Is that a feat, or a coincidence?

In Moneyball, Bill James works out whether Jack Chesbro's 41–12 season was the pitcher or the team behind him. Chesbro's side won 52% of its games, so James asks how likely 41–12 is from an ordinary pitcher on that team. The number separates what happened from what the circumstances already explain — and almost every figure on this site shows the first half and none of the second.

The longest run 50 Manchester City, no draw in 50 matches

The model expected 9.1 draws across those same 50 fixtures

Chance of that run 1 in 26,400 asked of this run alone — the overstated figure

Runs that long, expected anywhere 0.46 across every run in the database. There is 1.

Those last two tiles are the whole page. One in 26,400 sounds like a miracle. But the run was not picked at random — it was picked for being the longest, out of every run every team has ever had here. Ask instead how many runs of 50 ought to turn up somewhere in a database this size, and the answer is about 0.46. A record is not the same thing as a miracle.

The records this is about are on the all-time no-draw leaderboard, and every team's own figure is on its team page. The run in those tiles is Manchester City's 50, match by match.

Two distributions, one dataset Poisson-binomial against binomial

James had one probability: his pitcher's team won 52% of its games, every game. Under a constant chance, the number of successes in n independent tries is the binomial distribution, and his factorial formula is exactly its probability mass function. Our matches do not share a chance. Liverpool at home to a promoted side and Liverpool away at Arsenal are not the same trial, and the five-feature logistic draw model, recalibrated by its isotonic map gives each of them its own figure. A sum of independent coin flips with different chances is not binomial — it is the Poisson-binomial distribution, and that is what every number on this page uses.

Reading?	Poisson-binomial?	Binomial at the average chance?	The binomial's error?
Spread over a career, summed across 1,595 teams ?	174,080	176,237	+1.24%
Chance of a record run happening at all, averaged over 664 of them ?	1 in 403	1 in 388	1.04× too likely

Measured, not assumed — and the honest reading is that the two rows disagree about how much this matters. Over a whole career the correction is worth about one percent, because draw chances live in a narrow band between roughly 7% and 40% and p(1−p) is nearly flat across it. Anyone claiming this page needs the Poisson-binomial because the binomial's spread is wrong would be overselling it. Over a single run it is worth far more, and always in the same direction: the binomial makes a record look more ordinary than it was.

The real reason for it is neither. The expectation is only available per match. Comparing a team against the sum of its own fixtures' chances — what these matches deserved — is the entire point, and once the average is per-match, the matching distribution is this one. Putting a binomial beside a per-match average is mixing two models.

The longest runs, and what each was worth 664 runs of 20+ measured · the full leaderboard ›

For each run: how many draws the model expected across those exact fixtures, the chance that none of them landed, and what a binomial at the run's own average chance would have said instead. Every figure in this table is asked of a run that was selected for being long, which overstates it. The table underneath is the version that is not.

Team	Run?	Between	Draws expected?	Chance of none?	A binomial would say?
Manchester City	50	Dec 2020 – Sep 2021	9.1	1 in 26,400	1 in 23,700
Wales	46	Feb 2008 – Mar 2013	10.1	1 in 104,200	1 in 92,600
East Stirlingshire	42	Sep 2003 – Sep 2004	5.3	1 in 315	1 in 295
Borussia Dortmund	39	Apr 2021 – Dec 2021	7.4	1 in 3,900	1 in 3,500
SL Benfica	37	Jul 2010 – Mar 2011	7.3	1 in 3,500	1 in 3,300
Cambodia	37	Jun 2015 – Mar 2018	6.9	1 in 2,400	1 in 2,100
Gaziantep FK	36	Jan 2023 – Dec 2023	7.9	1 in 8,000	1 in 7,300
PSV Eindhoven	36	Dec 2013 – Oct 2014	7.6	1 in 5,300	1 in 5,100
Arsenal	35	Feb 2022 – Oct 2022	8.3	1 in 14,200	1 in 13,600
Hebei	35	Jun 2022 – Dec 2022	7.3	1 in 4,100	1 in 3,600
RKC Waalwijk	35	Aug 2009 – May 2010	7.3	1 in 4,000	1 in 3,700
Celtic	35	Aug 2001 – Jan 2002	6.3	1 in 1,100	1 in 1,000
Spain	35	Jun 2008 – Jul 2010	5.9	1 in 729	1 in 647
Kashima Antlers	34	Jul 2013 – May 2014	8.0	1 in 10,400	1 in 9,700
Manchester United	34	Apr 2023 – Nov 2023	8.1	1 in 10,300	1 in 10,000

How often should a run that long turn up anywhere? the honest question

Asking how unlikely this run was, after picking it for being the longest, is asking the wrong question. The right one is how many runs of at least that length ought to exist somewhere in the database at all. That is worked out by walking every position a run could start from — every match after a draw, and every match after a gap in coverage — and adding up the chance that a run starts there and survives.

A run of?	On record?	The model expects?	One flat draw rate expects?	Observed ÷ expected?
5+	52,415	53,120	55,599	0.99
10+	11,094	11,506	13,484	0.96
15+	2,624	2,723	3,414	0.96
20+	664	676	872	0.98
25+	183	175	223	1.05
30+	52	48	57	1.09
35+	13	14	15	0.96
40+	3	4.18	3.82	0.72
45+	2	1.36	0.99	1.47
50+	1	0.46	0.26	2.16

Expectations add whether or not the matches are independent, so this column does not lean on that assumption at all — only the spreads and the tails above it do.

