markov/tmatrix.R

In singlearity-sports/singlearity-R: R Package Client for Singlearity Baseball API

# Functions (in separate file) to get transition matrix

library(singlearity)
source(file = "markov/tmatrix_std.R")
sing <- GetSinglearityClient()

suppressPackageStartupMessages(library(assertthat))
suppressPackageStartupMessages(library(tidyverse))

# Permittable error, standard transition probabilities, league averages:
# All now contained within tmatrix_sing.R

# Function to get results of a plate appearance
# This is essentially copied/pasted from pa_pred_simple.R

get_results <- function(bat, pitch, stad, home, temp, date,
                        away, inning = 1, pitch_ct = 0) {

  # Create list of states to iterate over
  states <- list(State$new(top = away, inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, top = away, inning = inning, 
                           pitch_number = pitch_ct), 
                 State$new(on_2b = T, top = away, inning = inning, 
                           pitch_number = pitch_ct), 
                 State$new(on_3b = T, top = away, inning = inning, 
                           pitch_number = pitch_ct),
                 State$new(on_1b = T, on_2b = T, top = away, 
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, on_3b = T, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(on_2b = T, on_3b = T, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, on_2b = T, on_3b = T, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(outs = 1, top = away, inning = inning, 
                           pitch_number = pitch_ct), 
                 State$new(on_1b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_2b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_3b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(on_1b = T, on_2b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, on_3b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(on_2b = T, on_3b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, on_2b = T, on_3b = T, outs = 1, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(outs = 2, top = away, inning = inning, 
                           pitch_number = pitch_ct), 
                 State$new(on_1b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_2b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_3b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(on_1b = T, on_2b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, on_3b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct),
                 State$new(on_2b = T, on_3b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct), 
                 State$new(on_1b = T, on_2b = T, on_3b = T, outs = 2, top = away,
                           inning = inning, pitch_number = pitch_ct))
  
  #initialize empty lists/vectors
  candidate_batters <- list()
  candidate_pitchers <- list()
  id <- vector()
  
  for (batter in bat) {
    if (is.numeric(batter)) {
      candidate_batters <- append(candidate_batters, pluck(sing$GetPlayers(id=batter), 1))
      id <- append(id, batter)
    }
    else {
      if (batter == "Will Smith") {
        smith <- sing$GetPlayers(name="Will Smith")[[2]]
        candidate_batters <- append(candidate_batters, smith)
        id <- append(id, smith$mlb_id)
      } else {
        player <- sing$GetPlayers(name=batter)[[1]]
        candidate_batters <- append(candidate_batters, player)
        id <- append(id, player$mlb_id)
      }
    }
  }
  
  for (pitcher in pitch) {
    if (is.numeric(pitcher)) {
      candidate_pitchers <- append(candidate_pitchers, sing$GetPlayers(id=pitcher)[[1]])
    } else {
      if (pitcher == "Will Smith") {
        candidate_pitchers <- append(candidate_pitchers, sing$GetPlayers(name="Will Smith")[[1]])
      } else {
        candidate_pitchers <- append(candidate_pitchers, sing$GetPlayers(name=pitcher)[[1]])
      }
    }
  }
  
  venue <- sing$GetVenues(stadium.name = stad)[[1]]
  atmosphere <- Atmosphere$new(venue = venue, 
                               temperature = temp, 
                               home_team = sing$GetTeams(name = home)[[1]])
  
  d <- date
  
  matchups <- list()
  
  batter_num <- 1
  
  for (b in candidate_batters) {
    if (length(candidate_batters) > 1) {
      # Create list of states to iterate over
      states <- list(State$new(top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, 
                               top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_2b = T, 
                               top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_3b = T, 
                               top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(on_1b = T, on_2b = T, 
                               top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, on_3b = T, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(on_2b = T, on_3b = T, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, on_2b = T, on_3b = T, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(outs = 1, 
                               top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_2b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_3b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(on_1b = T, on_2b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, on_3b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(on_2b = T, on_3b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, on_2b = T, on_3b = T, 
                               outs = 1, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(outs = 2, 
                               top = away, 
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_2b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_3b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(on_1b = T, on_2b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, on_3b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)),
                     State$new(on_2b = T, on_3b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)), 
                     State$new(on_1b = T, on_2b = T, on_3b = T, 
                               outs = 2, 
                               top = away,
                               inning = inning, 
                               pitch_number = pitch_ct + 
                                 4 * (batter_num - 1)))
      
    }
    for (p in candidate_pitchers) {
      for (s in states) {
        matchups <- append(matchups, Matchup$new(batter = b, pitcher = p,
                                                 atmosphere = atmosphere,
                                                 state = s, date = d))
      }
    }
    batter_num <- batter_num + 1
  }
  
  results <- sing$GetPaSim(matchup = matchups) %>%
    dplyr::mutate(num_on = purrr::reduce(dplyr::select(., tidyselect::starts_with("on_")), `+`)) %>%
    dplyr::arrange(match(batter, id), outs, num_on, desc(on_1b), desc(on_2b)) %>%
    dplyr::mutate(lineup_spot = match(batter, unique(batter))) %>% 
    dplyr::select(-c(num_on))
  
  return(results)
  
}

# Singlearity-based function

tmatrix_sing <- function(batters, pitcher, stadium, home, temp, date,
                         away, inning = 1, pitch_ct = 0) {
  
  # Uses predicted results to get the transition matrix
  # Initializes nine matrices
  
  tmatrix_1 <- matrix(0, 25, 25)
  tmatrix_2 <- matrix(0, 25, 25)
  tmatrix_3 <- matrix(0, 25, 25)
  tmatrix_4 <- matrix(0, 25, 25)
  tmatrix_5 <- matrix(0, 25, 25)
  tmatrix_6 <- matrix(0, 25, 25)
  tmatrix_7 <- matrix(0, 25, 25)
  tmatrix_8 <- matrix(0, 25, 25)
  tmatrix_9 <- matrix(0, 25, 25)

  # Initializes list to improve speed and functionality
  
  tmatrices <- list(tmatrix_1, tmatrix_2, tmatrix_3, tmatrix_4, tmatrix_5,
                    tmatrix_6, tmatrix_7, tmatrix_8, tmatrix_9)

  # Gets results of plate appearance simulations
  
  results <- get_results(batters, pitcher, stadium, home, temp, date,
                         away, inning, pitch_ct)

  # Each of these transitions includes probabilities for impossible events
  # i.e., DP probability with nobody on base, or two outs
  # These are used when summing what's judged to be the most relevant probability
  # In the DP/nobody on situation, the DP prob. will be included in the +1 out prob.
  
  for (i in 1:9) {
    
    # Probability of --- to ---, starting with no outs and no increase
    
    tmatrices[[i]][1,1] <- results[1 + 24 * (i - 1),]$hr_exp
    
    # Probability of --- to 1--, starting with no outs and no increase
    
    tmatrices[[i]][1,2] <- results[1 + 24 * (i - 1),]$single_exp + 
      results[1 + 24 * (i - 1),]$hbp_exp + results[1 + 24 * (i - 1),]$ci_exp + 
      results[1 + 24 * (i - 1),]$bb_exp + results[1 + 24 * (i - 1),]$ibb_exp +
      p_error_1b * results[1 + 24 * (i - 1),]$e_exp + 
      results[1 + 24 * (i - 1),]$fc_exp
    
    # Probability of --- to -2-, starting with no outs and no increase

    tmatrices[[i]][1,3] <- results[1 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[1 + 24 * (i - 1),]$e_exp
    
    # Probability of --- to --3, starting with no outs and no increase

    tmatrices[[i]][1,4] <- results[1 + 24 * (i - 1),]$triple_exp

    # Probability of --- to ---, starting with no outs and one-out increase

    tmatrices[[i]][1,9] <- results[1 + 24 * (i - 1),]$f_out_exp + 
      results[1 + 24 * (i - 1),]$so_exp + results[1 + 24 * (i - 1),]$fc_o_exp +
      results[1 + 24 * (i - 1),]$fo_exp + results[1 + 24 * (i - 1),]$sf_exp +
      results[1 + 24 * (i - 1),]$sh_exp + results[1 + 24 * (i - 1),]$dp_exp +
      results[1 + 24 * (i - 1),]$gdp_exp + results[1 + 24 * (i - 1),]$sf_dp_exp +
      results[1 + 24 * (i - 1),]$so_dp_exp + results[1 + 24 * (i - 1),]$tp_exp

