Peter Goldstein


 
Peter Goldstein is a professor at Juniata College in Pennsylvania in the USA. He has been World Cup crazy since 1966. He will share his views about the past, present and future of this event.

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The Three-Point Myth Revisited



    After the disastrous 1990 World Cup, FIFA sought ways to promote more attacking football. Most prominently, they changed the group stage system from 2 points for a win to 3 points for a win. Reaction was overwhelmingly positive; indeed, the change is generally believed to have revitalized the group stage. Maybe so. But the theoretical difference between 2-1-0 and 3-1-0 is in fact very small. Shortly before the 2002 tournament I posted a study to that effect, and now, with the 2006 tournament in the offing, Iíd like to revisit the topic. The first part of this article will repeat the earlier study with appropriate revisions/additions; the second will be all new material. The goal is to measure:

1) The theoretical difference between the old system and the new system;
2) The practical effects of the change.


1) Theory

    Over a long league season, the 3-1-0 system can have a significant effect on the standings. But in a 3-game group, its impact is severely limited. In fact, there is only one scenario in which first and second places could be reversed under 2-1-0 and 3-1-0. It looks like this:

Team A: WWL (4 or 6 points)
Team B: WDD (4 or 5 points)

    Under the 3-1-0 system, team A gets 6 points and team B gets 5, so team A always wins. But under the 2-1-0 system, both teams have 4 points, so team B can win if it has an advantage in the tiebreakers. A close look at this scenario reveals that team B's win must have been against team A: team A doesn't have a draw, so team B's draws must have come against the other two teams in the group. In other words, for this combination to turn up, team A must have been good enough to beat the other two teams in the group, while team B could only draw with them--yet team B was good enough to beat team A.

    Clearly, this doesn't figure to happen all that often. Since the modern group stage began in 1958, out of a total of 64 groups, this combination has only turned up 4 times. The first two came during the 2-1-0 era. In 1958, France was team A and Yugoslavia was team B. Yugoslavia defeated France 3:2 in the middle game for each team, but the French built up such a big goal difference in their two wins that they won the group comfortably. They would have won under 3-1-0 on points, and they actually won under 2-1-0 on goal difference. So there was no change. In 1978, Austria was team A and Brazil was team B. In the final round, Brazil beat Austria 1:0, and the teams wound up tied both on points and goal difference, but Austria had scored more goals, and thus finished on top. Once more, team A would have won under 3-1-0 on points, and actually won under 2-1-0 on tiebreakers. Again, no change.

    The remaining two examples of this combination occurred in the 3-1-0 era. In 1998, Brazil was team A and Norway team B, and Norway beat Brazil 2:1 in the final round. Since the rule was now 3-1-0, Brazil won automatically on points--and here again they would have won under 2-1-0 as well, because they had an advantage in goal difference. Finally, also in 1998, Nigeria was team A and Paraguay team B, and here, at last, we had a true reversal. Paraguay defeated Nigeria in the final round by two goals, 3:1, and thus obtained the lead in goal difference. So Paraguay would have won under the 2-1-0 system. But under 3-1-0, Nigeria won the group on points automatically. The bottom line: out of 64 groups, only once would the 3-1-0 system have made a difference between first and second place.

    This result should come as no surprise. Looking even more closely at the scenario, we can see that team A is going to have at least a +2 goal difference from its 2 wins, vs. team B's zero goal difference from its two draws. Under 3-1-0, team A will always win. Under 2-1-0, if either of team Aís wins is by more than 1 goal, team B has to beat team A, clearly a good team, by at least 2 goals (see the France/Yugoslavia and Brazil/Norway examples). Moreover, even if team A wins its two games by only 1 goal each, it's likely to have scored more goals in the wins than team B did in the draws, since high-scoring draws are rare. So under 2-1-0, even if team B manages to beat team A by 1 goal and even out the goal difference, they're likely to lose the next tiebreaker, goals scored (see the Austria/Brazil example). So team B still most likely has to beat team A by 2 goals. Add in the relative rarity of the WWL/WDD combination, and you'll see why it's only happened once.