Watch which way the flat column goes, because it reverses. It expects more short runs than the model and fewer long ones. Two different effects are at work and they point opposite ways. Inside a single run, averaging the chances first always makes the run look more likely — that is the concavity from the table above. Across the whole database, giving every team the same chance makes a long run far less likely, because a long run is overwhelmingly produced by the teams that hardly ever draw, and a flat rate deletes them. The second effect is the bigger one at the top of this table: teams are not alike, and a league in which they were would almost never produce a fifty.

Teams the model did not expect since 2015 · 100+ matches

Name?	Matches?	Drew?	Model expected?	League average expected?	Standard errors ?	Adjusted ?	Reading?
Bristol Rovers	592	123	160.8	156.1	−3.50	0.185	far fewer than expected — and still worth checking the model before the team
South Africa	146	56	36.9	37.4	+3.67	0.185	far more than expected — and still worth checking the model before the team
Sheffield United	582	119	155.3	153.1	−3.42	0.185	far fewer than expected — and still worth checking the model before the team
Deportivo La Coruña	345	121	92.5	93.7	+3.49	0.205	far more than expected — and still worth checking the model before the team
Kifisia	103	37	22.7	23.1	+3.41	0.226	far more than expected — and still worth checking the model before the team
Åsane Fotball	356	98	73.3	73.3	+3.26	0.226	far more than expected — and still worth checking the model before the team
PAS Lamia	311	99	74.7	72.1	+3.25	0.226	far more than expected — and still worth checking the model before the team
Fredrikstad FK	309	90	66.4	64.7	+3.29	0.226	far more than expected — and still worth checking the model before the team
Plymouth Argyle	580	125	157.9	154.4	−3.07	0.249	far fewer than expected — and still worth checking the model before the team
Lahti	357	114	88.8	85.5	+3.11	0.275	far more than expected — and still worth checking the model before the team
Cameroon	128	48	32.6	31.6	+3.15	0.289	far more than expected — and still worth checking the model before the team
ES Troyes AC	448	101	128.7	131.2	−2.90	0.307	clearly fewer than expected, though one subject in twenty looks like this by chance

Ordered by how far each sits from what the model expected of its own fixtures. The adjusted column is what makes an ordered table defensible at all: test this many subjects and a handful will clear any threshold on noise alone. Read it as "if I call every row above this one interesting, this is roughly the share that is not". Note that the top of this table has adjusted values nowhere near small — which is the finding, not a disappointment.

Referees the model did not expect all matches · 100+ matches

Name?	Matches?	Drew?	Model expected?	League average expected?	Standard errors ?	Adjusted ?	Reading?
C Scott	142	51	35.0	34.7	+3.13	0.326	far more than expected — and still worth checking the model before the team
J Linington	485	107	135.3	132.3	−2.87	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
T Harrington	365	76	100.0	98.1	−2.83	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
J Moss	511	105	132.5	134.8	−2.78	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
Grant Hegley	268	56	75.3	73.0	−2.63	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
Brian Curson	184	68	51.5	50.2	+2.72	0.326	clearly more than expected, though one subject in twenty looks like this by chance
P Wright	227	81	63.0	60.5	+2.68	0.326	clearly more than expected, though one subject in twenty looks like this by chance
C Hicks	304	64	83.5	81.2	−2.51	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
Steve Dunn	121	20	31.8	31.5	−2.44	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
Alan Freeland	123	17	28.7	29.9	−2.51	0.326	clearly fewer than expected, though one subject in twenty looks like this by chance
L Swabey	287	62	79.3	77.3	−2.28	0.554	clearly fewer than expected, though one subject in twenty looks like this by chance
J Busby	327	73	90.7	88.6	−2.19	0.630	clearly fewer than expected, though one subject in twenty looks like this by chance

What this does not say read before quoting anything above

Matches are not quite independent.: The distribution assumes they are, given their chances. They are not: the same squad, the same manager, the same injury list, and a side that starts playing for draws keeps doing it. The model's per-match figure absorbs much of that — it is built from recent form — but the leftover correlation makes the true spread a little wider than the one quoted here, so the tails above are, if anything, slightly too small. No fudge factor has been applied to hide that.
A small p-value is not skill.: It says the model did not expect this. For us that is as likely to be a gap in the model as a property of the team, and when the model is wrong that is a finding about the model.
The probabilities are in sample.: Every played match here was part of the five-feature logistic draw model, recalibrated by its isotonic map's own training set, so its chance was fitted already knowing the result. That flatters the model, and every figure built on it inherits the flattery. football:report:draw-holdout is the standing out-of-sample check.
How the tails were computed.: Exactly, by folding one match into the distribution at a time — no factorials, which lose every digit they have long before 700! overflows. Above 1,000 matches a skew-corrected normal approximation is used instead and the row says so; measured against the exact answer it is within 0.006 in the tails. Errors in the exact path accumulate at about 1e-13 over a thousand matches.
Draws are ninety-minute draws.: As everywhere on this site: a shoot-out win stays a draw.
Players and managers are missing.: The striker version of this question — "were those goals him, or the side around him?" — needs to know who was on the pitch, and there are no per-match appearances in this database. Managers have no source at all. Neither is being guessed at.

Probabilities from the five-feature logistic draw model, recalibrated by its isotonic map. Last measured 22 Sep 2026. Descriptive statistics over historical results, not betting advice.