    # Probability of 1-- to ---, starting with no outs and no increase
    
    tmatrices[[i]][2,1] <- results[2 + 24 * (i - 1),]$hr_exp

    # Probability of 1-- to -2-, starting with no outs and no increase
    
    tmatrices[[i]][2,3] <- p_2b_score_from_1b * results[2 + 24 * (i - 1),]$double_exp

    # Probability of 1-- to --3, starting with no outs and no increase

    tmatrices[[i]][2,4] <- results[2 + 24 * (i - 1),]$triple_exp
    
    # Probability of 1-- to 12-, starting with no outs and no increase
    
    tmatrices[[i]][2,5] <- p_1b_first_to_second * results[2 + 24 * (i - 1),]$single_exp +
      results[2 + 24 * (i - 1),]$hbp_exp + results[2 + 24 * (i - 1),]$ci_exp + 
      results[2 + 24 * (i - 1),]$bb_exp + results[2 + 24 * (i - 1),]$ibb_exp +
      p_error_1b * results[2 + 24 * (i - 1),]$e_exp + results[2 + 24 * (i - 1),]$fc_exp
    
    # Probability of 1-- to 1-3, starting with no outs and no increase

    tmatrices[[i]][2,6] <- p_1b_first_to_third * results[2 + 24 * (i - 1),]$single_exp
    
    # Probability of 1-- to -23, starting with no outs and no increase

    tmatrices[[i]][2,7] <- p_2b_go_to_3b * results[2 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[2 + 24 * (i - 1),]$e_exp
    
    # Probability of 1-- to 1--, starting with no outs and one-out increase

    tmatrices[[i]][2,10] <- results[2 + 24 * (i - 1),]$fc_o_exp + 
      results[2 + 24 * (i - 1),]$fo_exp + results[2 + 24 * (i - 1),]$so_exp + 
      results[2 + 24 * (i - 1),]$f_out_exp
    
    # Probability of 1-- to -2-, starting with no outs and one-out increase

    tmatrices[[i]][2,11] <- results[2 + 24 * (i - 1),]$sh_exp +
      results[2 + 24 * (i - 1),]$sf_exp
    
    # Probability of 1-- to ---, starting with no outs and two-out increase

    tmatrices[[i]][2,17] <- results[2 + 24 * (i - 1),]$dp_exp + 
      results[2 + 24 * (i - 1),]$gdp_exp + results[2 + 24 * (i - 1),]$sf_dp_exp + 
      results[2 + 24 * (i - 1),]$so_dp_exp + results[2 + 24 * (i - 1),]$tp_exp

    # Probability of -2- to ---, starting with no outs and no increase

    tmatrices[[i]][3,1] <- results[3 + 24 * (i - 1),]$hr_exp
    
    # Probability of -2- to 1--, starting with no outs and no increase

    tmatrices[[i]][3,2] <- results[3 + 24 * (i - 1),]$single_exp
    
    # Probability of -2- to -2-, starting with no outs and no increase

    tmatrices[[i]][3,3] <- results[3 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[3 + 24 * (i - 1),]$e_exp
    
    # Probability of -2- to --3, starting with no outs and no increase

    tmatrices[[i]][3,4] <- results[3 + 24 * (i - 1),]$triple_exp
    
    # Probability of -2- to 12-, starting with no outs and no increase

    tmatrices[[i]][3,5] <- results[3 + 24 * (i - 1),]$bb_exp + 
      results[3 + 24 * (i - 1),]$ibb_exp + results[3 + 24 * (i - 1),]$hbp_exp + 
      results[3 + 24 * (i - 1),]$ci_exp

    # Probability of -2- to 1-3, starting with no outs and no increase

    tmatrices[[i]][3,6] <- p_error_1b * results[3 + 24 * (i - 1),]$e_exp + 
      results[3 + 24 * (i - 1),]$fc_exp
    
    # Probability of -2- to 1--, starting with no outs and one-out increase

    tmatrices[[i]][3,10] <- results[3 + 24 * (i - 1),]$fc_o_exp +
      results[3 + 24 * (i - 1),]$fo_exp
    
    # Probability of -2- to -2-, starting with no outs and one-out increase

    tmatrices[[i]][3,11] <- results[3 + 24 * (i - 1),]$so_exp + 
      p_fo_second_stay * results[3 + 24 * (i - 1),]$f_out_exp
    
    # Probability of -2- to --3, starting with no outs and one-out increase

    tmatrices[[i]][3,12] <- p_fo_second_to_third * results[3 + 24 * (i - 1),]$f_out_exp + 
      results[3 + 24 * (i - 1),]$sh_exp + results[3 + 24 * (i - 1),]$sf_exp
    
    # Probability of -2- to ---, starting with no outs and two-out increase

    tmatrices[[i]][3,17] <- results[3 + 24 * (i - 1),]$dp_exp + 
      results[3 + 24 * (i - 1),]$gdp_exp + results[3 + 24 * (i - 1),]$sf_dp_exp + 
      results[3 + 24 * (i - 1),]$so_dp_exp + results[3 + 24 * (i - 1),]$tp_exp

    # Probability of --3 to ---, starting with no outs and no increase

    tmatrices[[i]][4,1] <- results[4 + 24 * (i - 1),]$hr_exp
    
    # Probability of --3 to 1--, starting with no outs and no increase

    tmatrices[[i]][4,2] <- results[4 + 24 * (i - 1),]$single_exp + 
      p_error_1b * results[4 + 24 * (i - 1),]$e_exp + results[4 + 24 * (i - 1),]$fc_exp

    # Probability of --3 to -2-, starting with no outs and no increase

    tmatrices[[i]][4,3] <- results[4 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[4 + 24 * (i - 1),]$e_exp
    
    # Probability of --3 to --3, starting with no outs and no increase

    tmatrices[[i]][4,4] <- results[4 + 24 * (i - 1),]$triple_exp
    
    # Probability of --3 to 1-3, starting with no outs and no increase
    
    tmatrices[[i]][4,6] <- results[4 + 24 * (i - 1),]$bb_exp + 
      results[4 + 24 * (i - 1),]$ibb_exp + results[4 + 24 * (i - 1),]$hbp_exp + 
      results[4 + 24 * (i - 1),]$ci_exp
    
    # Probability of --3 to ---, starting with no outs and one-out increase

    tmatrices[[i]][4,9] <- results[4 + 24 * (i - 1),]$sf_exp + 
      results[4 + 24 * (i - 1),]$f_out_exp + results[4 + 24 * (i - 1),]$fc_o_exp + 
      results[4 + 24 * (i - 1),]$sh_exp + results[4 + 24 * (i - 1),]$fo_exp
    
    # Probability of --3 to --3, starting with no outs and one-out increase
    
    tmatrices[[i]][4,12] <- results[4 + 24 * (i - 1),]$so_exp

    # Probability of --3 to ---, starting with no outs and two-out increase
    
    tmatrices[[i]][4,17] <- results[4 + 24 * (i - 1),]$dp_exp + 
      results[4 + 24 * (i - 1),]$gdp_exp + results[4 + 24 * (i - 1),]$sf_dp_exp + 
      results[4 + 24 * (i - 1),]$so_dp_exp + results[4 + 24 * (i - 1),]$tp_exp

    # Probability of 12- to ---, starting with no outs and no increase
    
    tmatrices[[i]][5,1] <- results[5 + 24 * (i - 1),]$hr_exp

    # Probability of 12- to -2-, starting with no outs and no increase

    tmatrices[[i]][5,3] <- p_2b_score_from_1b * results[5 + 24 * (i - 1),]$double_exp
    
    # Probability of 12- to --3, starting with no outs and no increase

    tmatrices[[i]][5,4] <- results[5 + 24 * (i - 1),]$triple_exp

    # Probability of 12- to 12-, starting with no outs and no increase
    
    tmatrices[[i]][5,5] <- p_1b_first_to_second * results[5 + 24 * (i - 1),]$single_exp

