# The three point rule

Back when I were a lad, you got only two points for winning a game in a group match, and one for a draw. From 1994 onwards, that was changed to three points for a win, and one for a draw, the intention being to give incentives to teams to try and score goals.

It occurred to me to wonder how much difference this rule has actually made in practice. There are not all that many mathematical permutations possible for how the group mathematics might end up for a group of four teams who each play a match against each of the other three. (3W, 2W.1D, 2W.1L, 1W.2D, 1W.1D.1L, 1W.2L, 3D, 2D.1L, 1D.2L, 3L and that's it.

The only three cases where I can see the three point rule making a difference are
1. a team with two wins and a loss now beats a team with one win and two draws on points, rather than potentially lose to them on goal difference;
2. a team that has a modest win, a big loss and a draw will now beat a team with three draws on points, rather than lose to them on goal difference; and
3. (least likely) a team that has one big win and two closer losses
1. will now beat a team with two draws and a loss on points, and
2. could beat a team with three draws on goal difference rather than lose to them on points. (Impossible, as pointed out by in comments.)
But did that situation ever arise before 1994? And since 1994, has there ever been a situation where the old two point system would have led to a different outcome?

The answer is yes, once or twice. I count 81 four-team groups in World Cup tournaments from 1930 to 2006, of which precisely one pre-1990 group would have had a different ranking with three points for a win (and none as far as I can tell that would have been ranked differently since 1994 had there been only two points for a win):
Group 3, Sweden 1958, as it happened:
 Team Pld W D L GF GA Pts Sweden 3 2 1 0 5 1 5 Wales 3 0 3 0 2 2 3 Hungary 3 1 1 1 6 3 3 Mexico 3 0 1 2 1 8 1
Group 3, 1958, as it might have been
 Team Pld W D L GF GA Pts Sweden 3 2 1 0 5 1 7 Hungary 3 1 1 1 6 3 4 Wales 3 0 3 0 2 2 3 Mexico 3 0 1 2 1 8 1
Hungary had beaten Mexico 4-0, but lost 2-1 to Sweden; Wales drew 1-1 with Mexico and 0-0 with Sweden. In fact the tie in points was decided by a play-off between Wales and Hungary, which Wales won 2-1 (having drawn 1-1 with Hungary in the original group match). Under the three-point rule, Hungary (who were runners-up in the previous final) would have faced Brazil instead of Wales but would probably still have lost (as Wales did, 1-0).

However, even this case is marginal. In the rules that applied later, Hungary would have gone ahead of Wales due to having a better goal average (as used in 1962 and 1966) or goal difference (as used since 1970), even if two points rather than three were earned for a victory.

There have been seven uses of a three-team group in World Cup tournaments (three in 1930 and four in 1982), and while the new scoring means that a team which wins one game and loses another now beats a team with two draws, it's not actually possible to have those results in a group of three teams where each plays the other two once.

There has been one other occasion when the new system would have made a difference. In 1986, the four best-performing third-placed teams from all six of the first round groups got through to the second round.
The 1986 third-place teams as they were scored:
 Group Team Pld W D L GF GA GD Pts B Belgium 3 1 1 1 5 5 0 3 F Poland 3 1 1 1 1 3 -2 3 A Bulgaria 3 0 2 1 2 4 -2 2 E Uruguay 3 0 2 1 2 7 -5 2 C Hungary 3 1 0 2 2 9 -7 2 D Northern Ireland 3 0 1 2 2 6 -4 1
The 1986 third-placed teams as they might have been scored:
 Group Team Pld W D L GF GA GD Pts B Belgium 3 1 1 1 5 5 0 4 F Poland 3 1 1 1 1 3 -2 4 C Hungary 3 1 0 2 2 9 -7 3 A Bulgaria 3 0 2 1 2 4 -2 2 E Uruguay 3 0 2 1 2 7 -5 2 D Northern Ireland 3 0 1 2 2 6 -4 1
Once again, Hungary would have benefited from the three-point system, this time to the disadvantage of Uruguay (who were beaten 1-0 by Argentina in their next match anyway).

Variations on this scheme were used also in 1990 and 1994 but, while the different point allocation would have changed the rankings slightly, it wouldn't have made a difference to which teams went through.

Fans will complain with justification that the three point rule hasn't made much appreciable difference to the number of goals scored per match. It is a bit surprising, however, to find that it would have made so little difference to the results of past tournaments.
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