Aces and Postseason Rotation Timing

The Tigers lost game five of the ALDS Friday night after 15 innings of both teams politely refusing to get any hits. Tarik Skubal was again masterful, going 6 innings with 13 Ks, 0 walks, and 1 run allowed over 2 hits. His FIP for the game was -1.20, which is just crazy.

Had the Tigers won, he would have been available for games 3 and 7 of the series against the Blue Jays. This got me wondering what impact having him start those games instead of 1 and 4 would have on their odds of winning the ALCS. This is all hypothetical now, but we all work through the disappointment in different ways.

First, let’s make some assumptions. We want to keep this fairly simple, so we’ll say that if anybody but Skubal (or your team’s given ace) is pitching, then your team has a 50% chance of winning. This will vary in reality, of course, but in this case a simple model will suffice. We’ll also assume that if Skubal is on the mound the Tiger’s chance of winning is 55%. That may not seem like a big difference, but Skubal doesn’t hit, and since the Tiger batters often don’t either, there’s only so much he can do to swing the odds. He had a masterful start Friday and they still lost.*

*This is one of the main reasons that win-loss records for pitchers aren’t useful - they rely too heavily on factors outside of the pitcher’s control.

Having that in place, we’ll run three simulations: one where he starts games 1 and 5, another where he starts 2 and 6, and finally 3 and 7. We’ll assume that no manager is so negligent as to start their ace only in game 4. We’ll simulate the ALCS 10,000 times for each scenario*, running each game independently.

*For some reason, teams object to playing the same series even a mere thousand times, so we have to run simulations instead.

Show the code

library(hrbrthemes)
library(janitor)
library(gt)
library(gtExtras)
library(tidyverse)

set.seed(202510)

sim_game <- function(winning_odds){
  
game_simmed <- rbinom(10000, 1, winning_odds) %>%
  as_tibble() %>%
  mutate(sim_id = row_number()) %>%
  select(sim_id, value) %>%
  rename(w = value) %>%
  mutate(l = ifelse(w == 0, 1, 0))

game_simmed
  
}

sim_series <- function(data){

series_simmed <- data %>%
  mutate(sim = map(tigers,\(code) .f = sim_game(code))) %>%
  unnest(sim) %>%
  arrange(sim_id) %>%
  group_by(sim_id) %>%
  mutate(n = row_number(),
         w = cumsum(w),
         l = cumsum(l)) %>%
  mutate(series_over = w >= 4 | l >= 4,
         series_over2 = cumsum(series_over)) %>%
  filter(series_over2 == 1) %>%
  mutate(won_series = ifelse(w > l, 1, 0)) %>%
  select(n, w, l, won_series) %>%
  rename(g = n)

series_simmed
}

alcs_three <- tribble(~game, ~tigers, ~toronto,
                     1, .5, .5,
                     2, .5, .5,
                     3, .6, .4,
                     4, .5, .5,
                     5, .5, .5,
                     6, .5, .5,
                     7, .6, .4)

alcs_two <- alcs_three %>%
  mutate(game = ((game - 2) %% 7) + 1) %>%
  arrange(game)

alcs_one <- alcs_three %>%
  mutate(game = ((game - 3) %% 7) + 1) %>%
  arrange(game)

scenario_3_and_7 <- sim_series(alcs_three)

scenario_2_and_6 <- sim_series(alcs_two)

scenario_1_and_5 <- sim_series(alcs_one)

tribble(~starts, ~exp,
        '1 and 5', mean(scenario_1_and_5$won_series),
        '2 and 6', mean(scenario_2_and_6$won_series),
        '3 and 7', mean(scenario_3_and_7$won_series)) %>%
  gt() %>%
  gt_theme_espn() %>%
  fmt_percent(columns = c(exp), decimals = 2) %>%
  cols_label(exp = 'Odds of Winning Series')

starts	Odds of Winning Series
1 and 5	56.56%
2 and 6	56.25%
3 and 7	56.54%

This is closer than I expected. But it makes sense - your best pitcher is going twice, so as long as you have respectable odds the rest of the series you can close out the series with your best pitcher and win the whole thing.

Show the code

scenario_1_and_5_agg <- scenario_1_and_5 %>%
  group_by(g, w, l) %>%
  summarise(n1 = n()) %>%
  ungroup() %>%
  mutate(p1 = n1 / sum(n1)) %>%
  arrange(w, l)

scenario_2_and_6_agg <- scenario_2_and_6 %>%
  group_by(g, w, l) %>%
  summarise(n2 = n()) %>%
  ungroup() %>%
  mutate(p2 = n2 / sum(n2)) %>%
  arrange(w, l)

scenario_3_and_7_agg <- scenario_3_and_7 %>%
  group_by(g, w, l) %>%
  summarise(n3 = n()) %>%
  ungroup() %>%
  mutate(p3 = n3 / sum(n3)) %>%
  arrange(w, l)

scenario_1_and_5_agg %>%
  inner_join(scenario_2_and_6_agg) %>%
  inner_join(scenario_3_and_7_agg) %>%
  mutate(winning_team = ifelse(w == 4, 'Tigers', 'Blue Jays')) %>%
  select(winning_team, g, w, l, n1, p1, n2, p2, n3, p3) %>%
  gt() %>%
  gt_theme_espn() %>%
  fmt_number(columns = c(n1, n2, n3), decimals = 0) %>%
  fmt_percent(columns = c(p1, p2, p3), decimals = 1) %>%
  tab_spanner(
    label = "One and Five",
    columns = c(n1, p1)
  ) %>%
  tab_spanner(
    label = "Two and Six",
    columns = c(n2, p2)
  ) %>%
tab_spanner(
  label = "Three and Seven",
  columns = c(n3, p3)
)

winning_team	g	w	l	One and Five		Two and Six		Three and Seven
winning_team	g	w	l	n1	p1	n2	p2	n3	p3
Blue Jays	4	0	4	493	4.9%	502	5.0%	467	4.7%
Blue Jays	5	1	4	864	8.6%	1,090	10.9%	1,107	11.1%
Blue Jays	6	2	4	1,352	13.5%	1,222	12.2%	1,532	15.3%
Blue Jays	7	3	4	1,635	16.4%	1,561	15.6%	1,240	12.4%
Tigers	4	4	0	734	7.3%	776	7.8%	784	7.8%
Tigers	5	4	1	1,673	16.7%	1,346	13.5%	1,404	14.0%
Tigers	6	4	2	1,677	16.8%	1,947	19.5%	1,632	16.3%
Tigers	7	4	3	1,572	15.7%	1,556	15.6%	1,834	18.3%

The breakdown here is interesting - it shows better odds for a shorter series the sooner Skubal starts. So while the overall odds come out close enough that we don’t care, this shows that, if you’re able to start your ace sooner, you should. A shorter series means less wear on your players - especially the bullpen - and gives you time to situate your rotation for the next series. Of course, your opponents may start their ace as well, which may negate your advantage depending on how good he is.

Analyst takeaways:

Running simulations is a quick, powerful way to test different scenarios. Your assumptions will play a huge role, so make sure you take the time to understand the underlying processes so you can be as realistic as possible.
An aggregate number won’t always tell the whole story. Looking at its composition or a supporting metric (in this case, mean games played) provides additional information.
Just because you found the mathematically optimal solution doesn’t mean it will work in practice. Skubal wouldn’t have been available for games 1 or 2, so telling leadership that those are better options when they’re not available would not go over well and would likely erode trust.