    # Probability of 12- to 1-3, starting with no outs and no increase

    tmatrices[[i]][5,6] <- p_1b_first_to_third * results[5 + 24 * (i - 1),]$single_exp

    # Probability of 12- to -23, starting with no outs and no increase

    tmatrices[[i]][5,7] <- p_2b_go_to_3b * results[5 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[5 + 24 * (i - 1),]$e_exp

    # Probability of 12- to 123, starting with no outs and no increase
    
    tmatrices[[i]][5,8] <- results[5 + 24 * (i - 1),]$bb_exp + 
      results[5 + 24 * (i - 1),]$ibb_exp + results[5 + 24 * (i - 1),]$hbp_exp + 
      results[5 + 24 * (i - 1),]$ci_exp + p_error_1b * results[5 + 24 * (i - 1),]$e_exp +
      results[5 + 24 * (i - 1),]$fc_exp
    
    # Probability of 12- to 12-, starting with no outs and one-out increase

    tmatrices[[i]][5,13] <- results[5 + 24 * (i - 1),]$f_out_exp + 
      results[5 + 24 * (i - 1),]$so_exp
    
    # Probability of 12- to 1-3, starting with no outs and one-out increase
    
    tmatrices[[i]][5,14] <- results[5 + 24 * (i - 1),]$fo_exp + 
      results[5 + 24 * (i - 1),]$fc_o_exp + results[5 + 24 * (i - 1),]$sf_exp

    # Probability of 12- to -23, starting with no outs and one-out increase

    tmatrices[[i]][5,15] <- results[5 + 24 * (i - 1),]$sh_exp
    
    # Probability of 12- to 1--, starting with no outs and two-out increase
    
    tmatrices[[i]][5,18] <- results[5 + 24 * (i - 1),]$sf_dp_exp

    # Probability of 12- to -2-, starting with no outs and two-out increase
    
    tmatrices[[i]][5,19] <- results[5 + 24 * (i - 1),]$so_dp_exp + 
      results[5 + 24 * (i - 1),]$dp_exp

    # Probability of 12- to --3, starting with no outs and two-out increase

    tmatrices[[i]][5,20] <- results[5 + 24 * (i - 1),]$gdp_exp

    # Probability of 12- to end of inning, starting with no outs

    tmatrices[[i]][5,25] <- results[5 + 24 * (i - 1),]$tp_exp

    # Probability of 1-3 to ---, starting with no outs and no increase
    
    tmatrices[[i]][6,1] <- results[6 + 24 * (i - 1),]$hr_exp

    # Probability of 1-3 to -2-, starting with no outs and no increase
    
    tmatrices[[i]][6,3] <- p_2b_score_from_1b * results[6 + 24 * (i - 1),]$double_exp
    
    # Probability of 1-3 to --3, starting with no outs and no increase

    tmatrices[[i]][6,4] <- results[6 + 24 * (i - 1),]$triple_exp

    # Probability of 1-3 to 12-, starting with no outs and no increase

    tmatrices[[i]][6,5] <- p_1b_first_to_second * results[6 + 24 * (i - 1),]$single_exp +
      p_error_1b * results[6 + 24 * (i - 1),]$e_exp + results[6 + 24 * (i - 1),]$fc_exp
    
    # Probability of 1-3 to 1-3, starting with no outs and no increase
    
    tmatrices[[i]][6,6] <- p_1b_first_to_third * results[6 + 24 * (i - 1),]$single_exp
    
    # Probability of 1-3 to -23, starting with no outs and no increase

    tmatrices[[i]][6,7] <- p_2b_go_to_3b * results[6 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[6 + 24 * (i - 1),]$e_exp
    
    # Probability of 1-3 to 123, starting with no outs and no increase
    
    tmatrices[[i]][6,8] <- results[6 + 24 * (i - 1),]$bb_exp + 
      results[6 + 24 * (i - 1),]$ibb_exp + results[6 + 24 * (i - 1),]$hbp_exp + 
      results[6 + 24 * (i - 1),]$ci_exp

    # Probability to 1-3 to 1--, starting with no outs and one-out increase
    
    tmatrices[[i]][6,10] <- results[6 + 24 * (i - 1),]$sf_exp + 
      results[6 + 24 * (i - 1),]$fc_o_exp + results[6 + 24 * (i - 1),]$fo_exp

    # Probability of 1-3 to -2-, starting with no outs and one-out increase
    
    tmatrices[[i]][6,11] <- results[6 + 24 * (i - 1),]$sh_exp
    
    # Probability of 1-3 to 1-3, starting with no outs and one-out increase

    tmatrices[[i]][6,14] <- results[6 + 24 * (i - 1),]$so_exp + 
      results[6 + 24 * (i - 1),]$f_out_exp
    
    # Probability of 1-3 to ---, starting with no outs and two-out increase
    
    tmatrices[[i]][6,17] <- results[6 + 24 * (i - 1),]$dp_exp + 
      results[6 + 24 * (i - 1),]$gdp_exp

    # Probability of 1-3 to -2-, starting with no outs and two-out increase

    tmatrices[[i]][6,19] <- results[6 + 24 * (i - 1),]$sf_dp_exp

    # Probability of 1-3 to --3, starting with no outs and two-out increase
    
    tmatrices[[i]][6,20] <- results[6 + 24 * (i - 1),]$so_dp_exp

    # Probability of 1-3 to end of inning, starting with no outs

    tmatrices[[i]][6,25] <- results[6 + 24 * (i - 1),]$tp_exp
    
    # Probability of -23 to ---, starting with no outs and no increase

    tmatrices[[i]][7,1] <- results[7 + 24 * (i - 1),]$hr_exp
    
    # Probability of -23 to 1--, starting with no outs and no increase
    
    tmatrices[[i]][7,2] <- results[7 + 24 * (i - 1),]$single_exp
    
    # Probability of -23 to -2-, starting with no outs and no increase
    
    tmatrices[[i]][7,3] <- results[7 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[7 + 24 * (i - 1),]$e_exp

    # Probability of -23 to --3, starting with no outs and no increase

    tmatrices[[i]][7,4] <- results[7 + 24 * (i - 1),]$triple_exp
    
    # Probability of -23 to 1-3, starting with no outs and no increase
    
    tmatrices[[i]][7,6] <- p_error_1b * results[7 + 24 * (i - 1),]$e_exp + 
      results[7 + 24 * (i - 1),]$fc_exp + results[7 + 24 * (i - 1),]$fo_exp
    
    # Probability of -23 to 123, starting with no outs and no increase

    tmatrices[[i]][7,8] <- results[7 + 24 * (i - 1),]$bb_exp + 
      results[7 + 24 * (i - 1),]$ibb_exp + results[7 + 24 * (i - 1),]$hbp_exp + 
      results[7 + 24 * (i - 1),]$ci_exp
    
    # Probability of -23 to -2-, starting with no outs and one-out increase
    
    tmatrices[[i]][7,11] <- results[7 + 24 * (i - 1),]$sf_exp + 
      p_fo_second_stay * results[7 + 24 * (i - 1),]$f_out_exp
    
    # Probability of -23 to --3, starting with no outs and one-out increase
    
    tmatrices[[i]][7,12] <- results[7 + 24 * (i - 1),]$sh_exp + 
      p_fo_second_to_third * results[7 + 24 * (i - 1),]$f_out_exp
    
    # Probability of -23 to 1-3, starting with no outs and one-out increase
    
    tmatrices[[i]][7,14] <- results[7 + 24 * (i - 1),]$fc_o_exp

    # Probability of -23 to -23, starting with no outs and one-out increase
    
    tmatrices[[i]][7,15] <- results[7 + 24 * (i - 1),]$so_exp
    
    # Probability of -23 to --3, starting with no outs and two-out increase

    tmatrices[[i]][7,20] <- results[7 + 24 * (i - 1),]$sf_dp_exp + 
      results[7 + 24 * (i - 1),]$so_dp_exp + results[7 + 24 * (i - 1),]$dp_exp + 
      results[7 + 24 * (i - 1),]$gdp_exp

    # Probability of -23 to end of inning, starting with no outs

    tmatrices[[i]][7,25] <- results[7 + 24 * (i - 1),]$tp_exp
    
    # Probability of 123 to ---, starting with no outs and no increase
    
    tmatrices[[i]][8,1] <- results[8 + 24 * (i - 1),]$hr_exp

    # Probability of 123 to -2-, starting with no outs and no increase

    tmatrices[[i]][8,3] <- p_2b_score_from_1b * results[8 + 24 * (i - 1),]$double_exp
    
