R • Sports analysis • Ratings • Monte Carlo • Forecasts
Sports are noisy. Teams change. Injuries happen. Disruptions happen. But uncertainty is not the enemy – it is the input. In this practical guide, you will build a practical sports prediction workflow R to use tidal verses, Player RatingsAnd NFLSimulatorRand then attach reviews Monte Carlo simulations And prediction models (logistic regression & Poisson).
Goal
Probabilities, not ‘choices’
Core tools
Reviews + models + simulation
Export
Reproducible code and scenarios
Table of contents
Everything below is intended to be copied into an R script and executed. Swap the toy data for your league data (soccer, basketball, American football, tennis, baseball, esports, you name it).
1) Design: a reproducible R project
Prediction work quickly gets messy if you can’t reproduce it. Start each project with: (1) a clean package configuration, (2) a fixed random seed, (3) clean data conventions.
# Install (run once)
install.packages(c("tidyverse", "lubridate", "PlayerRatings"))
# If you plan to use NFLSimulatoR (CRAN/GitHub availability varies):
# install.packages("NFLSimulatoR")
# or, if needed:
# install.packages("remotes"); remotes::install_github(".../NFLSimulatoR")
library(tidyverse)
library(lubridate)
library(PlayerRatings)
set.seed(2026) # reproducibility: simulation + model splits will matchRule of thumb: if your analysis cannot be redone from start to finish from a new session, it is not ready for decisions (betting, scouting or strategy).
2) A small data set (so we can focus on methods)
We build a compact competition table with team names, dates and results. You can later replace this with real data (e.g. football leagues, NBA matches, tennis matches).
# Create toy match results
teams <- c("Lions", "Tigers", "Bears", "Wolves", "Hawks", "Sharks")
n_games <- 120
matches <- tibble(
date = sample(seq.Date(as.Date("2025-08-01"), as.Date("2026-01-31"), by = "day"), n_games, replace = TRUE),
home = sample(teams, n_games, replace = TRUE),
away = sample(teams, n_games, replace = TRUE)
) %>%
filter(home != away) %>%
arrange(date) %>%
mutate(
# "true" (hidden) team strengths to generate outcomes (toy world)
home_strength = recode(home,
"Lions"=0.6,"Tigers"=0.5,"Bears"=0.4,"Wolves"=0.2,"Hawks"=0.1,"Sharks"=0.0),
away_strength = recode(away,
"Lions"=0.6,"Tigers"=0.5,"Bears"=0.4,"Wolves"=0.2,"Hawks"=0.1,"Sharks"=0.0),
# Convert strength difference into a win probability
p_home = plogis(0.4 + 2.0*(home_strength - away_strength)), # home advantage + skill gap
home_win = rbinom(n(), size = 1, prob = p_home)
) %>%
select(date, home, away, home_win, p_home)
matches %>% slice(1:8)This is deliberately minimal: just enough to demonstrate Elo/Glicko, win rates, simulation and modeling.
3) Elo Ratings with PlayerRatings
Elo is a rating system that is updated after every game. It’s not “magic” – it’s a controlled way to: (1) estimate team strength based on history, and (2) convert rating differences into expected winning probabilities.
3.1 Prepare the input format
# PlayerRatings expects a "competitionResult" object.
# We'll represent teams as "players" and each game as a head-to-head match.
elo_input <- matches %>%
transmute(
Date = date,
Player1 = home,
Player2 = away,
# For PlayerRatings: 1 = Player1 win, 0 = Player2 win (or use Score columns)
Result = if_else(home_win == 1, 1, 0)
)
head(elo_input)3.2 Try on now
# Run Elo with a K-factor (update speed). Tune K by sport and data volume.
elo_fit <- elo(elo_input, k = 20)
# Ratings after processing all games
elo_ratings <- as.data.frame(elo_fit$ratings) %>%
rownames_to_column("team") %>%
as_tibble() %>%
rename(elo = Rating) %>%
arrange(desc(elo))
elo_ratingsWhy Elo is useful: it’s lightweight, interpretable, and often surprisingly competitive as a baseline. Use it to sanity check more complex models.
4) Glicko Ratings (when uncertainty matters)
Elo tells you ‘power’. Glicko tells you “power + insecurity.” Early season? New team? Played few matches? Glicko’s rating bias helps you avoid false confidence.
