D | 1 | 1 | 1 | 1 | 1 | 0 | 2 | 7 |
F | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 6 |
Losses | 4 | 8 | 9 | 10 | 10 | 11 | 12 |
Thus team G would be tied with team E
for 4th place at the end of the regular season.
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