Scraping Betting Markets

I scraped historical betting lines and which teams actually made the playoffs each season from the “Archived NBA Futures Odds” section of Sports Odds History⁵. The Sports Odds History website is constructed in a way that makes it relatively straight-forward to scrape the requisite information.

The webpage for each season has a (mostly) consistent table structure and associated date of archive.

Each season has a consistent URL (with only the season year changing).

# Load packages
library(tidyverse)
library(rvest)
library(gt)
library(broom)

# Helper functions
# Some of the tables had the lines represented as character strings like "+400"
# "-300". This converts those to a numeric type (if they're not  already).
odds_to_numeric <- function(x){
  if(is.numeric(x)) return(x)
  sign <- str_sub(x, 1, 1)
  sign <- case_when(sign == "-" ~ -1,
                    sign == "+" ~ 1)
  x_dbl <- str_sub(x, 2) %>% as.double()
  x_dbl * sign
}

# -400 would be converted to 4, +400 to 0.25
line_to_odds <- function(x){
  positive <- sign(x) == 1
  abs_x <- abs(x)
  case_when(positive ~ 100 / abs_x ,
            !positive ~ abs_x / 100)
}

odds_to_prob <- function(odds){
  odds / (1 + odds)
}

# step 1
scrape_urls <- tibble(start_yr = 2014:2020, end_yr = 2015:2021) %>% 
  mutate(yr = paste0(start_yr, "-", end_yr),
         urls = glue::glue(
           "https://www.sportsoddshistory.com/nba-win/?y={yr}&sa=nba&t=post&o=s",
           yr = yr
         ))


scrape_urls %>% 
  gt::gt()

scrape_nba_playoffs_odds <- function(url){
  
  css_selector_tbl <- "#content > div > table.soh1"
  
  html_page <- url %>% 
    read_html()
  
  # step 3
  data <- html_page %>% 
    html_element(css = css_selector_tbl) %>% 
    html_table() %>% 
    janitor::clean_names() %>% 
    mutate(
      # step 4
      across(contains("odds"),
             list(dbl = ~odds_to_numeric(.x) %>% 
                    line_to_odds())),
      # step 5
      make_odds_avg = (make_odds_dbl + 1 / miss_odds_dbl) / 2)

  html_kids <- html_page %>% 
    html_element(css = "#content > div") %>% 
    html_children() %>% 
    html_text2()
  
  # step 6
  phrase_date <- "As of "
  date_taken <- html_kids %>% 
    str_subset(phrase_date) %>% 
    str_extract(glue::glue("(?<={phrase_date}).+")) %>% 
    lubridate::mdy()
  
  data %>% 
    mutate(forecast_date = date_taken) %>% 
    # type varied between webpages so force to chr so can bind multiple...
    mutate(across(c(make_odds, miss_odds), as.character)) %>% 
    relocate(forecast_date)
}

# Step 2 (applies steps 3 through 6 on each URL)
scraped_urls <- scrape_urls %>% 
  mutate(data = map(urls, scrape_nba_playoffs_odds))

odds_data_prepped <- scraped_urls %>% 
  select(season = end_yr, data) %>% 
  # step 7
  unnest(data) %>% 
  arrange(desc(season)) %>% 
  mutate(
    # step 8
    make_playoffs_bookies = odds_to_prob(make_odds_avg),
    result = ifelse(result == "MAKE", 1, 0)
    ) %>% 
  select(season, forecast_date, team, result, make_playoffs_bookies) %>% 
  mutate(team = str_extract(team, "(?<=[:blank:])[:alnum:]+$"))

Joining with FiveThirtyEight data

9. All FiveThirtyEight NBA playoff forecasts were available in a .csv on github here.
10. FiveThirtyEight updates their forecasts every day. For the archived betting market payouts there is only one day of odds for each season. I filtered FiveThirtyEight forecasts to just those days where I also had market data⁸.
11. Joined FiveThirtyEight forecasts with market and outcome data.
12. In a few instances market data was not available, in which case I also filtered out the corresponding FiveThirtyEight records.