# Glicko uses a similar input, but the function differs (depends on PlayerRatings version). # Many workflows look like this: glicko_input <- elo_input # same structure works for many head-to-head methods # Some installs provide a glicko() function: # glicko_fit <- glicko(glicko_input) # If your PlayerRatings build doesn't expose glicko() directly, # you can still rely on Elo for the main pipeline and add uncertainty via modeling/simulation. # Pseudo-example structure: # glicko_ratings <- glicko_fit$ratings
NB: package APIs may change. If your local PlayerRatings version is not direct glicko() helper, you can still make uncertainty-aware predictions by combining judgments with a probabilistic model (logistic regression/Bayesian) and then simulating forward.
5) Turn reviews into winning opportunities
Ratings become useful once you connect them to probabilities. The classic Elo forecast uses a logistic curve. You can also learn this mapping empirically (recommended) by applying a model to previous games.
5.1 Add Elo back to the competition rows
matches_w_elo <- matches %>%
left_join(elo_ratings %>% rename(home_elo = elo), by = c("home" = "team")) %>%
left_join(elo_ratings %>% rename(away_elo = elo), by = c("away" = "team")) %>%
mutate(elo_diff = home_elo - away_elo)
matches_w_elo %>% select(date, home, away, home_win, home_elo, away_elo, elo_diff) %>% slice(1:10)5.2 A simple Elo-to-probability mapping
# Classic Elo expected score mapping (base-10 logistic).
# "scale" controls steepness. For chess Elo it's 400 by convention.
elo_prob <- function(diff, scale = 400) {
1 / (1 + 10^(-diff / scale))
}
matches_w_elo <- matches_w_elo %>%
mutate(p_home_elo = elo_prob(elo_diff, scale = 250)) # scale tuned for our toy world
matches_w_elo %>%
summarize(
avg_p = mean(p_home_elo),
brier = mean((home_win - p_home_elo)^2)
)Elo gives a basic probability. We will then simulate seasons and then improve the mapping using regression models.
6) Monte Carlo: Simulate a season and playoff chances
With Monte Carlo simulation you turn game odds into season-level questions: “What is the probability that we will finish in the top 2?” “How often do we play play-offs?” “What is the distribution of victories?”
6.1 Draw up a future schedule
# Create a "future" schedule (e.g., the next 60 games)
n_future <- 60
future <- tibble(
date = seq.Date(as.Date("2026-02-01"), by = "day", length.out = n_future),
home = sample(teams, n_future, replace = TRUE),
away = sample(teams, n_future, replace = TRUE)
) %>%
filter(home != away) %>%
left_join(elo_ratings %>% rename(home_elo = elo), by = c("home" = "team")) %>%
left_join(elo_ratings %>% rename(away_elo = elo), by = c("away" = "team")) %>%
mutate(
elo_diff = home_elo - away_elo,
p_home = elo_prob(elo_diff, scale = 250)
)
future %>% slice(1:8)6.2 Simulate the remaining season many times
simulate_season <- function(future_games, n_sims = 5000) {
# We'll simulate all games n_sims times, then compute win totals.
sims <- replicate(n_sims, {
future_games %>%
mutate(home_win = rbinom(n(), 1, p_home)) %>%
transmute(
home, away,
home_w = home_win,
away_w = 1 - home_win
) %>%
pivot_longer(cols = c(home, away), names_to = "side", values_to = "team") %>%
mutate(win = if_else(side == "home", home_w, away_w)) %>%
group_by(team) %>%
summarize(wins = sum(win), .groups = "drop")
}, simplify = FALSE)
bind_rows(sims, .id = "sim") %>%
mutate(sim = as.integer(sim))
}
season_sims <- simulate_season(future, n_sims = 3000)
# Win distribution by team
win_dist <- season_sims %>%
group_by(team) %>%
summarize(
avg_wins = mean(wins),
p_top2 = mean(rank(-wins, ties.method = "random") <= 2),
p_top3 = mean(rank(-wins, ties.method = "random") <= 3),
.groups = "drop"
) %>%
arrange(desc(avg_wins))
win_distInterpretation tip: simulation answers “distribution” questions (ranges, tails, probabilities). That’s exactly what decision makers care about.
7) “What-if” analysis: injuries, transfers, roster changes
In counterfactuals, modeling becomes practical: you change the assumptions about team strength and see how the outcomes change. For Elo-based pipelines, this is as simple as adding/subtracting rating points.