    # Probability of 123 to --3, starting with no outs and no increase

    tmatrices[[i]][8,4] <- results[8 + 24 * (i - 1),]$triple_exp

    # Probability of 123 to 12-, starting with no outs and no increase
    
    tmatrices[[i]][8,5] <- p_1b_first_to_second * results[8 + 24 * (i - 1),]$single_exp
    
    # Probability of 123 to 1-3, starting with no outs and no increase
    
    tmatrices[[i]][8,6] <- p_1b_first_to_third * results[8 + 24 * (i - 1),]$single_exp
    
    # Probability of 123 to -23, starting with no outs and no increase
    
    tmatrices[[i]][8,7] <- p_2b_go_to_3b * results[8 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[8 + 24 * (i - 1),]$e_exp
    
    # Probability of 123 to 123, starting with no outs and no increase
    
    tmatrices[[i]][8,8] <- results[8 + 24 * (i - 1),]$bb_exp + 
      results[8 + 24 * (i - 1),]$ibb_exp + results[8 + 24 * (i - 1),]$hbp_exp + 
      results[8 + 24 * (i - 1),]$ci_exp + p_error_1b * results[8 + 24 * (i - 1),]$e_exp +
      results[8 + 24 * (i - 1),]$fc_exp
    
    # Probability of 123 to 12-, starting with no outs and one-out increase

    tmatrices[[i]][8,13] <- results[8 + 24 * (i - 1),]$sf_exp +
      0.5 * p_fo_second_stay * results[8 + 24 * (i - 1),]$f_out_exp
    
    # Probability of 123 to 1-3, starting with no outs and one-out increase

    tmatrices[[i]][8,14] <- p_fo_second_to_third * results[8 + 24 * (i - 1),]$f_out_exp +
      results[8 + 24 * (i - 1),]$fc_o_exp

    # Probability of 123 to -23, starting with no outs and one-out increase

    tmatrices[[i]][8,15] <- results[8 + 24 * (i - 1),]$sh_exp
    
    # Probability of 123 to 123, starting with no outs and one-out increase

    tmatrices[[i]][8,16] <- 0.5 * p_fo_second_stay * results[8 + 24 * (i - 1),]$f_out_exp +
      results[8 + 24 * (i - 1),]$so_exp + results[8 + 24 * (i - 1),]$fo_exp

    # Probability of 123 to --3, starting with no outs and two-out increase
    
    tmatrices[[i]][8,20] <- results[8 + 24 * (i - 1),]$gdp_exp

    # Probability of 123 to 12-, starting with no outs and two-out increase
    
    tmatrices[[i]][8,21] <- results[8 + 24 * (i - 1),]$so_dp_exp + 
      results[8 + 24 * (i - 1),]$dp_exp

    # Probability of 123 to 1-3, starting with no outs and two-out increase
    
    tmatrices[[i]][8,22] <- results[8 + 24 * (i - 1),]$sf_dp_exp

    # Probability of 123 to end of inning, starting with no outs
    
    tmatrices[[i]][8,25] <- results[8 + 24 * (i - 1),]$tp_exp

    # Probability of --- to ---, starting with one out and no increase
    
    tmatrices[[i]][9,9] <- results[9 + 24 * (i - 1),]$hr_exp

    # Probability of --- to 1--, starting with one out and no increase

    tmatrices[[i]][9,10] <- results[9 + 24 * (i - 1),]$single_exp + 
      results[9 + 24 * (i - 1),]$hbp_exp + results[9 + 24 * (i - 1),]$ci_exp + 
      results[9 + 24 * (i - 1),]$bb_exp + results[9 + 24 * (i - 1),]$ibb_exp +
      p_error_1b * results[9 + 24 * (i - 1),]$e_exp +
      results[9 + 24 * (i - 1),]$fc_exp

    # Probability of --- to -2-, starting with one out and no increase

    tmatrices[[i]][9,11] <- results[9 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[9 + 24 * (i - 1),]$e_exp

    # Probability of --- to --3, starting with one out and no increase

    tmatrices[[i]][9,12] <- results[9 + 24 * (i - 1),]$triple_exp

    # Probability of --- to ---, starting with one out and one-out increase

    tmatrices[[i]][9,17] <- results[9 + 24 * (i - 1),]$f_out_exp + 
      results[9 + 24 * (i - 1),]$so_exp + results[9 + 24 * (i - 1),]$fc_o_exp +
      results[9 + 24 * (i - 1),]$fo_exp + results[9 + 24 * (i - 1),]$sf_exp +
      results[9 + 24 * (i - 1),]$sh_exp + results[9 + 24 * (i - 1),]$dp_exp +
      results[9 + 24 * (i - 1),]$gdp_exp + results[9 + 24 * (i - 1),]$sf_dp_exp +
      results[9 + 24 * (i - 1),]$so_dp_exp + results[9 + 24 * (i - 1),]$tp_exp

    # Probability of 1-- to ---, starting with one out and no increase
    
    tmatrices[[i]][10,9] <- results[10 + 24 * (i - 1),]$hr_exp

    # Probability of 1-- to -2-, starting with one out and no increase

    tmatrices[[i]][10,11] <- p_2b_score_from_1b * results[10 + 24 * (i - 1),]$double_exp
    
    # Probability of 1-- to --3, starting with one out and no increase

    tmatrices[[i]][10,12] <- results[10 + 24 * (i - 1),]$triple_exp

    # Probability of 1-- to 12-, starting with one out and no increase

    tmatrices[[i]][10,13] <- p_1b_first_to_second * results[10 + 24 * (i - 1),]$single_exp +
      results[10 + 24 * (i - 1),]$bb_exp + results[10 + 24 * (i - 1),]$ibb_exp + 
      results[10 + 24 * (i - 1),]$hbp_exp + results[10 + 24 * (i - 1),]$ci_exp + 
      p_error_1b * results[10 + 24 * (i - 1),]$e_exp + results[10 + 24 * (i - 1),]$fc_exp
    
    # Probability of 1-- to 1-3, starting with one out and no increase

    tmatrices[[i]][10,14] <- p_1b_first_to_third * results[10 + 24 * (i - 1),]$single_exp

    # Probability of 1-- to -23, starting with one out and no increase

    tmatrices[[i]][10,15] <- p_2b_go_to_3b * results[10 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[10 + 24 * (i - 1),]$e_exp
    
    # Probability of 1-- to 1--, starting with one out and one-out increase
    
    tmatrices[[i]][10,18] <- results[10 + 24 * (i - 1),]$fc_o_exp + 
      results[10 + 24 * (i - 1),]$fo_exp + results[10 + 24 * (i - 1),]$so_exp + 
      results[10 + 24 * (i - 1),]$f_out_exp
    
    # Probability of 1-- to -2-, starting with one out and one-out increase

    tmatrices[[i]][10,19] <- results[10 + 24 * (i - 1),]$sh_exp +
      results[10 + 24 * (i - 1),]$sf_exp

    # Probability of 1-- to end of inning, starting with one out

    tmatrices[[i]][10,25] <- results[10 + 24 * (i - 1),]$dp_exp + 
      results[10 + 24 * (i - 1),]$gdp_exp + results[10 + 24 * (i - 1),]$sf_dp_exp + 
      results[10 + 24 * (i - 1),]$so_dp_exp + results[10 + 24 * (i - 1),]$tp_exp
    
    # Probability of -2- to ---, starting with one out and no increase
    
    tmatrices[[i]][11,9] <- results[11 + 24 * (i - 1),]$hr_exp
    
    # Probability of -2- to 1--, starting with one out and no increase

    tmatrices[[i]][11,10] <- results[11 + 24 * (i - 1),]$single_exp

    # Probability of -2- to -2-, starting with one out and no increase

    tmatrices[[i]][11,11] <- results[11 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[11 + 24 * (i - 1),]$e_exp

