Teams win more often at home. Using the IRW’s competition tables, we estimate home advantage net of team strength in every season of baseball, basketball, hockey, American football and English and Italian football back to the nineteenth century, ask how it has changed, and then use the 2020-21 seasons played in empty stadiums to ask how much of it the crowd supplies.
October 23, 2026
This vignette — including the dataset search, the compute script, the analysis design, and the writing below — was produced largely by Claude (Anthropic), working from a task specification and with human review. Treat the methodological choices and interpretations accordingly, and check the compute script (home_advantage_compute.R) directly if you’re relying on the numbers here.
Home teams win more often than away teams. This is among the oldest and best documented regularities in sport: Pollard (1986) documented it for English football, Pollard and Pollard (2005) traced it across professional team sports in North America and England back to 1876, and Jamieson (2010)’s meta-analysis found it across every sport and era studied. Two questions about it remain live.
The IRW’s competition tables are well suited to both. They store one row per game between two agents, with a common coding of which side was at home, across sports and back as far as 1871. Home advantage is then a single parameter in a paired-comparison model, estimated net of the strength of the two sides. In IRW terms it is something like an item parameter that every game shares, estimated across hundreds of tables, and the question is whether it is stable.
library(irw)
# every comp table with a real home side and a long run of seasons
tables <- c(
"retrosheet_mlb_1871_2025", "fivethirtyeight_nba_1946_2023",
"fivethirtyeight_nhl_1917_2023", "fivethirtyeight_nfl_1920_2023",
"nflverse_nfl_1999_2025", "footbayes_england", "footbayes_italy",
"fivethirtyeight_soccer_2016_2023", "rugby_union_tier1_1871_2026",
"intlfootball_men_1872-2026", "intlfootball_women_1956-2026"
)
games <- lapply(tables, irw_fetch, source = "comp")The IRW’s competition collection has over a hundred tables, from professional leagues and esports to animal dominance encounters and pairwise judgments. Most have no home side. We used the 11 tables that have one and that run over many seasons. Each table codes the home side the same way: homefield is "agent_a" when agent_a is at home and missing at a neutral venue. Tables left out, and why:
| Table(s) | Why left out |
|---|---|
| mlb_through2023 | superseded by retrosheet_mlb_1871_2025 (same games, plus 2024-25 and attendance) |
| eufootball_2010-2020 | same leagues and seasons as footbayes and the 538 soccer table |
| openfootball_* (9 tables) | the leagues duplicate the 538 soccer table; the club cups are too small per season |
| collegefb_2021and2022 | two seasons, too short for a trend and no 2020 |
| cricsheet_* (5 tables) | the ‘home’ side is ambiguous (toss, venue, host board) |
| lichess_2013_*, tcec_engines_2010_2026 | white’s first-move edge is not a home advantage |
| UEFA cups in fivethirtyeight_soccer_2016_2023 | group stages and two-legged ties, not leagues; many sides win or lose every game |
The analysis unit is a league-season (for rugby and internationals, which have too few games per year, a decade). Within each unit we fit a Bradley-Terry model (Bradley and Terry 1952) with a home term:
\[ \text{logit}\, P(a \text{ beats } b) = h \cdot \text{home}_{ab} + \theta_a - \theta_b, \]
where \(\text{home}_{ab}\) is 1 if \(a\) is at home, \(-1\) if \(b\) is, and 0 at a neutral venue. The \(\theta\)s are team strengths, so \(h\) is the home advantage in logits, net of who played whom. For a sense of scale, \(h = 0.4\) means two evenly matched teams would see the home side win about 60% of decided games. Where a sport has draws, we fit the ordinal version of the model (Agresti 1992), in which a draw sits between a win and a loss on the same latent scale, so \(h\) keeps the same meaning.
