9.10 Simulate Season

set.seed(20250611)
schedule_talent <- schedule_talent |>
  mutate(
    outcome = rbinom(nrow(schedule_talent), 1, prob_home),
    winner = if_else(outcome == 1, Home, Visitor)
)

Detroit Tigers 1968 Schedule
sample of 10 games
lgID	Home	Visitor	talent_home	talent_visitor	prob_home	outcome	winner
AL	BAL	DET	−0.10	0.35	0.39	0	DET
AL	DET	NYA	0.35	−0.02	0.59	1	DET
AL	DET	MIN	0.35	−0.15	0.62	1	DET
AL	CLE	DET	0.26	0.35	0.48	1	CLE
AL	NYA	DET	−0.02	0.35	0.41	0	DET
AL	BAL	DET	−0.10	0.35	0.39	0	DET
AL	NYA	DET	−0.02	0.35	0.41	1	NYA
AL	CLE	DET	0.26	0.35	0.48	1	CLE
AL	BOS	DET	−0.24	0.35	0.36	0	DET
AL	DET	BAL	0.35	−0.10	0.61	0	BAL

table code

set.seed(20250611)
schedule_talent |>
  filter(Home == "DET" | Visitor == "DET") |>
  slice_sample(n = 10) |>
  gt() |>
  cols_align(align = "center") |>
  fmt_number(columns = c(talent_home, talent_visitor, prob_home),
             decimals = 2) |>
  tab_header(title = "Detroit Tigers 1968 Schedule",
             subtitle = "sample of 10 games") |>
  tab_style(
    locations = cells_body(columns = c(Home, prob_home), rows = Home == "DET" ),
    style = list(cell_fill(color = "#FA4616"), cell_text(color = "#0C2340"))) |>
  tab_style(
    locations = cells_body(columns = Visitor, rows = Visitor == "DET" ),
    style = list(cell_fill(color = "#FA4616"), cell_text(color = "#0C2340"))) |>
  tab_style(
    locations = cells_body(columns = c(Home, prob_home), rows = Home != "DET" ),
    style = list(cell_fill(color = "#0C2340"), cell_text(color = "#FA4616"))) |>
  tab_style(
    locations = cells_body(columns = Visitor, rows = Visitor != "DET" ),
    style = list(cell_fill(color = "#0C2340"), cell_text(color = "#FA4616")))

results <- schedule_talent |> 
  group_by(winner) |>
  summarize(Wins = n()) |>
  inner_join(teams_68, by = c("winner" = "teamID"))

9.10.1 Standings

win_league <- function(res) {
  set.seed(20250611)
  res |>
    group_by(lgID) |>
    mutate(
      tiebreaker = runif(n = length(talent)),
      wins_total = Wins + tiebreaker,
      rank = min_rank(desc(wins_total)),
      is_winner_lg = wins_total == max(wins_total)
    )
}
sim_1968 <- win_league(results) |>
  rename(team = winner)

1968 Season Standings
via simulation
team	Wins	talent	tiebreaker	wins_total	rank	is_winner_lg
AL
DET	98	0.35	0.78	98.78	1	TRUE
CHA	97	0.07	0.85	97.85	2	FALSE
CLE	95	0.26	0.19	95.19	3	FALSE
NYA	86	−0.02	0.58	86.58	4	FALSE
MIN	80	−0.15	0.65	80.65	5	FALSE
OAK	74	−0.14	0.90	74.90	6	FALSE
WS2	74	−0.02	0.75	74.75	7	FALSE
BAL	74	−0.10	0.31	74.31	8	FALSE
CAL	71	−0.17	0.12	71.12	9	FALSE
BOS	61	−0.24	0.05	61.05	10	FALSE
NL
SLN	99	0.31	0.67	99.67	1	TRUE
HOU	99	0.19	0.45	99.45	2	FALSE
CIN	95	0.18	0.23	95.23	3	FALSE
CHN	85	0.03	0.54	85.54	4	FALSE
SFN	85	−0.01	0.46	85.46	5	FALSE
ATL	78	−0.05	0.46	78.46	6	FALSE
NYN	73	−0.18	0.28	73.28	7	FALSE
PHI	67	−0.32	0.24	67.24	8	FALSE
LAN	65	−0.08	0.47	65.47	9	FALSE
PIT	64	−0.08	0.48	64.48	10	FALSE

table code

sim_1968 |>
  arrange(rank) |>
  gt() |>
  cols_align(align = "center") |>
  data_color(columns = Wins,
             palette = "inferno") |>
  fmt_number(columns = c(talent, tiebreaker, wins_total),
             decimals = 2) |>
  tab_header(title = "1968 Season Standings",
             subtitle = "via simulation")

9.10.2 Simulate World Series

set.seed(20250611)
ws_winner <- sim_1968 |>
  filter(is_winner_lg) |>
  ungroup() |>
  mutate(
    outcome = as.numeric(rmultinom(1, 7, exp(talent))),
    is_winner_ws = outcome > 3
  )

1968 Post-Season
via simulation
team	Wins	lgID	talent	outcome	is_winner_ws
DET	98	AL	0.35	4	TRUE
SLN	99	NL	0.31	3	FALSE

table code

ws_winner |>
  select(team, Wins, lgID, talent, outcome, is_winner_ws) |>
  gt() |>
  cols_align(align = "center") |>
  fmt_number(columns = talent,
             decimals = 2) |>
  tab_header(title = "1968 Post-Season",
             subtitle = "via simulation") |>
  tab_style(
    locations = cells_body(columns = c(team, outcome, is_winner_ws), 
                           rows = team == "DET" ),
    style = list(cell_fill(color = "#FA4616"), cell_text(color = "#0C2340"))) |>
  tab_style(
    locations = cells_body(columns = c(team, outcome, is_winner_ws), 
                           rows = team == "SLN" ),
    style = list(cell_fill(color = "#C41E3A"), cell_text(color = "#0C2340"))) |>
  tab_style(locations = cells_body(columns = outcome),
            style = cell_text(weight = "bold"))