    # Probability of -2- to --3, starting with one out and no increase

    tmatrices[[i]][11,12] <- results[11 + 24 * (i - 1),]$triple_exp

    # Probability of -2- to 12-, starting with one out and no increase

    tmatrices[[i]][11,13] <- results[11 + 24 * (i - 1),]$bb_exp + 
      results[11 + 24 * (i - 1),]$ibb_exp + results[11 + 24 * (i - 1),]$hbp_exp + 
      results[11 + 24 * (i - 1),]$ci_exp
    
    # Probability of -2- to 1-3, starting with one out and no increase

    tmatrices[[i]][11,14] <- p_error_1b * results[11 + 24 * (i - 1),]$e_exp + 
      results[11 + 24 * (i - 1),]$fc_exp

    # Probability of -2- to 1--, starting with one out and one-out increase

    tmatrices[[i]][11,18] <- results[11 + 24 * (i - 1),]$fc_o_exp +
      results[11 + 24 * (i - 1),]$fo_exp

    # Probability of -2- to -2-, starting with one out and one-out increase

    tmatrices[[i]][11,19] <- results[11 + 24 * (i - 1),]$so_exp + 
      p_fo_second_stay * results[11 + 24 * (i - 1),]$f_out_exp
    
    # Probability of -2- to --3, starting with one out and one-out increase
    
    tmatrices[[i]][11,20] <- p_fo_second_to_third * results[11 + 24 * (i - 1),]$f_out_exp +
      results[11 + 24 * (i - 1),]$sh_exp + results[11 + 24 * (i - 1),]$sf_exp

    # Probability of -2- to end of inning, starting with one out

    tmatrices[[i]][11,25] <- results[11 + 24 * (i - 1),]$dp_exp + 
      results[11 + 24 * (i - 1),]$gdp_exp + results[11 + 24 * (i - 1),]$sf_dp_exp + 
      results[11 + 24 * (i - 1),]$so_dp_exp + results[11 + 24 * (i - 1),]$tp_exp

    # Probability of --3 to ---, starting with one out and no increase

    tmatrices[[i]][12,9] <- results[12 + 24 * (i - 1),]$hr_exp

    # Probability of --3 to 1--, starting with one out and no increase

    tmatrices[[i]][12,10] <- results[12 + 24 * (i - 1),]$single_exp + 
      p_error_1b * results[12 + 24 * (i - 1),]$e_exp + results[12 + 24 * (i - 1),]$fc_exp
    
    # Probability of --3 to -2-, starting with one out and no increase

    tmatrices[[i]][12,11] <- results[12 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[12 + 24 * (i - 1),]$e_exp
    
    # Probability of --3 to --3, starting with one out and no increase
    
    tmatrices[[i]][12,12] <- results[12 + 24 * (i - 1),]$triple_exp

    # Probability of --3 to 1-3, starting with one out and no increase
    
    tmatrices[[i]][12,14] <- results[12 + 24 * (i - 1),]$bb_exp + 
      results[12 + 24 * (i - 1),]$ibb_exp + results[12 + 24 * (i - 1),]$hbp_exp + 
      results[12 + 24 * (i - 1),]$ci_exp

    # Probability of --3 to ---, starting with one out and one-out increase
    
    tmatrices[[i]][12,17] <- results[12 + 24 * (i - 1),]$sf_exp + 
      results[12 + 24 * (i - 1),]$f_out_exp + results[12 + 24 * (i - 1),]$sh_exp
    
    # Probability of --3 to 1--, starting with one out and one-out increase

    tmatrices[[i]][12,18] <- results[12 + 24 * (i - 1),]$fc_o_exp +
      results[12 + 24 * (i - 1),]$fo_exp

    # Probability of --3 to --3, starting with one out and one-out increase

    tmatrices[[i]][12,20] <- results[12 + 24 * (i - 1),]$so_exp
    
    # Probability of --3 to end of inning, starting with one out

    tmatrices[[i]][12,25] <- results[12 + 24 * (i - 1),]$dp_exp + 
      results[12 + 24 * (i - 1),]$gdp_exp + results[12 + 24 * (i - 1),]$sf_dp_exp + 
      results[12 + 24 * (i - 1),]$so_dp_exp + results[12 + 24 * (i - 1),]$tp_exp

    # Probability of 12- to ---, starting with one out and no increase
    
    tmatrices[[i]][13,9] <- results[13 + 24 * (i - 1),]$hr_exp
    
    # Probability of 12- to -2-, starting with one out and no increase
    
    tmatrices[[i]][13,11] <- p_2b_score_from_1b * results[13 + 24 * (i - 1),]$double_exp

    # Probability of 12- to --3, starting with one out and no increase

    tmatrices[[i]][13,12] <- results[13 + 24 * (i - 1),]$triple_exp

    # Probability of 12- to 12-, starting with one out and no increase
    
    tmatrices[[i]][13,13] <- p_1b_first_to_second * results[13 + 24 * (i - 1),]$single_exp

    # Probability of 12- to 1-3, starting with one out and no increase
    
    tmatrices[[i]][13,14] <- p_1b_first_to_third * results[13 + 24 * (i - 1),]$single_exp

    # Probability of 12- to -23, starting with one out and no increase

    tmatrices[[i]][13,15] <- p_2b_go_to_3b * results[13 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[13 + 24 * (i - 1),]$e_exp

    # Probability of 12- to 123, starting with one out and no increase
    
    tmatrices[[i]][13,16] <- results[13 + 24 * (i - 1),]$bb_exp + 
      results[13 + 24 * (i - 1),]$ibb_exp + results[13 + 24 * (i - 1),]$hbp_exp + 
      results[13 + 24 * (i - 1),]$ci_exp + p_error_1b * results[13 + 24 * (i - 1),]$e_exp +
      results[13 + 24 * (i - 1),]$fc_exp
    
    # Probability of 12- to 12-, starting with one out and one-out increase

    tmatrices[[i]][13,21] <- results[13 + 24 * (i - 1),]$f_out_exp + 
      results[13 + 24 * (i - 1),]$so_exp

    # Probability of 12- to 1-3, starting with one out and one-out increase
    
    tmatrices[[i]][13,22] <- results[13 + 24 * (i - 1),]$fo_exp + 
      results[13 + 24 * (i - 1),]$fc_o_exp + results[13 + 24 * (i - 1),]$sf_exp

    # Probability of 12- to -23, starting with one out and one-out increase

    tmatrices[[i]][13,23] <- results[13 + 24 * (i - 1),]$sh_exp

    # Probability of 12- to end of inning, starting with one out
    
    tmatrices[[i]][13,25] <- results[13 + 24 * (i - 1),]$dp_exp + 
      results[13 + 24 * (i - 1),]$gdp_exp + results[13 + 24 * (i - 1),]$sf_dp_exp + 
      results[13 + 24 * (i - 1),]$so_dp_exp + results[13 + 24 * (i - 1),]$tp_exp

    # Probability of 1-3 to ---, starting with one out and no increase
    
    tmatrices[[i]][14,9] <- results[14 + 24 * (i - 1),]$hr_exp

    # Probability of 1-3 to -2-, starting with one out and no increase

    tmatrices[[i]][14,11] <- p_2b_score_from_1b * results[14 + 24 * (i - 1),]$double_exp

    # Probability of 1-3 to --3, starting with one out and no increase

    tmatrices[[i]][14,12] <- results[14 + 24 * (i - 1),]$triple_exp
    
    # Probability of 1-3 to 12-, starting with one out and no increase
    
    tmatrices[[i]][14,13] <- p_1b_first_to_second * results[14 + 24 * (i - 1),]$single_exp +
      p_error_1b * results[14 + 24 * (i - 1),]$e_exp + results[14 + 24 * (i - 1),]$fc_exp
    
    # Probability of 1-3 to 1-3, starting with one out and no increase
    
    tmatrices[[i]][14,14] <- p_1b_first_to_third * results[14 + 24 * (i - 1),]$single_exp

    # Probability of 1-3 to -23, starting with one out and no increase

    tmatrices[[i]][14,15] <- p_2b_go_to_3b * results[14 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[14 + 24 * (i - 1),]$e_exp

    # Probability of 1-3 to 123, starting with one out and no increase
    
    tmatrices[[i]][14,16] <- results[14 + 24 * (i - 1),]$bb_exp + 
      results[14 + 24 * (i - 1),]$ibb_exp + results[14 + 24 * (i - 1),]$hbp_exp + 
      results[14 + 24 * (i - 1),]$ci_exp
    