# Every second game is written from the away side's point of view, so that the
# home column is not constant (and so not absorbed by the ordinal cutpoints).
fit_h <- function(a, b, y, home, nocrowd = NULL) {
flip <- seq_along(a) %% 2 == 0
a2 <- ifelse(flip, b, a); b2 <- ifelse(flip, a, b)
y <- ifelse(flip, 1 - y, y); home <- ifelse(flip, -home, home)
# team-strength design, one reference team per connected component
cmp <- components(a2, b2)
keep <- setdiff(sort(unique(c(a2, b2))), tapply(names(cmp), cmp, `[`, 1))
X <- matrix(0, length(a2), length(keep))
ia <- match(a2, keep); ib <- match(b2, keep)
X[cbind(which(!is.na(ia)), ia[!is.na(ia)])] <- 1
X[cbind(which(!is.na(ib)), ib[!is.na(ib)])] <- -1
H <- cbind(home = home)
if (!is.null(nocrowd)) H <- cbind(H, home_nocrowd = home * nocrowd)
Z <- cbind(H, X)
if (any(y == 0.5)) { # draws: ordinal Bradley-Terry
m <- MASS::polr(factor(y, levels = c(0, 0.5, 1)) ~ Z, Hess = TRUE)
} else {
m <- glm(y ~ Z - 1, family = binomial)
}
# ... returns h, its SE, and delta (below) when nocrowd is given
}A few details matter for what follows:
The no-crowd test. For each league we pool the 2016-2023 seasons into one fit, with a strength for every team-season and a second home term for games played in the no-crowd window, 13 March 2020 to 31 May 2021:
\[ \text{logit}\, P(a \text{ beats } b) = (h + \delta \cdot \text{nocrowd}) \cdot \text{home}_{ab} + \theta_{a,s} - \theta_{b,s}. \]
\(\delta\) is the change in home advantage when the stands were empty. One window is used for every league; for MLB, whose Retrosheet table records attendance, we also define “no crowd” directly as a 2020 game with no recorded attendance.
Of the units built, 887 produced estimates; the season fits used the ordinal model in 608 and the binary model in 279.
To reproduce with current IRW holdings, re-run home_advantage_compute.R and commit the updated home_advantage_data/home_advantage_results.rds.
A logit is not a natural unit, so it helps to ask what \(h\) means for a single game between two equally strong teams, \(\theta_a = \theta_b\). Then the strengths cancel and the model’s prediction depends on \(h\) alone.
To put every sport on one scale, we use the home side’s expected score for equal teams, scoring a win as 1, a draw as ½ and a loss as 0, as in chess: \(P(\text{home win}) + \tfrac{1}{2} P(\text{draw})\). This is a scoring of the outcome only; the margin of victory and the goals, runs or points scored in the game play no part in it or in the model. It is 50% when there is no home advantage, and in a sport without draws it is just the home win probability. The figure shows it by era; hover over a point for \(h\) and the win, draw and loss probabilities behind it.
era_cols <- c("before 1950" = "grey75", "1950-1989" = "grey45", "1990-2019" = "black")
pd <- era_size |>
left_join(distinct(summary_df, league, sport), by = "league") |>
mutate(group = sport_group(sport),
league = factor(league, levels = rev(recent$league)),
text = paste0(league, ", ", era, "<br>h = ", fmt(h), " (SE ", fmt(h_se), ")",
"<br>equal teams: home win ", pct(p_win),
if_else(p_draw > 0.005, paste0(", draw ", pct(p_draw)), ""),
", away win ", pct(p_loss),
"<br>expected score ", pct(share), " (SE ", fmt(100 * share_se, 1), " pts)",
"<br>", n_units, if_else(grepl("intern|Rugby", league), " decades, ", " seasons, "),
format(n_games, big.mark = ","), " games"))
# one row per league: the three eras sit on the same line, joined by a grey
# segment, with the most recent era darkest; the SEs are in the hover text
pd <- arrange(pd, league, era)
p <- ggplot(pd, aes(share, league, text = text)) +
geom_vline(xintercept = 0.5, colour = irw_grey) +
geom_path(aes(group = league), colour = "grey70", linewidth = 0.8) +
geom_point(aes(colour = era), size = 2.6) +
scale_colour_manual(values = era_cols) +
scale_x_continuous(labels = function(x) paste0(round(100 * x), "%")) +
labs(x = "home side's expected score, equal teams", y = NULL, colour = NULL)
lab_groups <- distinct(pd, league, group) |> arrange(league)
ggplotly(p, tooltip = "text") |>
layout(legend = list(orientation = "h", y = -0.15)) |>
colour_y_labels(as.character(lab_groups$league), lab_groups$group)| Series | h | Odds ratio | Home win | Draw | Away win | Expected score |
|---|---|---|---|---|---|---|
| Rugby union (tier-1 tests) | 0.64 (0.08) | 1.90 | 64% | 3% | 33% | 67% |
| Men’s internationals | 0.67 (0.02) | 1.95 | 49% | 31% | 20% | 64% |
| Basketball (NBA) | 0.52 (0.01) | 1.69 | 63% | — | 37% | 63% |
| Italy (Serie A) | 0.57 (0.02) | 1.78 | 45% | 34% | 21% | 62% |
| American football (NFL) | 0.44 (0.03) | 1.55 | 61% | — | 39% | 61% |
| England (all divisions) | 0.41 (0.01) | 1.51 | 44% | 30% | 26% | 59% |
| Women’s internationals | 0.36 (0.05) | 1.44 | 44% | 29% | 27% | 59% |
| Ice hockey (NHL) | 0.23 (0.01) | 1.26 | 52% | 7% | 40% | 56% |
| Baseball (MLB) | 0.16 (0.01) | 1.17 | 54% | — | 46% | 54% |
Every series has a home advantage, and they differ a great deal. In 1990-2019, two equally strong NBA teams would see the home side win 63% of the time; in the NFL, 61%. Hockey, which still had ties for much of this era, comes out at a home expected score of 56%. Baseball’s is the smallest: 54%, barely more than a coin flip. The largest are in international matches, rugby tests and men’s football, where the home side’s expected score against an equal opponent is about two-thirds.
