Watching Sport – Third Place in the Group

29th June 202

The bloated nature of the 2026 FIFA World Cup has necessitated 72 Group matches to be played in order to reduce the number of participants from 48 to 32.

There have been 12 Groups of 4 teams from which the top two in each Group – along with the 8 third-placed teams with the best records – have qualified for the knock-out phase of the Last 32. The hierarchy of criteria for deciding the “best” third-placed teams was: points obtained in the Group (3 for a win, 1 for a draw); goal difference; goals scored; and “fair play”, based on the number of red and yellow cards obtained. (The Last 32 phase began yesterday when Canada beat South Africa in Los Angeles).

The table shows the rank order of the third-placed teams at the Group stage:

Rank	Group	Team	Points	Goal difference
Qualifiers for Last 32
1	K	DR Congo	4	+ 1
2	F	Sweden	4	0
3	L	Ghana	4	0
4	E	Ecuador	4	0
5	B	Bosnia-Herzegovina	4	– 1
6	J	Algeria	4	– 2
7	D	Paraguay	4	– 2
8	I	Senegal	3	+ 2
Non-qualifiers
9	G	Iran	3	0
10	A	South Korea	3	– 1
11	C	Scotland	3	– 3
12	H	Uruguay	2	– 1

Scotland’s failure to qualify for the knock-out phase – a key objective in this tournament, given that the country had never previously done so when fewer sides took part in the Finals – has had an immediate effect, with the resignation of the manager, Steve Clarke. In addition, not surprisingly, it has prompted an avalanche of analysis, explanation and anguish in the media from ex-players, experts, non-experts, supporters et al: the manager’s tactics, the under-performance of leading players, the absence of genuine stars, the lack of opportunity given to young Scottish players by the major domestic clubs… The cottage industry of opinion and solutions will no doubt flourish for some time.

In their Group, Scotland – 42nd in the FIFA world rankings before the tournament started – beat Haiti (ranked 83rd) 1-0 before losing 0-1 to Morocco (ranked 7th) and 0-3 to Brazil (ranked 6th): one win and two defeats with only one goal scored and four conceded.

An inevitable characteristic of the Scotland post mortem is that lots of “what if” questions are posed. “What if the score had been B rather than A?” “What if Country X had only drawn with Country Y rather than scoring a last-minute winner?”. This type of counterfactual conjecture can be interesting, but it is limited for the simple reason that nothing changes in isolation. The dynamics of a Group’s evolution are just that – dynamic – and a change in one detail is likely to have brought about a reaction (and possible effect) elsewhere.

Nonetheless, one argument being widely put forward is that, given the difficult nature of the Group (as shown by the FIFA rankings of Morocco and Brazil), Scotland should not have been satisfied with the slender lead they obtained against lowly Haiti – the single goal registered by a deflected shot by John McGinn – but gone all out to register a bigger win.

The table shows the limitations of this argument. Other things being equal – a crucial caveat – Scotland could have scored another 4 goals against Haiti (to win 5-0 and produce a final goal difference of +1 rather than -3), but this would not have produced any more points in the Group table and still left them behind Senegal in the third-placed rankings given in the table above.

The stand-out feature of the third-placed table is that 7 of the 8 qualifiers secured 4 points at the Group stage. Only Senegal qualified with 3 points – their goal difference of +2 courtesy of a 5-0 win over Iraq in their last match – and they would not have done so had Iran not had what they thought was a late winner disallowed in their final Group match against Egypt. (Those “what ifs” again).

Given that the World Cup Finals now have 48 teams and this method of qualification for the Last 32 knock-out phase is in place, there is no guarantee that securing 4 points in the Group stage will be a sufficient condition to progress. At the extreme, it is possibly that the third-placed teams in all 12 Groups could have 4 points. Likewise, it is possible that they all have 3 points. Or, indeed, one point.

A statistical exercise provides some illumination. Let us assume that, for a team playing in a Group match, there is an equal probability (i.e. one in three) of a win, draw or loss. The total number of permutations of results in a 4-team Group (in which 6 matches are played) is therefore 3 to the power 6, or 729.

Each of these permutations produces final points totals for the 4 teams. In 271 cases (37%), the third-placed team will have 3 points, whilst in another 286 cases (39%), the third-placed team will have 4 points. However, there is also a small number of cases – 12 in all, or 1.6% – in which the third-placed team would have 5 or 6 points, which means that the probability of coming third and having 4 points or higher is almost 41%. (For completeness, the probability of the third-placed team having only 1 or 2 points is 22%).

In practice, the assumption used here of a drawn match – a one-in-three probability – is probably too high. In this year’s Group stage, 20 of the 72 matches – 28% – were draws. This means that more matches than I have assumed will generate 3 points (to the winning side) rather than 2 points (shared between the two teams), with the result that a higher proportion of third-placed sides will be likely to reach 4 points or more than the base estimate of 41%.

In terms of this tournament, what all this confirmed, of course, was my view after Scotland’s first match that, notwithstanding the media frenzy and general euphoria surrounding the win over Haiti, they had not necessarily done enough to qualify for the Last 32 by virtue of that result alone. The single goal margin of victory meant that, in the event of defeat by both Morocco and Brazil, Scotland would end up with 3 points and a negative goal difference. This is precisely what happened.

What also happened was that some of the lowly-ranked teams in other Groups obtained vital draws against supposedly much higher ranked opposition: DR Congo (ranked 46th) against Portugal (5th), Bosnia-Herzegovina (64th) against Canada (30th) and, especially, Ghana (64th) against England (4th). When combined with their wins against the sides that came bottom of their respective Groups (Uzbekistan, Qatar and Panama), this gave them 4 points and a secure place amongst the list of third-placed Group qualifiers for the Last 32. This effect was compounded when Ecuador (ranked 23rd) unexpectedly won their last Group E match against Germany (10th) – who had already qualified for the Last 32 – also taking them to 4 points.

In retrospect, I would judge that Scotland’s inability to secure a point from their Group match against Morocco was the crucial factor in their non-qualification for the knock-out phase. As noted, it was only a narrow loss (0-1) – and Scottish supporters will argue long into the night that their side should have been awarded at least one penalty kick. However, a 1-1 result – again with the significant caveat of “other things being equal” – would have put them amongst the list of qualifiers at the expense of Senegal.

Finally, a statistical quirk. The performance of Cape Verde (ranked 67th by FIFA) in Group H yielded 3 points and a zero net goal difference. From the table above, it can be seen that this outcome was the same as that of Iran in Group G and inferior to any of the third-placed qualifiers for the Last 32 knock-out phase.

But Cape Verde are in the knock-outs: they play Argentina in Miami on Friday. The reason: they came second in their Group and qualified automatically. Three matches: three draws – against Spain (ranked 2nd), Uruguay (16th) and Saudi Arabia (61st). It was Uruguay that came third in the group – with 2 points – thereby taking the lowest place (below Scotland) amongst the third-placed non-qualifiers.