    # Probability to 1-3 to 1--, starting with one out and one-out increase

    tmatrices[[i]][14,18] <- results[14 + 24 * (i - 1),]$sf_exp + 
      results[14 + 24 * (i - 1),]$fc_o_exp + results[14 + 24 * (i - 1),]$fo_exp

    # Probability of 1-3 to -2-, starting with one out and one-out increase

    tmatrices[[i]][14,19] <- results[14 + 24 * (i - 1),]$sh_exp

    # Probability of 1-3 to 1-3, starting with one out and one-out increase
    
    tmatrices[[i]][14,22] <- results[14 + 24 * (i - 1),]$so_exp + 
      results[14 + 24 * (i - 1),]$f_out_exp
    
    # Probability of 1-3 to end of inning, starting with one out

    tmatrices[[i]][14,25] <- results[14 + 24 * (i - 1),]$dp_exp + 
      results[14 + 24 * (i - 1),]$gdp_exp + results[14 + 24 * (i - 1),]$sf_dp_exp + 
      results[14 + 24 * (i - 1),]$so_dp_exp + results[14 + 24 * (i-1),]$tp_exp

    # Probability of -23 to ---, starting with one out and no increase
    
    tmatrices[[i]][15,9] <- results[15 + 24 * (i - 1),]$hr_exp
    
    # Probability of -23 to 1--, starting with one out and no increase
    
    tmatrices[[i]][15,10] <- results[15 + 24 * (i - 1),]$single_exp
    
    # Probability of -23 to -2-, starting with one out and no increase
    
    tmatrices[[i]][15,11] <- results[15 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[15 + 24 * (i - 1),]$e_exp

    # Probability of -23 to --3, starting with one out and no increase

    tmatrices[[i]][15,12] <- results[15 + 24 * (i - 1),]$triple_exp

    # Probability of -23 to 1-3, starting with one out and no increase

    tmatrices[[i]][15,14] <- p_error_1b * results[15 + 24 * (i - 1),]$e_exp + 
      results[15 + 24 * (i - 1),]$fc_exp
    
    # Probability of -23 to 123, starting with one out and no increase

    tmatrices[[i]][15,16] <- results[15 + 24 * (i - 1),]$bb_exp + 
      results[15 + 24 * (i - 1),]$ibb_exp + results[15 + 24 * (i - 1),]$hbp_exp + 
      results[15 + 24 * (i - 1),]$ci_exp

    # Probability of -23 to -2-, starting with one out and one-out increase

    tmatrices[[i]][15,19] <- results[15 + 24 * (i - 1),]$sf_exp +
      p_fo_second_stay * results[15 + 24 * (i - 1),]$f_out_exp
    
    # Probability of -23 to --3, starting with one out and one-out increase

    tmatrices[[i]][15,20] <- results[15 + 24 * (i - 1),]$sh_exp +
      p_fo_second_to_third * results[15 + 24 * (i - 1),]$f_out_exp
    
    # Probability of -23 to 1-3, starting with one out and one-out increase

    tmatrices[[i]][15,22] <- results[15 + 24 * (i - 1),]$fc_o_exp +
      results[15 + 24 * (i - 1),]$fo_exp
    
    # Probability of -23 to -23, starting with one out and one-out increase

    tmatrices[[i]][15,23] <- results[15 + 24 * (i - 1),]$so_exp

    # Probability of -23 to end of inning, starting with one out

    tmatrices[[i]][15,25] <- results[15 + 24 * (i - 1),]$dp_exp + 
      results[15 + 24 * (i - 1),]$gdp_exp + results[15 + 24 * (i - 1),]$sf_dp_exp + 
      results[15 + 24 * (i - 1),]$so_dp_exp + results[15 + 24 * (i - 1),]$tp_exp

    # Probability of 123 to ---, starting with one out and no increase

    tmatrices[[i]][16,9] <- results[16 + 24 * (i - 1),]$hr_exp

    # Probability of 123 to -2-, starting with one out and no increase

    tmatrices[[i]][16,11] <- p_2b_score_from_1b * results[16 + 24 * (i - 1),]$double_exp

    # Probability of 123 to --3, starting with one out and no increase

    tmatrices[[i]][16,12] <- results[16 + 24 * (i - 1),]$triple_exp

    # Probability of 123 to 12-, starting with one out and no increase
    
    tmatrices[[i]][16,13] <- p_1b_first_to_second * results[16 + 24 * (i - 1),]$single_exp

    # Probability of 123 to 1-3, starting with one out and no increase

    tmatrices[[i]][16,14] <- p_1b_first_to_third * results[16 + 24 * (i - 1),]$single_exp
    
    # Probability of 123 to -23, starting with one out and no increase
    
    tmatrices[[i]][16,15] <- p_2b_go_to_3b * results[16 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[16 + 24 * (i - 1),]$e_exp

    # Probability of 123 to 123, starting with one out and no increase

    tmatrices[[i]][16,16] <- results[16 + 24 * (i - 1),]$bb_exp + 
      results[16 + 24 * (i - 1),]$ibb_exp + results[16 + 24 * (i - 1),]$hbp_exp + 
      results[16 + 24 * (i - 1),]$ci_exp + p_error_1b * results[16 + 24 * (i - 1),]$e_exp +
      results[16 + 24 * (i - 1),]$fc_exp

    # Probability of 123 to 12-, starting with one out and one-out increase

    tmatrices[[i]][16,21] <- results[16 + 24 * (i - 1),]$sf_exp +
      0.5 * p_fo_second_stay * results[16 + 24 * (i - 1),]$f_out_exp

    # Probability of 123 to 1-3, starting with one out and one-out increase

    tmatrices[[i]][16,22] <- p_fo_second_to_third * results[16 + 24 * (i - 1),]$f_out_exp +
      results[16 + 24 * (i - 1),]$fc_o_exp

    # Probability of 123 to -23, starting with one out and one-out increase
    
    tmatrices[[i]][16,23] <- results[16 + 24 * (i - 1),]$sh_exp
    
    # Probability of 123 to 123, starting with one out and one-out increase
    
    tmatrices[[i]][16,24] <- 0.5 * p_fo_second_stay * results[16 + 24 * (i - 1),]$f_out_exp +
      results[16 + 24 * (i - 1),]$so_exp + results[16 + 24 * (i - 1),]$fo_exp
    
    # Probability of 123 to end of inning, starting with one out
    
    tmatrices[[i]][16,25] <- results[16 + 24 * (i - 1),]$dp_exp + 
      results[16 + 24 * (i - 1),]$gdp_exp + results[16 + 24 * (i - 1),]$sf_dp_exp + 
      results[16 + 24 * (i - 1),]$so_dp_exp + results[16 + 24 * (i - 1),]$tp_exp
    
    # Probability of --- to ---, starting with two outs and no increase
    
    tmatrices[[i]][17,17] <- results[17 + 24 * (i - 1),]$hr_exp

    # Probability of --- to 1--, starting with two out and no increase

    tmatrices[[i]][17,18] <- results[17 + 24 * (i - 1),]$single_exp + 
      results[17 + 24 * (i - 1),]$bb_exp + results[17 + 24 * (i - 1),]$ibb_exp + 
      results[17 + 24 * (i - 1),]$hbp_exp + results[17 + 24 * (i - 1),]$ci_exp + 
      p_error_1b * results[17 + 24 * (i - 1),]$e_exp +
      results[17 + 24 * (i - 1),]$fc_exp

    # Probability of --- to -2-, starting with two out and no increase

    tmatrices[[i]][17,19] <- results[17 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[17 + 24 * (i - 1),]$e_exp

    # Probability of --- to --3, starting with two out and no increase

    tmatrices[[i]][17,20] <- results[17 + 24 * (i - 1),]$triple_exp

    # Probability of --- to end of inning, starting with two out

    tmatrices[[i]][17,25] <- results[17 + 24 * (i - 1),]$f_out_exp + 
      results[17 + 24 * (i - 1),]$so_exp + results[17 + 24 * (i - 1),]$fc_o_exp +
      results[17 + 24 * (i - 1),]$fo_exp + results[17 + 24 * (i - 1),]$sf_exp +
      results[17 + 24 * (i - 1),]$sh_exp + results[17 + 24 * (i - 1),]$dp_exp +
      results[17 + 24 * (i - 1),]$gdp_exp + results[17 + 24 * (i - 1),]$sf_dp_exp +
      results[17 + 24 * (i - 1),]$so_dp_exp + results[17 + 24 * (i - 1),]$tp_exp

