9.3 Tracking Runs Scored
\[\text{runs} = (N_{\text{runners}}^{(b)} + O^{(b)} + 1) - (N_{\text{runners}}^{(a)} + O^{(a)})\]
- \(N_{\text{runners}}\): number of runners in a state
- \(O\): number of outs
num_havent_scored <- function(s) {
# INPUT: game state
# OUTPUTS: number of runners and outs
s |> str_split("") |> pluck(1) |> as.numeric() |> sum(na.rm = TRUE)}# apply to all possible states
runners_out <- T_matrix |> row.names() |> set_names() |> map_int(num_havent_scored)# for all possible pairs of states
R_runs <- outer(runners_out + 1, runners_out,
FUN = "-") |> #difference in runs
cbind("3" = rep(0, 24)) #ensure square matrix| Tracking Runs Scored | |||||||||||||||||||||||||
| 2016 Season | |||||||||||||||||||||||||
| state | 000 0 | 000 1 | 000 2 | 001 0 | 001 1 | 001 2 | 010 0 | 010 1 | 010 2 | 011 0 | 011 1 | 011 2 | 100 0 | 100 1 | 100 2 | 101 0 | 101 1 | 101 2 | 110 0 | 110 1 | 110 2 | 111 0 | 111 1 | 111 2 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 000 0 | 1 | 0 | -1 | 0 | -1 | -2 | 0 | -1 | -2 | -1 | -2 | -3 | 0 | -1 | -2 | -1 | -2 | -3 | -1 | -2 | -3 | -2 | -3 | -4 | 0 |
| 000 1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 1 | 0 | -1 | 0 | -1 | -2 | 0 | -1 | -2 | -1 | -2 | -3 | 0 |
| 000 2 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 001 0 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 1 | 0 | -1 | 0 | -1 | -2 | 0 | -1 | -2 | -1 | -2 | -3 | 0 |
| 001 1 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 001 2 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 010 0 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 1 | 0 | -1 | 0 | -1 | -2 | 0 | -1 | -2 | -1 | -2 | -3 | 0 |
| 010 1 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 010 2 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 011 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 011 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 011 2 | 5 | 4 | 3 | 4 | 3 | 2 | 4 | 3 | 2 | 3 | 2 | 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 0 |
| 100 0 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 1 | 0 | -1 | 0 | -1 | -2 | 0 | -1 | -2 | -1 | -2 | -3 | 0 |
| 100 1 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 100 2 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 101 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 101 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 101 2 | 5 | 4 | 3 | 4 | 3 | 2 | 4 | 3 | 2 | 3 | 2 | 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 0 |
| 110 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 2 | 1 | 0 | 1 | 0 | -1 | 1 | 0 | -1 | 0 | -1 | -2 | 0 |
| 110 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 110 2 | 5 | 4 | 3 | 4 | 3 | 2 | 4 | 3 | 2 | 3 | 2 | 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 0 |
| 111 0 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 3 | 2 | 1 | 2 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | -1 | 0 |
| 111 1 | 5 | 4 | 3 | 4 | 3 | 2 | 4 | 3 | 2 | 3 | 2 | 1 | 4 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 0 | 0 |
| 111 2 | 6 | 5 | 4 | 5 | 4 | 3 | 5 | 4 | 3 | 4 | 3 | 2 | 5 | 4 | 3 | 4 | 3 | 2 | 4 | 3 | 2 | 3 | 2 | 1 | 0 |