    At this point up-to-date readers may point out that the recent change in tiebreakers invalidates part of this analysis. The first tiebreaker is now match result, not goal difference--and if we look at the WWL/WDD scenario under 2-1-0, we find that since team B defeats team A, team B automatically wins the tiebreaker. If the first tiebreaker is match result, under 2-1-0 B always wins, and under 3-1-0 A always wins. In other words, if the first tiebreaker had been match result all along, the change from 2-1-0 to 3-1-0 would have changed the results of four groups, not just one. Does this invalidate the analysis?

    No. Thatís because what weíre measuring here is the theoretical change from the old system to the new system. The old system never used match result first. A tiebreaker change in the new system canít retroactively change the old system. Moreover, the change from 3-1-0 plus goal difference to 3-1-0 plus match result will have no effect on this scenario. In WWL/WDD under 3-1-0, team A always wins, so thereís no need for the tiebreaker. The conclusion is the same. Under the change from the old system (2-1-0 plus goal difference) to the new system (3-1-0 plus goal difference, or 3-1-0 plus match result), still only one of 64 groups would have reversed their top two finishers.

    The theoretical effect of 3-1-0 is even weaker when we come to decide second and third places, and thus the crucial line between qualifiers and non-qualifiers. The only scenario in which second and third places might be reversed looks like this:

Team A: WDL (3 or 4 points)
Team B: DDD (always 3 points)

    Under the 3-1-0 system, team A gets 4 points and team B gets 3 points, so team A always wins. But under the 2-1-0 system, both teams have 3 points, so team B can win if it has an advantage in the tiebreakers. Note that here thereís no difference between match result and goal difference, because under this scenario, team A and team B must have drawn their game. Team B has drawn all three games, and so must have drawn with team A. This scenario wonít come up very often, because itís rare for any team to draw all three of its games.

    In fact, the WDL/DDD combination has turned up only twice. Both times were in 1958, and the irony here is that 1958 was the only modern group stage in which there were no tiebreakers at all--team A and team B had to play off for the spot. So the 2-1-0 vs. 3-1-0 analysis here is purely theoretical. But let's look at the numbers as if tiebreakers had been in effect. In one group, Hungary was team A and Wales was team B. Hungary would have qualified on points under 3-1-0, and they had a big lead in goal difference, so they would also have qualified under 2-1-0. In the other group, Russia was team A and England was team B. Under 3-1-0, Russia would have qualified on points; as it turned out, the two teams were dead even in goal difference and goals scored. So under 2-1-0 it would have gone to lots, in which Russia would have had a 50% chance. (For the record, Wales and Russia won the playoffs.) The bottom line here: out of 64 groups, only once has there even been a chance that second and third places might have been reversed, and then only by the luck of the draw.

    Again, a closer look shows why the reversal is so unlikely. The team with three draws will naturally have a zero goal difference, so the standings under 2-1-0 will depend on the goal difference of team A. Team A has a win and a loss, the win almost certainly coming against the last-place team, and the loss coming against the first-place team. (There's a possibility it could be the reverse, but it's extremely unlikely.) For the reversal to be theoretically possible, team A has to lose to the top team by more goals than they beat the bottom team. But groups are more likely to have a particularly weak bottom team than a particularly dominant top team. For example, there have been 14 teams that won all 3 group games, but 22 that have lost all 3. Again, throw in the rarity of the WDL/DDD, and you'll see why there's never been a clear-cut reversal and isn't likely to be one any time soon.

    Add all this up, and you find that the theoretical effect of the change from 2-1-0 to 3-1-0 is in fact very small. Out of 64 groups, only one would have reversed the top two places, and only one would have had even a 50% chance of reversing qualifier and non-qualifier. The big change is a myth. If the teams have changed their game because of the change in the system, theyíve been conned.


2) Practice (and a little bit of theory too)

    That brings us to the second question: what evidence is there that the teams have in fact changed their game? Itís an article of faith among fans and press that teams are playing significantly more aggressively under 3-1-0. But do the numbers bear this out?

    The primary effect of the 3-1-0 system is to make wins more valuable. If teams have changed their play accordingly, we would expect them to risk more to win, and be less satisfied with a draw. The clearest index of the change would thus be an increase in decisive results and a decrease in draws.