    # Probability of 1-- to ---, starting with two out and no increase
    
    tmatrices[[i]][18,17] <- results[18 + 24 * (i - 1),]$hr_exp

    # Probability of 1-- to -2-, starting with two out and no increase

    tmatrices[[i]][18,19] <- p_2b_score_from_1b * results[18 + 24 * (i - 1),]$double_exp

    # Probability of 1-- to --3, starting with two out and no increase

    tmatrices[[i]][18,20] <- results[18 + 24 * (i - 1),]$triple_exp

    # Probability of 1-- to 12-, starting with two out and no increase

    tmatrices[[i]][18,21] <- p_1b_first_to_second * results[18 + 24 * (i - 1),]$single_exp +
      results[18 + 24 * (i - 1),]$bb_exp + results[18 + 24 * (i - 1),]$ibb_exp + 
      results[18 + 24 * (i - 1),]$hbp_exp + results[18 + 24 * (i - 1),]$ci_exp +
      p_error_1b * results[18 + 24 * (i - 1),]$e_exp + results[18 + 24 * (i - 1),]$fc_exp
    
    # Probability of 1-- to 1-3, starting with two out and no increase

    tmatrices[[i]][18,22] <- p_1b_first_to_third * results[18 + 24 * (i - 1),]$single_exp

    # Probability of 1-- to -23, starting with two out and no increase

    tmatrices[[i]][18,23] <- p_2b_go_to_3b * results[18 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[18 + 24 * (i - 1),]$e_exp

    # Probability of 1-- to end of inning, starting with two out

    tmatrices[[i]][18,25] <- results[18 + 24 * (i - 1),]$f_out_exp + 
      results[18 + 24 * (i - 1),]$fc_o_exp + results[18 + 24 * (i - 1),]$fo_exp + 
      results[18 + 24 * (i - 1),]$so_exp + results[18 + 24 * (i - 1),]$sf_exp +
      results[18 + 24 * (i - 1),]$sh_exp + results[18 + 24 * (i - 1),]$dp_exp +
      results[18 + 24 * (i - 1),]$gdp_exp + results[18 + 24 * (i - 1),]$sf_dp_exp +
      results[18 + 24 * (i - 1),]$so_dp_exp + results[18 + 24 * (i - 1),]$tp_exp
    
    # Probability of -2- to ---, starting with two out and no increase

    tmatrices[[i]][19,17] <- results[19 + 24 * (i - 1),]$hr_exp
    
    # Probability of -2- to 1--, starting with two out and no increase

    tmatrices[[i]][19,18] <- results[19 + 24 * (i - 1),]$single_exp

    # Probability of -2- to -2-, starting with two out and no increase
    
    tmatrices[[i]][19,19] <- results[19 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[19 + 24 * (i - 1),]$e_exp

    # Probability of -2- to --3, starting with two out and no increase

    tmatrices[[i]][19,20] <- results[19 + 24 * (i - 1),]$triple_exp

    # Probability of -2- to 12-, starting with two out and no increase

    tmatrices[[i]][19,21] <- results[19 + 24 * (i - 1),]$bb_exp + 
      results[19 + 24 * (i - 1),]$ibb_exp + results[19 + 24 * (i - 1),]$hbp_exp + 
      results[19 + 24 * (i - 1),]$ci_exp

    # Probability of -2- to 1-3, starting with two out and no increase

    tmatrices[[i]][19,22] <- p_error_1b * results[19 + 24 * (i - 1),]$e_exp + 
      results[19 + 24 * (i - 1),]$fc_exp

    # Probability of -2- to end of inning, starting with two out

    tmatrices[[i]][19,25] <- results[19 + 24 * (i - 1),]$fc_o_exp + 
      results[19 + 24 * (i - 1),]$f_out_exp + results[19 + 24 * (i - 1),]$so_exp +
      results[19 + 24 * (i - 1),]$fo_exp + results[19 + 24 * (i - 1),]$sf_exp +
      results[19 + 24 * (i - 1),]$sh_exp + results[19 + 24 * (i - 1),]$dp_exp +
      results[19 + 24 * (i - 1),]$gdp_exp + results[19 + 24 * (i - 1),]$sf_dp_exp +
      results[19 + 24 * (i - 1),]$so_dp_exp + results[19 + 24 * (i - 1),]$tp_exp

    # Probability of --3 to ---, starting with two out and no increase
    
    tmatrices[[i]][20,17] <- results[20 + 24 * (i - 1),]$hr_exp

    # Probability of --3 to 1--, starting with two out and no increase

    tmatrices[[i]][20,18] <- results[20 + 24 * (i - 1),]$single_exp + 
      p_error_1b * results[20 + 24 * (i - 1),]$e_exp +
      results[20 + 24 * (i - 1),]$fc_exp

    # Probability of --3 to -2-, starting with two out and no increase

    tmatrices[[i]][20,19] <- results[20 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[20 + 24 * (i - 1),]$e_exp

    # Probability of --3 to --3, starting with two out and no increase

    tmatrices[[i]][20,20] <- results[20 + 24 * (i - 1),]$triple_exp

    # Probability of --3 to 1-3, starting with two out and no increase

    tmatrices[[i]][20,22] <- results[20 + 24 * (i - 1),]$bb_exp + 
      results[20 + 24 * (i - 1),]$ibb_exp + results[20 + 24 * (i - 1),]$hbp_exp + 
      results[20 + 24 * (i - 1),]$ci_exp

    # Probability of --3 to end of inning, starting with two out

    tmatrices[[i]][20,25] <- results[20 + 24 * (i - 1),]$f_out_exp + 
      results[20 + 24 * (i - 1),]$fc_o_exp + results[20 + 24 * (i - 1),]$so_exp +
      results[20 + 24 * (i - 1),]$fo_exp + results[20 + 24 * (i - 1),]$sf_exp +
      results[20 + 24 * (i - 1),]$sh_exp + results[20 + 24 * (i - 1),]$dp_exp +
      results[20 + 24 * (i - 1),]$gdp_exp + results[20 + 24 * (i - 1),]$sf_dp_exp +
      results[20 + 24 * (i - 1),]$so_dp_exp + results[20 + 24 * (i - 1),]$tp_exp

    # Probability of 12- to ---, starting with two out and no increase

    tmatrices[[i]][21,17] <- results[21 + 24 * (i - 1),]$hr_exp

    # Probability of 12- to -2-, starting with two out and no increase

    tmatrices[[i]][21,19] <- p_2b_score_from_1b * results[21 + 24 * (i - 1),]$double_exp

    # Probability of 12- to --3, starting with two out and no increase

    tmatrices[[i]][21,20] <- results[21 + 24 * (i - 1),]$triple_exp

    # Probability of 12- to 12-, starting with two out and no increase
    
    tmatrices[[i]][21,21] <- p_1b_first_to_second * results[21 + 24 * (i - 1),]$single_exp

    # Probability of 12- to 1-3, starting with two out and no increase

    tmatrices[[i]][21,22] <- p_1b_first_to_third * results[21 + 24 * (i - 1),]$single_exp

    # Probability of 12- to -23, starting with two out and no increase
    
    tmatrices[[i]][21,23] <- p_2b_go_to_3b * results[21 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[21 + 24 * (i - 1),]$e_exp

    # Probability of 12- to 123, starting with two out and no increase
    
    tmatrices[[i]][21,24] <- results[21 + 24 * (i - 1),]$bb_exp + 
      results[21 + 24 * (i - 1),]$ibb_exp + results[21 + 24 * (i - 1),]$hbp_exp + 
      results[21 + 24 * (i - 1),]$ci_exp + p_error_1b * results[21 + 24 * (i - 1),]$e_exp +
      results[21 + 24 * (i - 1),]$fc_exp

