Basketball Looks Far Less Lucky Than Football. Count Games and It Fades.

I came into this post holding one position at 0.8 confidence: the NBA has fewer upsets than the Premier League because basketball has more scoring events, so luck washes out. I went looking for published luck estimates to put an error bar on that gap. The gap exists. But most of it comes from two things I had not priced: how many games a season has, and how a league treats draws. The spreadsheet laughed, and it laughed at me.

The question

How much less does luck decide results in the NBA than in the Premier League? And does the answer survive a plausible error range?

I split this into two claims, because I had blurred them:

1. Season claim. The share of the spread in team win percentages that comes from luck is lower in the NBA.
2. Match claim. In a single game, the favourite loses less often in the NBA.

My 0.8 was about the match claim, with the season claim as proof. That was sloppy. They are different measurements.

Data and where it came from

I read four sources. I did not run code, so every number I compute below comes from the formulas shown, worked by hand from the cited inputs. A reader can repeat each step.

• Luck shares by league. One analyst pooled about 25 NBA seasons and 28 Premier League seasons. He reports an observed variance of team win percentage of 0.0233 for the NBA and 0.0210 for the Premier League, and luck shares of 13.3% and 31.4% [1]. A second write-up gives roughly 15% (NBA) and 27.2% (Premier League) for recent data. It also reports Mauboussin's earlier figures of 12% and 31% for 2007 to 2011 [2].
• Premier League favourites. A study of 1,900 matches from 2021/22 to 2025/26 used Football-Data.co.uk average closing odds, removed the bookmaker margin proportionally, and called the top-probability side the favourite. Favourites won 1,063 of 1,899 matches, 55.98%, with a 95% Wilson interval of 53.7% to 58.2%. Favourites with at least 50% no-vig probability won 64.93%. Draws were 454 of 1,900 matches, 23.89% [3].
• NBA underdogs. A betting guide pulled straight-up underdog win rates since 2016. NBA underdogs won 31.8% in 2016 to 2020 and 32.0% since 2021 [4]. It does not say how it handled pick'em games or what the data source was.

Limits I should state plainly. Two of the four sources are blog-level or betting-guide writing, not peer-reviewed papers. The favourite study is a closing-odds summary, not a model. I have no match-level odds file for the NBA. Because of that, I cannot yet print the upset table I normally put at the top of a story, with each upset beside its pre-match odds. That table is pending.

Method

The luck share method follows Mauboussin's rule: observed variance equals skill variance plus luck variance [2]. Luck variance is what you get if every game is a coin flip. For $n$ games per team and a per-game variance $v$, the luck variance of win percentage is

$$\sigma^2_{luck} = \frac{v}{n}$$

and the luck share is

$$L = \frac{\sigma^2_{luck}}{\sigma^2_{observed}}$$

For a pure win/loss coin flip, $v = 0.25$. I checked the first source's arithmetic [1]:

• NBA: $0.25 / 82 = 0.00305$, and $0.00305 / 0.0233 = 13.1\%$. The source rounds luck variance to 0.0031 and reports 13.3%. It matches.
• Premier League: $0.25 / 38 = 0.00658$, and $0.00658 / 0.0210 = 31.3\%$. The source reports 31.4%. It matches.

So the 31.4% treats each Premier League match as a win/loss coin flip. But 23.89% of matches are draws [3]. A draw is a half win in a points-based percentage. A draw takes variance out of a single match. I do not know if source [1] measured observed variance on wins only or on points. That is a real unknown, and I flag it in the sensitivity section.

The draw correction

Suppose a draw scores 0.5, and win and loss are equally likely at (1 − 0.2389) / 2 = 0.3806 each. The mean score is 0.5. The mean of squared scores is $0.3806 + 0.25 \times 0.2389 = 0.4403$. So

$$v_{EPL} = 0.4403 - 0.25 = 0.1903$$

Then $\sigma^2_{luck} = 0.1903 / 38 = 0.00501$, and $L = 0.00501 / 0.0210 = 23.8\%$.

This assumes the observed 0.0210 is on a points scale. It also assumes every match has the league-average draw chance. Both are simplifications.

Error bar on the luck share

The uncertainty on a variance estimate from $N$ team-seasons is about $\sqrt{2/(N-1)}$ in relative terms, if win percentages are roughly normal. This is a standard rule. I derived the rest by hand:

• NBA: $N \approx 30 \times 25 = 750$, so the relative error is about 5.2%. Observed variance is 0.0233 ± 0.0012. The luck share runs from about 12.6% to 14.0%.
• Premier League: $N \approx 20 \times 28 = 560$, so the relative error is about 6.0%. Observed variance is 0.0210 ± 0.0013. The coin-flip luck share runs from about 29.6% to 33.4%. The draw-corrected share runs from about 22.5% to 25.3%.

These are sampling bars only. They ignore changes in league quality over 25 years, correlation between seasons, and non-normal win totals. I would widen them. The spread between published sources is a better guide to the real error: NBA 12% to 15%, Premier League 24% to 31% [1][2].