    But in fact there has been no increase in decisive results. From 1958-1990, there were 181 decisive results in 252 group stage games, 71.8%. From 1994-2002, there were 94 decisive results in 132 group stage games, 71.2%. The percentage of decisive results is virtually unchanged. Thereís no evidence here that teams have been willing to risk more to win.

    OK, but perhaps in the years immediately preceding the change, draws had gone up, and thus the last three cups represent a return to an older, more decisive mode of play. But that doesnít work either. In 1982-1990, the three cups preceding the change, there were 77 decisive results in 108 games, 71.3%, again virtually identical. (In fact, this figure has been pretty constant over the years.) So thereís still no evidence of a change in style of play.

    Some may respond that if both teams are trying harder to win, theyíll cancel each other out, and youíll see no change. But under 3-1-0, itís the result which is the reward. If both teams are trying harder simply because they care more, thatís one thing. But the change to 3-1-0 doesnít make the games more important in the abstract sense; it makes wins more important. If youíre trying harder to win, you should get more wins and fewer draws.

    But there is in fact a small piece of evidence to that effect. Although, as pointed out, the overall theoretical difference between 2-1-0 and 3-1-0 is minor, the 3-1-0 system does put a premium on wins early in the group stage. Under 2-1-0, if you win your first two games, you have 4 points, and may still be in reach of teams that have drawn their first two games, and have 2 points. But under 3-1-0, if you win your first two games, you have 6 points, and teams with 2 points are entirely out of reach. In other words, under 3-1-0, if you win early, you may have less need to get results later.

    This theoretical advantage is in fact quite small. Assuming you win your first two games, there are nine possible scenarios (this table assumes the first-round games are 1v2 and 3v4, and the second-round games are 1v3 and 2v4):

Team Results 1 WW WW WW 2 LW LW LW 3 WL LL DL 4 LL WL DL 1 WW WW WW 2 LL LL LL 3 WL LL DL 4 LW WW DW 1 WW WW WW 2 LD LD LD 3 WL LL DL 4 LD WD DD
    Itís only in the last of these nine scenarios, where team 4 has two draws, that 3-1-0 makes a difference. Under 2-1-0, if team 4 can beat team 1 in the final round, the teams are equal on points. Under 3-1-0, team 1 has nothing to fear.

    So if the teams have changed their approach under 3-1-0, weíre likely to find a small increase in decisive results in the first two rounds of the group stage. And thatís exactly what weíve got. Hereís the table, with percentages of decisive games for each round of the group stage:

Years Rd. 1 Rd. 2 Rd. 3 Total 1958-1990 72.4 67.9 75.0 71.8 1994-2002 72.7 68.2 72.7 71.2
    As noted before, the percentage of total decisive games is very close. But we can see that a small drop in decisive third-round games has been partly balanced by smaller rises in decisive first- and second-round games. Although the total percentage of decisive games has actually gone down, the percentage of decisive games in the first and second rounds has gone up. This would be a natural consequence of the change to 3-1-0.

    But letís face it: thatís not much to go on. The practical change is very small--yet the general belief is that teams have changed their style of play significantly. If we want decisive evidence, weíll have to look elsewhere.

    Letís try another tack. If teams are trying harder to win, then teams ahead 1:0 should be pressing for more goals, and not sitting on their leads. They might score more goals, or they might allow equalizers, but in any case we should see fewer 1:0 games. But in fact thereís been a rise. From 1958-1990, 43 out of 252 games finished 1:0, a total of 17.1%. From 1994-2002, itís 26 out of 132, 19.7%.

    So that doesnít help. But letís try the same trick as before, looking at the three tournaments preceding the change. From 1982-1990, 24 games out of 108 finished 1:0, a total of 22.2%, compared to the 19.7% under 3-1-0. Thereís been a drop of 2.5%, not huge, yet perceptible.

    But the problem here is that 1990, known far and wide as the worst of the World Cups, is an anomaly. It was by several miles the lowest scoring tournament, and it finishes well down on every index of excitement. (As noted, it was the primary reason for the change to 3-1-0.) If you look only at 1982 and 1986, you find that the percentage of 1:0 games was 19.5%, almost identical with the 19.7% under 3-1-0.