The football numbers read differently because about a quarter to a third of games are drawn. Between two equal English sides, the home team wins 44%, the game is drawn 30% and the away team wins 26%. That is a home expected score of 59%, about the same edge as in the NFL, even though the home side wins less than half its games. Serie A and men’s international football are larger still: an equal visiting side wins only about one game in five.
Two cautions in reading the table. First, \(h\) itself is comparable only within a model family. In the ordinal model a given \(h\) shifts a latent scale with a draw band in the middle, so the same \(h\) implies a smaller home win probability than it would in a sport without draws; the expected score is the comparable number. Second, “equally strong” is a model statement. In a real league most games are not between equal teams, and the home side’s actual win rate depends on the schedule. The point of \(h\) is that it does not.
pd <- league_538 |>
mutate(league = factor(league, levels = league),
text = paste0(league, "<br>h = ", fmt(h), " (SE ", fmt(h_se), ")",
"<br>equal teams: home win ", pct(p_win), ", draw ", pct(p_draw),
", away win ", pct(p_loss), "<br>", n_units, " seasons, ",
format(n_games, big.mark = ","), " games"))
p <- ggplot(pd, aes(share, league, text = text)) +
geom_vline(xintercept = 0.5, colour = irw_grey) +
geom_vline(xintercept = median(pd$share), colour = irw_blue, linetype = "dashed", linewidth = 0.3) +
geom_linerange(aes(xmin = share - 2 * share_se, xmax = share + 2 * share_se), colour = irw_blue, alpha = 0.6) +
geom_point(colour = irw_blue, size = 1.6) +
scale_x_continuous(labels = function(x) paste0(round(100 * x), "%")) +
labs(x = "home side's expected score, equal teams", y = NULL)
ggplotly(p, tooltip = "text") |>
colour_y_labels(levels(pd$league), rep("Club football", nlevels(pd$league)))The same measure across 36 club leagues in the late 2010s and early 2020s ranges from 52% in Austrian T-Mobile Bundesliga to 65% in Major League Soccer (median 59%). Some of that spread is noise, since a league contributes only a few seasons here; the error bars show how much.
trend_df <- summary_df |>
filter(sport != "Football (538 leagues)") |>
mutate(covid = period %in% covid & league %in% season_series,
year = if_else(league %in% season_series, period, period + 5),
text = paste0(league, " ", period, if_else(league %in% season_series, "", "s"),
"<br>h = ", fmt(h), " (SE ", fmt(h_se), ")<br>", n_games, " games, ",
n_agents, " teams<br>", table))
p <- ggplot(trend_df, aes(year, h, text = text)) +
geom_hline(yintercept = 0, colour = irw_grey, linewidth = 0.3) +
geom_linerange(aes(ymin = h - 2 * h_se, ymax = h + 2 * h_se, colour = covid), alpha = 0.4) +
geom_point(aes(colour = covid), size = 0.9) +
geom_smooth(data = filter(trend_df, !covid), mapping = aes(year, h, weight = 1 / h_se^2),
method = "loess", span = 0.5, se = FALSE, colour = irw_blue, linewidth = 0.6,
inherit.aes = FALSE) +
scale_colour_manual(values = c(`FALSE` = "grey30", `TRUE` = irw_red), guide = "none") +
facet_wrap(~ league, ncol = 3) +
labs(x = NULL, y = "home advantage h (logits)")
ggplotly(p, tooltip = "text")| Series | From | Whole series | 1990-2019 |
|---|---|---|---|
| American football (NFL) | 1922 | -0.005 (0.009) | -0.062 (0.033) |
| Baseball (MLB) | 1871 | -0.011 (0.001) | -0.001 (0.009) |
| Basketball (NBA) | 1947 | -0.046 (0.009) | -0.086 (0.017) |
| England (all divisions) | 1888 | -0.054 (0.003) | -0.087 (0.012) |
| Ice hockey (NHL) | 1925 | -0.044 (0.005) | -0.043 (0.016) |
| Italy (Serie A) | 1929 | -0.067 (0.006) | -0.172 (0.023) |
Over the whole of each series, home advantage has fallen in 5 of the 6 leagues measured season by season, by more than twice its standard error. The steepest declines are in European football: in English football \(h\) has roughly halved since before 1950, and in Serie A it has fallen by about 40%. Among the North American sports the decline is clearest in hockey and in basketball, where \(h\) rose to a peak in the middle of the century before falling. Baseball’s small advantage has drifted down slowly, and has been essentially flat since 1990. American football shows no long-run trend. Since 1990 the decline is significant in 4 series (basketball, hockey and both football leagues); the NFL’s estimate points the same way but is too noisy to say.