# Example: star injury reduces Lions by 60 Elo points for the rest of the season
adjusted_ratings <- elo_ratings %>%
mutate(elo_adj = if_else(team == "Lions", elo - 60, elo))
future_counterfactual <- future %>%
select(date, home, away) %>%
left_join(adjusted_ratings %>% select(team, home_elo = elo_adj), by = c("home" = "team")) %>%
left_join(adjusted_ratings %>% select(team, away_elo = elo_adj), by = c("away" = "team")) %>%
mutate(
elo_diff = home_elo - away_elo,
p_home = elo_prob(elo_diff, scale = 250)
)
baseline <- simulate_season(future, n_sims = 2000) %>% mutate(scenario = "baseline")
injury <- simulate_season(future_counterfactual, n_sims = 2000) %>% mutate(scenario = "lions_injury")
compare <- bind_rows(baseline, injury) %>%
group_by(scenario, team) %>%
summarize(avg_wins = mean(wins), .groups = "drop") %>%
pivot_wider(names_from = scenario, values_from = avg_wins) %>%
mutate(delta = lions_injury - baseline) %>%
arrange(delta)
compareThe same idea works for transfers, coaching changes, or “rest days” – anything you can reasonably code as a power shift.
8) Poisson models for score lines
If you’re predicting scores (not just wins/losses), Poisson models provide a strong baseline, especially in low-scoring sports. The classic setup models goals scored as Poisson with attack/defense effects and home advantage.
8.1 Generate toy score data
# Create toy goals (home_goals, away_goals) driven by hidden strengths.
# This mimics soccer/hockey-like scoring.
scores <- matches %>%
mutate(
lambda_home = exp(-0.2 + 1.2*home_strength - 0.9*away_strength + 0.25),
lambda_away = exp(-0.2 + 1.2*away_strength - 0.9*home_strength),
home_goals = rpois(n(), lambda_home),
away_goals = rpois(n(), lambda_away),
home_win = as.integer(home_goals > away_goals),
draw = as.integer(home_goals == away_goals)
) %>%
select(date, home, away, home_goals, away_goals, home_win, draw)
scores %>% slice(1:8)8.2 Mounting Poisson GLMs
# Two-model approach: predict home_goals and away_goals separately.
# Features: team identifiers (as factors) can capture attack/defense proxies in simple form.
po_home <- glm(home_goals ~ home + away, data = scores, family = poisson())
po_away <- glm(away_goals ~ home + away, data = scores, family = poisson())
# Predict expected goals for upcoming games
future_xg <- future %>%
select(date, home, away) %>%
mutate(
xg_home = predict(po_home, newdata = ., type = "response"),
xg_away = predict(po_away, newdata = ., type = "response")
)
future_xg %>% slice(1:8)8.3 Convert expected goals into profit opportunities
# Approximate match outcome probabilities by simulating scorelines from the Poisson rates.
scoreline_probs <- function(lambda_home, lambda_away, n = 20000) {
hg <- rpois(n, lambda_home)
ag <- rpois(n, lambda_away)
tibble(
p_home_win = mean(hg > ag),
p_draw = mean(hg == ag),
p_away_win = mean(hg < ag)
)
}
example_probs <- scoreline_probs(future_xg$xg_home[1], future_xg$xg_away[1], n = 30000)
example_probsWhy this works: If you can predict scoring percentages, you can also predict every downstream event: win, draw, total goals, both teams scoring, etc.
9) Logistic regression for match results
A clean upgrade from ‘rough Elo mapping’ is to fit a logistic regression that learns how rating differences translate into win probability, optionally adding context features (rest, travel, injuries, lineup quality).
# Train on historical matches: outcome ~ elo_diff
train <- matches_w_elo %>% drop_na(home_elo, away_elo)
logit <- glm(home_win ~ elo_diff, data = train, family = binomial())
summary(logit)
# Predict probabilities for future games using the fitted mapping
future_logit <- future %>%
left_join(elo_ratings %>% rename(home_elo = elo), by = c("home" = "team")) %>%
left_join(elo_ratings %>% rename(away_elo = elo), by = c("away" = "team")) %>%
mutate(
elo_diff = home_elo - away_elo,
p_home = predict(logit, newdata = ., type = "response")
)
future_logit %>% slice(1:8)Logistic regression also makes it easy to include additional predictors besides ratings.
10) Using NFLSimulatorR as a simulator backbone
If you’re working specifically on American football, a purpose-built simulator can speed up your pipeline: schedule generation, game simulation, season simulation and rankings logic.
Remark: The exact function names may differ depending on the NFLSimulator version you have. The pattern below shows a practical structure that you can adapt: prepare team strengths → simulate matches → collect rankings → repeat.
