The story: PSG signed Messi, Neymar and Mbappé and never won the Champions League. After they left, PSG won it in 2024-25 and again in 2025-26.

So: did the team actually get better, or does it just look that way?

Three questions, each answered with the same statistical tool:

1. Is PSG better at home than away? (Ligue 1)
2. Which players are associated with winning?
3. Did PSG’s win rate change between the superstar era (2021-23) and the post-superstar era (2024-26)?

• 206 PSG matches across four seasons: 2021-22, 2022-23, 2024-25, 2025-26 (Ligue 1, Champions League and the other competitions in the dataset).
• Superstar era = 2021-22 and 2022-23. 2021-22 is the only season with Messi, Neymar and Mbappé together.
• Opponent strength = sum of the opponent squad’s player market values in the year before kickoff. “Top-half” means above the median of all PSG opponents.
• A win is a win in 90 or 120 minutes. A penalty shoot-out win counts as a draw.

Source: transfermarkt-datasets (D. Cariboo), sourced from Transfermarkt (CC0 1.0 Universal). The data has no Coupe de France or Coupe de la Ligue matches. The 2025-26 Champions League final (30 May 2026) is missing from it, so I added it by hand: 1-1 against Arsenal, PSG won 4-3 on penalties.

Every question asks the same thing: are two win rates different, or is the gap just noise?

• Each match is a win or not, so a win rate is a proportion \(\hat p = x/n\).
• With few matches, a gap of 5 or 10 points can easily appear by chance.
• A hypothesis test asks: if the true win rates were equal, how often would we see a gap this big?
• That probability is the p-value. A small one (under 0.05) is evidence the rates differ.

Null hypothesis \(H_0: p_1 = p_2\). With \(\hat p_1 = x_1/n_1\) and \(\hat p_2 = x_2/n_2\):

\[\hat p = \frac{x_1 + x_2}{n_1 + n_2} \qquad SE = \sqrt{\hat p\,(1-\hat p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}\]

\[z = \frac{\hat p_1 - \hat p_2}{SE}\]

If \(H_0\) is true, \(z\) is approximately standard normal, so the two-sided p-value is

\[p\text{-value} = 2\,\bigl(1 - \Phi(|z|)\bigr)\]

A p-value says whether a gap exists, not how large it is. A 95% confidence interval for the gap:

\[(\hat p_1 - \hat p_2) \;\pm\; 1.96\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}}\]

• If the interval contains 0, the data are consistent with no difference.
• A wide interval means we have little information, not that the true gap is zero.

two_prop <- function(w1, n1, w2, n2) {
  t <- prop.test(c(w1, w2), c(n1, n2), correct = FALSE)   # z-test for 2 proportions
  list(diff = w1 / n1 - w2 / n2,                          # gap in win rate
       p    = t$p.value,                                  # two-sided p-value
       ci   = t$conf.int)                                # 95% CI for the gap
}

# Q3: post-superstar era vs superstar era, all matches
two_prop(sum(post$win), nrow(post), sum(sup$win), nrow(sup))

Home win rate is 12.5 points higher, 95% CI [-2.1, 27.1] points, p = 0.10. That is not significant at 0.05, but the interval is wide and mostly above zero. Home advantage is plausible; 72 matches per venue cannot settle it.

33 players with 20+ starts and 10+ matches missed. Above the dashed line = PSG wins more when the player starts. Dot size = number of starts; hover for names.

• Most players sit within a few points of zero. Top of the list: Désiré Doué (+9 points).
• Bottom: Keylor Navas (-15 points).
• This is association, not causation. Starters play the biggest games, and the same players started in both eras. A defender who plays every hard match will look worse than a backup who plays easy ones.
• No player-level test is run: 33 players means 33 tests, and a few would look “significant” by luck.

• All matches: 4.6 points higher after the superstars left, p = 0.48.
• Against top-half opponents: 12.3 points, p = 0.22.

More matches played means deeper runs: 8 each in the superstar seasons, 17 in both title seasons. That is the clearest difference in the data, but it is a count of rounds survived, not a test.

• A non-significant p-value is not proof of no difference. With 94 and 112 matches, the era comparison only detects gaps of roughly 18 points or more.
• Four seasons is a small sample. Knockout football is also high-variance: one penalty shoot-out decides a final.
• Opponent strength is approximate, built from market values rather than match-time form.
• Missing competitions (domestic cups) and one hand-added final mean “all matches” is not every match PSG played.

• Win rate did not detectably change after the superstars left: 66.0% before, 70.5% after (p = 0.48). Against top-half opponents the gap is larger (p = 0.22) but still not significant.
• PSG’s Champions League results did change: round-of-16 exits in both superstar seasons, two titles after.
• Home advantage is plausible but unproven in this sample (p = 0.10).
• No single player stands out as the reason PSG wins.
• The takeaway: the data cannot show that PSG became a better team. It shows they went further in Europe. Whether that is skill, depth or luck in knockout games, win rates over four seasons cannot say.