This is the familiar result, and it is worth seeing that it survives conditioning on team strength: the decline is not an artefact of who hosted whom. What the model cannot say is why. Better travel, standardised stadiums, and changes in officiating are all candidates, and all of them moved over the same decades.
Rugby and international football, estimated by decade, show no such decline. The estimates are noisy, but they are also a different kind of home advantage: a national side playing at home has often travelled less far, in a stadium it chose, in front of a crowd that is almost entirely its own.
nc <- nocrowd_df |>
mutate(label = if_else(definition == "attendance column", paste(league, "(attendance)"), league),
group = sport_group(sport),
text = paste0(label, "<br>δ = ", fmt(delta), " (SE ", fmt(delta_se), ")<br>h with crowds = ",
fmt(h), "<br>", n_nocrowd, " home games without a crowd")) |>
arrange(delta) |>
mutate(label = factor(label, levels = label))
p <- ggplot(nc, aes(delta, label, text = text, colour = group)) +
geom_vline(xintercept = 0, colour = irw_grey) +
geom_linerange(aes(xmin = delta - 2 * delta_se, xmax = delta + 2 * delta_se), alpha = 0.6) +
geom_point(size = 1.5) +
scale_colour_manual(values = group_cols) +
labs(x = "change in home advantage without crowds (δ, logits)", y = NULL, colour = NULL)
ggplotly(p, tooltip = "text") |>
layout(legend = list(orientation = "h", y = -0.08)) |>
colour_y_labels(levels(nc$label), nc$group[order(nc$label)])In club football the answer is yes. Home advantage fell in 25 of the 32 leagues, and the precision-weighted average change is -0.13 logits (SE 0.02), against a typical advantage with crowds of about 0.39: about 34% of it went with the crowd. The leagues differ by more than chance would explain (heterogeneity \(Q\) = 43.8 on 31 df). Several of the largest drops were in top divisions (the Premier League, Ligue 1, the Bundesliga), while two second divisions, Ligue 2 and the 2. Bundesliga, show none (England’s lower divisions did lose some). Fischer and Haucap (2021) found exactly this pattern for Germany and traced it to occupancy: a stadium that is usually half empty loses less when it is fully empty.
The North American leagues split. Basketball lost home advantage (\(\delta\) = -0.16, SE 0.07), as did American football, more noisily. Hockey barely moved. Baseball did not lose any: the estimate is positive whether “no crowd” is read from the calendar (\(\delta\) = 0.06) or from the attendance column (\(\delta\) = 0.11, SE 0.07). Higgs and Stavness (2021), with a different model, found home advantage fell in the NBA’s and NHL’s 2020 playoffs, played in bubbles, and changed little in MLB and the NFL. We agree on basketball and baseball. Our hockey and American football estimates come from the regular season, not the bubble playoffs, which may be why they differ. Baseball’s advantage was small to begin with, and the sport has a structural home edge (the home side bats last) that does not depend on anyone watching.
| Setting | Home games | h | Change from normal | SE |
|---|---|---|---|---|
| Normal seasons (crowd and travel) | NA | 0.37 | NA | 0.02 |
| 2020 bubble (no crowd, no travel) | 172 | 0.07 | -0.30 | 0.16 |
| 2020-21 season (travel, no crowd) | 1080 | 0.20 | -0.17 | 0.07 |
The NBA gives one more contrast. Its 2020 restart was played in a bubble at Walt Disney World: no crowd, and no travel either, since every team lived on site. The season that followed was played in home arenas, with travel but with few or no fans. 538 flags the bubble games as neutral, but its agent_a is still the designated home team (in the 2020 Finals, the Lakers in games 1, 2 and 5 and the Heat in 3, 4 and 6, as scheduled), so we can estimate a nominal home advantage for them. It nearly vanished in the bubble and about halved in 2020-21. With only 172 bubble games the first estimate is imprecise, and the two do not differ significantly, but the ordering is what you would expect if both the crowd and travel contribute.
Source code for this page: home_advantage.qmd · home_advantage_compute.R
These results were computed against approximately IRW v512 (the corpus as of October 2, 2026).
The version was inferred from when the results were computed, not recorded during the run, so it may be off by a version or more. 2 IRW versions were released that day, so the exact one is ambiguous. To pin data to an exact version, use irw_use_version().
Results were computed on October 02, 2026. To regenerate: