Forgive my lack of creativity at coming up with a dull title. Ever since the world cup group stage draws, we've been seeing threads about how 'easy' and 'difficult' groups are. This thread is a continuation of that debate. I suggested this in the other thread, and expected the squid or arthur to do it. Here is a simple excel based analysis to see how 'easy' and 'difficult' groups have been ever since the WCs began in the 1930s. The Assumptions 1) The difficulty or ease of a group is not decided by how the group appears on paper, or any other such preconceived notions. Difficulty is solely decided by how the teams perform actually during a group game. 2) A difficult group is one where the disparity in the strength of the teams is the least and not necessarily a team which has 2 world cup contenders. for eg, Italy, Brazil, Bhutan and Laos is not a difficult group, but one with Liechtenstein, Luxembourg, Andorra and San Marino is. The Procdeure Group match scores from all world cups were collated. (except for 1934 and 1938 because those WCs didn't have group matches). The mean of the goal differences in all the group games for each world cup were calculated.These are called the 'overall means' So were the standard deviations. After this, the means and standard deviations of goal differences of the world cup groups for 8 major (current) nations - Argentina, Brazil, England, France, Germany, Italy, Netherlands and Spain were collated. this too was done for all the world cups. The Inference If we find that the average of goal difference in a particular world cup for a nation are lower than that of the overall average, then we can conclude that the nation has had a 'difficult' group. If the same average is higher, we conclude that the group is easier ( relative to that world cup). I took a difference of 0.1 on either side of the overall mean to be insignificant. I.e if the overall goal difference average in a world cup is 2.33 and Germany's group averages 2.29, then the group is neither easy nor difficult. If Germany's group averages 2.55, then the group is easy and if Germany's group averages 1.96, then it is a difficult group. Another way of determining the ease/difficulty of a group from the overall average is to test the data (nation wise) a set level of significance against the overall average for a WC. But that would have been extremely tedious and overtly statistical. This is the excel sheet: http://www.megafileupload.com/en/file/169629/Goal-difference-analysis-xls.html The Observations This graph says it all Here the bold blue line represents the overall goal difference average across the world cups. Surprisingly it is Germany and Argentina who has had the easier groups over the years and England and Italy the more difficult ones. Here are how the major countries line up in WCs from 1954: Country ( easy groups/ appearances) Argentina (8/12) Brazil (6/14) England (0/11) France (2/9) Germany (10/14) Italy (4/13) Netherlands (2/6) Spain (4/9) What say? PS: All mistakes are mine
Well, I think the entire premise is flawed. Groups can only be easy or difficult from the point of view of one of the participants. For Liechtenstein, a Liechtenstein, Luxembourg, Andorra and San Marino group would be an easy group, as most other possibilities would be much more difficult for them. The other group you mentioned would be almost hopelessly difficult for Laos, but easy for Brazil or Italy. And I don't think you can actually find out how difficult a group was from the actual results. At least that's not was commonly understood when people talk about difficulty. See Germany's 2004 Euro qulaifying campaign. That they only managed narrow wins in that group doesn't mean it was difficult, it just means that Germany utterly sucked in 2004 . On the other hand, I thought that Germany always getting the easiest groups was common knowledge
Something like that is almost impossible to conclude with a statistical analysis in my opinion. Aside from what Alex said, goal difference as a means of measuring difficulty fails to tell the whole story. Football is a game of chances, a lot of which are missed. It is therefore easy to gloss over and misinterpret a team's performance based on a scoreline that is deceiving. A team can win by one goal and still be entirely dominant during the match. At the same time, a team can win by one goal and be outplayed completely by the opposition. That skews the picture and your analysis. Anyways, great post and interesting attempt at answering that question.
Also, goal difference comes with tactics. An attack-minded team will have a high goal difference, a defense-oriented team will win with lower differences. Another flaw is that a single very bad team will an otherwise difficult group "easy" - take Germanys group 2002 with Saudi Arabia, Argentina '06 thanks to the Argentina-Serbia match alone - and I'd expect that the Brazil-Portugal-Ivory Coast group will also end up being "easy" by your definition. Nevertheless, interesting approach. I'd try it with points first. But then, I fear 6 matches in a group are simply not enough for a statistical approach to work.