Steps 9 to 12

# step 9
data_538 <- read_csv("https://raw.githubusercontent.com/fivethirtyeight/checking-our-work-data/master/nba_playoffs.csv")

bookies_538_joined <- data_538 %>% 
  # step 10
  filter(forecast_date %in% unique(odds_data_prepped$forecast_date)) %>% 
  select(season, forecast_date, team, make_playoffs_538 = make_playoffs) %>% 
  # step 11
  left_join(odds_data_prepped, by = c("season", "team", "forecast_date")) %>% 
  # step 12
  na.omit() %>% 
  # mutate(make_playoffs_avg = (make_playoffs_538 + make_playoffs_bookies) / 2) %>% 
  relocate(result, .after = team)

Resulting table for analysis (preview of 5 rows)

bookies_538_joined %>% 
  head(5) %>% 
  gt::gt() %>% 
  gt::fmt_number(decimals = 3, columns = c("make_playoffs_538", "make_playoffs_bookies"))

How much does FiveThirtyEight differ from markets?

Overall performance may be similar even when individual forecasts are quite different. Circling back to the start of NBA Playoffs and the Lakers, what got me writing was noticing FiveThirtyEight’s divergence from the betting markets in their recent view of the Lakers’ playoff chances.

At -460 the markets had an implied probability of the Lakers making the playoffs of ~82%¹². FiveThirtyEight’s forecast of 27% means a difference of ~55 percentage points (ppt)¹³.

Is this difference atypical?

Across five seasons of data (145 observations), the correlation coefficient was 0.92 (strong correlation). The average difference between FiveThirtyEight and betting markets was ~10 percentage points.

bookies_538_joined %>% 
  mutate(diff = abs(make_playoffs_538 - make_playoffs_bookies)) %>% 
  # summarise(mean_diff = mean(diff)) %>% 
  with(t.test(diff)) %>%
  broom::tidy() %>%
  select(avg_abs_ppt_diff_538_bookies = estimate, contains("conf")) %>%
  gt::gt() %>%
  gt::fmt_number(columns = everything(),
                 decimals = 3)

A difference of 55 ppt is bigger than any I saw in the historical data. The closest was 48 ppt¹⁴:

bookies_538_joined %>% 
  mutate(make_playoffs_diff = abs(make_playoffs_538 - make_playoffs_bookies)) %>% 
  arrange(desc(make_playoffs_diff)) %>% 
  head(1) %>% 
  gt::gt() %>%
  gt::fmt_number(columns = contains("make_playoffs"),
                 decimals = 3)

In the Appendix I give some Potential Reasons for the Difference, though on its surface 55 ppt does seem like a historically large disagreement between FiveThirtyEight and the betting markets.

Potential Reasons for the Difference

Some reasons why the observed 55 ppt difference in expectations between FiveThirtyEight and betting markets may not be as extreme as it seems:

• My historical data is looking at individual time-point comparisons at just one point for each season – perhaps betting markets and FiveThirtyEight vary more from one another at different points in the year than those at the points I have..
• Market odds (according to Sports Odds History) are archived come from BetMGM. I don’t know where I was looking when I saw the -460 odds on the Lakers. Each betting market is different and may have different levels of covariation with FiveThirtyEight’s forecasts.
• I was looking at just the “odds of making the playoffs” not the average of that with the inverse of “odds to miss the playoffs” as I did in step 5 of Steps¹⁷.
• Changes in methodology of more recent forecasts may have made it depart more from betting markets compared to in prior years

Calculating percentiles of diff

Initially I’d planned on including the calculation of some percentiles of various differences in percentage points. Saved code from examples below.

one_off_diff <- 0.27 - odds_to_prob(line_to_odds(-460))

bookies_538_joined %>% 
  mutate(diff = abs(make_playoffs_538 - make_playoffs_bookies)) %>% 
  summarise(percentile_of_difference = sum(diff < one_off_diff) / n())

# Alternative approach for calculating one-off diff
ecdf_diffs <- bookies_538_joined %>% 
  mutate(diff = abs(make_playoffs_538 - make_playoffs_bookies)) %>% 
  with(ecdf(diff))

ecdf_diffs(one_off_diff)