    So letís try yet another idea. If teams are risking more to win, then when a team comes from behind and levels the score, both sides will be less likely to be satisfied with the result and more likely to push for a win. In other words, we should see more games in which a 1:1 tie (or, in rare cases, an even higher tie score) was broken by a later goal.

    At first glance the statistics are only mildly encouraging. Under 2-1-0, there were 49 such games out of 252, a total of 19.4%. Under 3-1-0, itís 28 out of 132, which is 21.2%. A small rise.

    But letís again look at the three cups preceding the change--and at last we strike gold. From 1982-1990 there are only 12 such games out of 108, 11.1%, substantially less than the 21.2% under 3-1-0. And even if we throw out 1990, we get only 9 out of 72, 12.5%, still substantially less.

    So at least one piece of evidence implies that teams are more actively seeking wins in the group stage. Although 1:0 games have not significantly decreased, when the game is tied at 1:1, teams have consistently pushed more for wins than they did in the preceding three tournaments. Is the 3-1-0 the reason? We canít say, but itís likely.

    Thereís another curious set of data that may suggest a change of play under 3-1-0. In previous articles Iíve written about the surprising difference between average goals scored in group stage games and average goals scored in knockout games. Before 2002, average goals scored in knockout games were virtually half a goal higher: 3.10 to 2.61. Hereís a table showing the year, the average goals in group stage games, and the average goals in knockout games (the group stage numbers only include first group stage games, not the second group stage from 1974-1982):

GS KO 1958 3.5 3.82 1962 2.71 3.0 1966 2.42 3.875 1970 2.54 4.25 1974 2.625 2.0 1978 2.5 3.5 1982 2.78 4.25 1986 2.38 3.0 1990 2.28 2.06 1994 2.58 3.0 1998 2.625 2.75 2002 2.71 1.94 -------------------------- Total 2.625 2.95
    Youíll see that from 1958 through 1986, knockout goals were substantially higher than group stage goals in almost every tournament. (The exception is 1974, where there were only two knockout games, and the sample is too small.) The 1990 tournament was anomalous, as usual. But then look what happened. The 1994 figures are fairly normal, but in 1998 knockout goals werenít much higher than group stage goals, and in 2002 knockout goals fell through the floor.

    Is this because of 3-1-0? Hard to say. Goal totals arenít the best indicator of how much teams want to win--you can have hard-fought games with lots of goals or few. Nevertheless, the stats are striking. Pre-1994, knockout goals averaged .585 more per game than group stage goals. Post-1994, knockout goals are actually .08 goals per game fewer. Itís just possible that teams are now playing more intensely in the group stage, leaving less energy for the knockouts.

    But there are two objections to this conclusion. First, 2002 skews the stats significantly. It may be an anomaly, although presumably weíll know more after 2006. Second, and more importantly, this conclusion doesnít quite gibe with our prior analysis. When looking at 1:1 games with subsequent goals, the effect only showed up when we compared 1994-2002 to 1982-1990, and 1990 was a part of the difference. But when we look at knockout goals, we find that although 1982 and 1986 are high, 1990 is very low, just like now. In other words, when we analyze 1:1 games, 1990 is what current trends are reacting against; when we analyze knockout and group stage goals, 1990 is what current trends are heading towards. So Iím not sure we can put the two effects together. Maybe the drop in knockout goals is due to something else, or maybe 1990 is just a freak.

To conclude:

1) The big change to 3-1-0 is in theory a very small change. Where you finish will almost always be the same. There is a small premium on winning games earlier in the group stage.

2) Although under 3-1-0 decisive games have not gone up, thereís been a very slight change favoring wins early in the group stage. Although 1:0 games have not gone down, thereís been a clear increase over 1982-1990 in 1:1 games that produced further goals. Thereís also been a significant decrease in knockout goals in relation to group stage goals, although not so much in relation to 1982-1990 as in relation to the 2-1-0 period as a whole.

    When I first looked at this subject, I was convinced that the big change to 3-1-0 was a complete myth, both in theory and practice. I still feel that way about the theory, but there does seem to be some evidence for the practice. Remember, though, itís a con. Playing harder to win because of 3-1-0 is a waste of effort. (But if you like the group stage the way it is, donít tell anybody.)



 

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