    # Probability of 12- to end of inning, starting with two out

    tmatrices[[i]][21,25] <- results[21 + 24 * (i - 1),]$f_out_exp + 
      results[21 + 24 * (i - 1),]$fc_o_exp + results[21 + 24 * (i - 1),]$fo_exp + 
      results[21 + 24 * (i - 1),]$so_exp + results[21 + 24 * (i - 1),]$sf_exp +
      results[21 + 24 * (i - 1),]$sh_exp + results[21 + 24 * (i - 1),]$dp_exp +
      results[21 + 24 * (i - 1),]$gdp_exp + results[21 + 24 * (i - 1),]$sf_dp_exp +
      results[21 + 24 * (i - 1),]$so_dp_exp + results[21 + 24 * (i - 1),]$tp_exp
    
    # Probability of 1-3 to ---, starting with two out and no increase
    
    tmatrices[[i]][22,17] <- results[22 + 24 * (i - 1),]$hr_exp

    # Probability of 1-3 to -2-, starting with two out and no increase

    tmatrices[[i]][22,19] <- p_2b_score_from_1b * results[22 + 24 * (i - 1),]$double_exp

    # Probability of 1-3 to --3, starting with two out and no increase

    tmatrices[[i]][22,20] <- results[22 + 24 * (i - 1),]$triple_exp

    # Probability of 1-3 to 12-, starting with two out and no increase
    
    tmatrices[[i]][22,21] <- p_1b_first_to_second * results[22 + 24 * (i - 1),]$single_exp +
      p_error_1b * results[22 + 24 * (i - 1),]$e_exp + results[22 + 24 * (i - 1),]$fc_exp

    # Probability of 1-3 to 1-3, starting with two out and no increase
    
    tmatrices[[i]][22,22] <- p_1b_first_to_third * results[22 + 24 * (i - 1),]$single_exp

    # Probability of 1-3 to -23, starting with two out and no increase
    
    tmatrices[[i]][22,23] <- p_2b_go_to_3b * results[22 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[22 + 24 * (i - 1),]$e_exp

    # Probability of 1-3 to 123, starting with two out and no increase

    tmatrices[[i]][22,24] <- results[22 + 24 * (i - 1),]$bb_exp + 
      results[22 + 24 * (i - 1),]$ibb_exp + results[22 + 24 * (i - 1),]$hbp_exp + 
      results[22 + 24 * (i - 1),]$ci_exp

    # Probability of 1-3 to end of inning, starting with two out

    tmatrices[[i]][22,25] <- results[22 + 24 * (i - 1),]$f_out_exp + 
      results[22 + 24 * (i - 1),]$fc_o_exp + results[22 + 24 * (i - 1),]$fo_exp + 
      results[22 + 24 * (i - 1),]$so_exp + results[22 + 24 * (i - 1),]$sf_exp +
      results[22 + 24 * (i - 1),]$dp_exp + results[22 + 24 * (i - 1),]$gdp_exp +
      results[22 + 24 * (i - 1),]$sf_dp_exp + results[22 + 24 * (i - 1),]$sh_exp +
      results[22 + 24 * (i - 1),]$so_dp_exp + results[22 + 24 * (i - 1),]$tp_exp

    # Probability of -23 to ---, starting with two out and no increase
    
    tmatrices[[i]][23,17] <- results[23 + 24 * (i - 1),]$hr_exp

    # Probability of -23 to 1--, starting with two out and no increase

    tmatrices[[i]][23,18] <- results[23 + 24 * (i - 1),]$single_exp

    # Probability of -23 to -2-, starting with two out and no increase

    tmatrices[[i]][23,19] <- results[23 + 24 * (i - 1),]$double_exp + 
      p_error_2b * results[23 + 24 * (i - 1),]$e_exp

    # Probability of -23 to --3, starting with two out and no increase
    
    tmatrices[[i]][23,20] <- results[23 + 24 * (i - 1),]$triple_exp

    # Probability of -23 to 1-3, starting with two out and no increase
    
    tmatrices[[i]][23,22] <- p_error_1b * results[23 + 24 * (i - 1),]$e_exp + 
      results[23 + 24 * (i - 1),]$fc_exp

    # Probability of -23 to 123, starting with two out and no increase

    tmatrices[[i]][23,24] <- results[23 + 24 * (i - 1),]$bb_exp + 
      results[23 + 24 * (i - 1),]$ibb_exp + results[23 + 24 * (i - 1),]$hbp_exp + 
      results[23 + 24 * (i - 1),]$ci_exp

    # Probability of -23 to end of inning, starting with two out

    tmatrices[[i]][23,25] <- results[23 + 24 * (i - 1),]$f_out_exp + 
      results[23 + 24 * (i - 1),]$fc_o_exp + results[23 + 24 * (i - 1),]$so_exp +
      results[23 + 24 * (i - 1),]$fo_exp + results[23 + 24 * (i - 1),]$sf_exp +
      results[23 + 24 * (i - 1),]$sh_exp + results[23 + 24 * (i - 1),]$dp_exp +
      results[23 + 24 * (i - 1),]$gdp_exp + results[23 + 24 * (i - 1),]$sf_dp_exp +
      results[23 + 24 * (i - 1),]$so_dp_exp + results[23 + 24 * (i - 1),]$tp_exp

    # Probability of 123 to ---, starting with two out and no increase

    tmatrices[[i]][24,17] <- results[24 + 24 * (i - 1),]$hr_exp

    # Probability of 123 to -2-, starting with two out and no increase

    tmatrices[[i]][24,19] <- p_2b_score_from_1b * results[24 + 24 * (i - 1),]$double_exp

    # Probability of 123 to --3, starting with two out and no increase

    tmatrices[[i]][24,20] <- results[24 + 24 * (i - 1),]$triple_exp

    # Probability of 123 to 12-, starting with two out and no increase

    tmatrices[[i]][24,21] <- p_1b_first_to_second * results[24 + 24 * (i - 1),]$single_exp

    # Probability of 123 to 1-3, starting with two out and no increase

    tmatrices[[i]][24,22] <- p_1b_first_to_third * results[24 + 24 * (i - 1),]$single_exp
    
    # Probability of 123 to -23, starting with two out and no increase

    tmatrices[[i]][24,23] <- p_2b_go_to_3b * results[24 + 24 * (i - 1),]$double_exp +
      p_error_2b * results[24 + 24 * (i - 1),]$e_exp

    # Probability of 123 to 123, starting with two out and no increase
    
    tmatrices[[i]][24,24] <- results[24 + 24 * (i - 1),]$bb_exp + 
      results[24 + 24 * (i - 1),]$ibb_exp + results[24 + 24 * (i - 1),]$hbp_exp + 
      results[24 + 24 * (i - 1),]$ci_exp + p_error_1b * results[24 + 24 * (i - 1),]$e_exp +
      results[24 + 24 * (i - 1),]$fc_exp

    # Probability of 123 to end of inning, starting with two out
    
    tmatrices[[i]][24,25] <- results[24 + 24 * (i - 1),]$f_out_exp + 
      results[24 + 24 * (i - 1),]$fc_o_exp + results[24 + 24 * (i - 1),]$fo_exp + 
      results[24 + 24 * (i - 1),]$so_exp + results[24 + 24 * (i - 1),]$dp_exp +
      results[24 + 24 * (i - 1),]$gdp_exp + results[24 + 24 * (i - 1),]$sf_exp +
      results[24 + 24 * (i - 1),]$sf_dp_exp + results[24 + 24 * (i - 1),]$sh_exp +
      results[24 + 24 * (i - 1),]$so_dp_exp + results[24 + 24 * (i - 1),]$tp_exp

    # Filling in the last element of the matrix
    
    tmatrices[[i]][25,25] <- 1
    
    # Asserts that row probabilities sum to about 1
    
    for (j in 1:25) {
      rowsum <- sum(tmatrices[[i]][j,])
      assert_that((1 - rowsum) < EPSILON,
                  msg = paste0("Probability for batter ", i, ", row ", j, ", is low."))
    }
    
  }

  # Normalizing the matrix for proper calculation
  # 
  # for (i in 1:9) {
  #   for (j in 1:25) {
  #     rowsum <- sum(tmatrices[[i]][j,])
  #     print(c(i, j, rowsum))
  #     tmatrices[[i]][j,] <- tmatrices[[i]][j,] / rowsum
  #   }
  # }
  
  return(tmatrices)
  
}