# library(NFLSimulatoR)
# 1) Define (or estimate) team strength inputs
team_strengths <- elo_ratings %>% select(team, elo)
# 2) Build or import a schedule (week, home, away)
# nfl_schedule <- NFLSimulatoR::load_schedule(season = 2026)
# or your own:
nfl_schedule <- tibble(
week = rep(1:10, each = 3),
home = sample(teams, 30, replace = TRUE),
away = sample(teams, 30, replace = TRUE)
) %>% filter(home != away)
# 3) Map strengths to win probs (Elo-based or model-based)
nfl_games <- nfl_schedule %>%
left_join(team_strengths %>% rename(home_elo = elo), by = c("home" = "team")) %>%
left_join(team_strengths %>% rename(away_elo = elo), by = c("away" = "team")) %>%
mutate(
elo_diff = home_elo - away_elo,
p_home = elo_prob(elo_diff, scale = 250)
)
# 4) Simulate a season many times
simulate_nfl_like <- function(games, n_sims = 5000) {
sims <- replicate(n_sims, {
games %>%
mutate(home_win = rbinom(n(), 1, p_home)) %>%
transmute(home, away, home_w = home_win, away_w = 1 - home_win) %>%
pivot_longer(cols = c(home, away), names_to = "side", values_to = "team") %>%
mutate(win = if_else(side == "home", home_w, away_w)) %>%
group_by(team) %>%
summarize(wins = sum(win), .groups = "drop")
}, simplify = FALSE)
bind_rows(sims, .id = "sim") %>%
mutate(sim = as.integer(sim))
}
nfl_sims <- simulate_nfl_like(nfl_games, n_sims = 3000)
nfl_summary <- nfl_sims %>%
group_by(team) %>%
summarize(
avg_wins = mean(wins),
p_10plus = mean(wins >= 10),
.groups = "drop"
) %>%
arrange(desc(avg_wins))
nfl_summaryKey idea: you don’t need a “perfect” game model to get useful season-level opportunities. An engine with a reasonable chance of winning + Monte Carlo is already powerful.
11) Evaluation: calibration + correct scoring
When predicting, accuracy alone is not enough. You want probabilities that are well calibrated and score well under the correct scoring rules (Brier score, log loss).
11.1 Brier Score
brier_score <- function(y, p) mean((y - p)^2)
# Compare Elo mapping vs logistic regression mapping (on the same historical set)
eval_tbl <- train %>%
mutate(
p_elo = elo_prob(elo_diff, scale = 250),
p_logit = predict(logit, newdata = ., type = "response")
) %>%
summarize(
brier_elo = brier_score(home_win, p_elo),
brier_logit = brier_score(home_win, p_logit)
)
eval_tbl11.2 Calibration table (quick check)
calibration_table <- function(y, p, bins = 10) {
tibble(y = y, p = p) %>%
mutate(bin = ntile(p, bins)) %>%
group_by(bin) %>%
summarize(
p_avg = mean(p),
y_avg = mean(y),
n = n(),
.groups = "drop"
)
}
calib <- train %>%
mutate(p_logit = predict(logit, newdata = ., type = "response")) %>%
calibration_table(y = home_win, p = p_logit, bins = 10)
calibInterpretation: In each probability class, the average predicted probability should approximately match the observed win rate. If not, your model is miscalibrated (common and can be resolved).
12) Wrap-up: a practical workflow that you can reuse
Here’s the repeatable blueprint you just built:
- Process results in a tidy competition table (one row per game).
- Estimate strengths (Elo/Glicko or something similar).
- Map strengths → opportunities (Elo curve or an appropriate logistic model).
- Simulate forward with Monte Carlo for season and play-off chances.
- Do counterfactuals by adjusting strengths or model features.
- Evaluate with proper scoring and calibration controls.
If you like this approach and want a compact, practical walkthrough that puts these parts together into one practical learning path – assessments (Elo/Glicko), Monte Carlo seasons/tournaments, and forecasting models with executable R code – you can find a focused guide here: Sports prediction and simulation with R.
It’s built to ‘open it, run the code, understand the method’ so you can apply the same pipeline to soccer, basketball, American football, tennis, baseball, esports and more.
Disclaimer: This article is educational and focuses on modeling and simulation techniques. Real-world performance depends on data quality, competition structure, and how well your features capture the game.
The message Predicting sports in R: Elo, Monte Carlo and real simulations appeared first on R Programming Books.
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