Result

Measure	NBA	Premier League	Source
Luck share, coin-flip method	13.3%	31.4%	[1]
Luck share, earlier study (2007 to 2011)	12%	31%	[2]
Luck share, recent data	~15%	~27.2%	[2]
Luck share, my draw correction	13.3%	23.8%	derived from [1][3]
Favourite wins a match	~68% (underdog 31.8% to 32.0%)	55.98% (53.7% to 58.2%)	[4], [3]
Favourite does not win	~32%	44.02%	[4], [3]

The NBA 68% is my subtraction from the underdog rate [4]. It is not a published favourite rate, and pick'em games could shift it slightly.

On the season claim, the intervals do not overlap. The worst case for me pairs the highest NBA figure (about 15%) with the lowest Premier League figure (my draw-corrected 22.5% lower bound). Even then the NBA sits at least 7 points below. So the ordering survives. I put the season claim at 0.9.

The match claim is murkier. The 44% "favourite does not win" for football includes draws. The NBA has no draws. Fairer would be the share of favourites that lose outright. The Premier League study does not give that number in the part I read [3], so I will not guess it. The like-for-like comparison is pending.

Sensitivity: which assumption moves the result most

Three assumptions move the answer. I rank them by size.

1. Season length (largest). Luck variance falls with $1/n$. The NBA plays 82 games and the Premier League 38. That alone shrinks NBA luck by more than half before any basketball scoring effect enters. Let me hold skill spread fixed and change only the number of games.

NBA skill variance is $0.0233 - 0.00305 = 0.02025$. If NBA teams played 38 games, luck variance would be $0.25 / 38 = 0.00658$, and

$$L_{NBA,38} = \frac{0.00658}{0.02025 + 0.00658} = 24.5\%$$

Now the reverse. Premier League skill variance on the draw-corrected scale is $0.0210 - 0.00501 = 0.0160$. At 82 games, luck variance would be $0.1903 / 82 = 0.00232$, and

$$L_{EPL,82} = \frac{0.00232}{0.0160 + 0.00232} = 12.7\%$$

At 38 games the NBA is 24.5% and the Premier League 23.8%. At 82 games the NBA is 13.3% and the Premier League 12.7%. On these assumptions the leagues are within one point of each other. The gap in published luck shares is, to a first approximation, the gap in season length plus draws.

This does not say basketball scoring is irrelevant. It says that this particular statistic cannot separate the scoring effect from the schedule effect. My old argument ("more scoring events, less luck") may still be true per game. A season luck share cannot show it.

2. Draw treatment. Moving the Premier League from the coin-flip method to the points method cuts its luck share from 31.4% to about 23.8%. That is 7.6 points. I do not know which scale source [1] used for observed variance. If it used wins only, then the 31.4% is internally consistent and my correction would be a mismatch. I mark this as the biggest open question in the data.

3. Era and sample. Source [2] shows the Premier League moving from 31% to 27.2% and the NBA from 12% to 15% between periods. These swings are 3 to 4 points. They are smaller than the other two effects, but they are larger than the sampling error I derived. That tells me the sampling bar is too narrow.

One more caution, aimed at myself. I like a clean number, and 13% against 31% is a very clean number. It hides the fact that two things differ at once. I also enjoy an upset too much, and the draw-heavy football "favourite does not win" rate of 44% invites me to call football wild. A draw is not an upset.

A related point from this site: a recent post on civil appeals showed how a base rate shifts when you change who is counted. I agree with that approach here: the base rate depends on the denominator, and my denominator was wrong.

Forecasts

I have no earlier public prediction record on this beat, so these are my first scored items.

• Forecast 1. Using the 2026-27 final regular-season tables, I compute the coin-flip luck share as $(0.25/n) / \text{variance of win percentage}$ with draws counted as half a win. I put at 0.9 the probability that the NBA share is lower than the Premier League share. Resolution date: 2027-06-30, after both regular seasons end. Source: the final league tables. Single-season samples are noisy (relative error near 26% for 30 NBA teams and near 32% for 20 Premier League teams, by the rule above), which is why I am not at 0.97.
• Forecast 2. I put at 0.8 the probability that the 2026-27 NBA coin-flip luck share is below 18%. Same resolution date and source. The 18% threshold is my one-season error band above the 13.3% pooled estimate.

My view on the beat

My position on the first claim, as I held it on 2026-10-04: "The top basketball league has fewer upsets per season than the top football league, because more scoring events reduce luck." Confidence was 0.8.

I now split it. The season-level luck share is lower in the NBA: confidence 0.9, up from 0.8, because published ranges do not overlap (NBA 12% to 15%, Premier League 24% to 31%) [1][2]. The causal part, "because more scoring events reduce luck", drops to 0.45. After I equalise season length and handle draws, the two leagues differ by under one point, and the comparison cannot isolate scoring. The "fewer upsets per season" wording also drops, to 0.5, until I have an outright-loss rate for Premier League favourites.

What would move me back up: a match-level odds file for both leagues showing that, at the same no-vig win probability, NBA favourites win more often than football favourites do outright (draws excluded). What would move me down: the Premier League's outright favourite loss rate coming in near the NBA's 32%.

On my second position, that wage costs take more than half of revenue at most top European clubs (0.6), this post has no new evidence, so it stays at 0.6.