Thanks for the encouraging responses. Since I am yet to master the art of multi quoting, I'll reply to you all in this one post: @ Alex_K : Groups can be easy or difficult from the point of view of one of the participants. But they can also be easy or difficult compared to how easy or difficult the other groups are. That is the basic premise of this analysis. I am not contesting that Liechtenstein would find the group mentioned easier than any other group, the group would still be a tough group. The example you cite of Euro 2004 qualifiers is precisely what I am talking about. A group with Iceland, Scotland, Lithuania, Faroe Islands etc doesn't look 'tough' on paper. But a round robin league with 10-12 games is a true indicator of a teams strength. And Germany struggled to beat even the minnows, beating the Faore's 2-1 IIRC, with the '10 goals in 10 years' Fredi Bobic scoring. It indicates that the group was a difficult one, and Germany played poorly. The two are not exclusive. Rather, Germany 'sucked' and hence the group was difficult. Difficulty is always measured after one has under gone the test. Everything else is a perception. A poor analogy is that you could appear for an exam thinking that it is a tough subject. But you could end up scoring 90/100. Would you still want to call it tough? @ ForeverRed: I take your point. What I can offer as an explanation is that if team A dominates over team B, and is still able to win by only 1 goal, then team A has found it difficult to score goal. Besides, a group contains 6 games. All teams are equally likely to have their share of missed chances, periods of domination without goals, bad calls, own goals suchlike. This would be the same across groups. I agree that this skews the goal difference analysis, but it skews it equally for all the groups and hence can be overlooked. I hope I convinced you. @Cirdan: You raise good points. This whole thing about 'attack' and 'defense' minded teams is debatable. For eg, in WM02, Germany wasn't really an attack minded team. They played with that mentality only vs Saudi Arabia. In fact, there is no such fixed strategy of being attack or defense minded. It is largely dependent on the strengths and weaknesses of your opponent. In the same WC, against Ireland or Paraguay or even the USA, Germany didn't look as 'attack' minded. And even if a team has an unnaturally high propensity for attack, it doesn't make much of a difference on the goal difference analysis. Attack minded teams are likely to score more and also concede more in the process. A defense minded team would score and concede lesser. So the goal difference would not be drastically affected. The other point you raise is also very valid and thought provoking. Yes, a single bad team or a single bad performance can make a group easy. That is true. But then again, in the Argentina, Ivory Coast, Holland and Serbia group, there were results in all the games apart from the Holland vs Argentina game ( and both the teams had already qualified by then). SO if it were such a difficult group, one would expect more drawn games. That would offset the trashing Serbia got and we would have a not so exaggerated goal difference. Germany's group in WC02 was easy. If all the teams trash North Korea, and there are no drawn games between Portugal, Ivory Coast and Brazil, this time around, then the group is easy. And that is because difficulty is purely decided by results and not by expectations. I did not follow your approach of doing the analysis by points. Could you please explain?
I don't have much time, so just a short reply: I think there's a difference between difficulty and competitiveness. You might be able to objectively measure the latter, but not the former. I don't think it would be right, if through a chain of freak results, Laos ends up winning their group with +23 goals over Brazil and Italy to call it an easy group. As for the exam - there the difficulty depends more on the effort thats needed, not on the result. Otherwise a examn in which you do good could never have been difficult.
Germany '02 was indeed not very attack-minded, but that doesn't mean that such a distinction doesn't exist. Look at the Bundesliga over the last 5 or 6 years, Werder was definitely an attack-minded team, while Schalke was rather defensive, that is reflected in goals per game ratios and in the point that Werders goal difference was always better, often by 10 goals and more, while the points hardly differed, Schalke was even ahead of Werder a couple of times. And in World Cups, for the most part Germany and Brazil had attacking teams, Italy on the other hand were mostly rather defensive. You can see that in the goals-per-game ratios again. Well, there's different possibilities... for example, calculate the mean points of a group and the standard deviation. If the standard deviation is high, the team strengths must have differed a lot, if it is low, they were close together. Though this will also tell you that the Argentina group in '06 was easy, and anyone who has actually watched the games between Argentina, Holland and Ivory Coast knows how close they were and how good those teams played. Like I said, with 6 matches, you will find it difficult to get a reliable statistic. And btw, Germanys '06 group wasn't really easy. No group of death, but Ireland and Cameroon both had very capable teams that year.
To test the hypothesis you mention, I have sourced data from the following website:http://www.planetworldcup.com/NATIONS/maraton.html Lets just take the top 3 nations: 1) Brazil - played 92, goals 201, against 84 goals/game = 2.187 . goal difference/game = 1.272 2) Germany - played 92, goals 190, against 112 goals/game = 2.065, goal difference/game = 0.8478 3) Italy - played 77, goals 122, against 69 goals/game = 1.5844 , goal difference/game = 0.6883 This data isn't conclusive. The point I'm trying to drive home is that an 'Attack minded' Germany doesn't win its games by a significantly bigger margin than a 'defensive Italy'. And 'defensive' Italy has a bigger goal difference ratio per game than the teams we traditionally consider 'attacking' like Holland and Spain. This is a great idea. Once we see the deviation, how do we know what is high or low? What is good, bad or ugly? For that we will need an overall benchmark, which can be the deviation from the average of all group games. I have a sneaking feeling that the analysis would throw the same results as this one. I'll compute it that way when I have some time.
You don't necessarily recognize an attack minded team by a big goal margin, since they often also concede a lot of goals. So, a better statistic to determine this would be goals per game that counts all goals scored, regardless whether they were for or against: Germany: 3.28 gpg France: 3.12 gpg Brazil: 3.09 gpg Argentina 2.87 gpg Spain: 2.80 gpg Netherlands: 2.69 gpg Italy: 2.48 gpg England: 2.2 gpg Unfortunately, the different eras of football screw with this statistic more than a bit - 1954 had more than 5 goals per game, 1990 hardly more than 2. The Netherlands played their first world cup 1974, when the goals per game ratios had already dropped below 3, England and Argentina didn't play at all or dropped out early in most of the early world cups... but I'm too lazy to make this stat per world cup, or remove the first 6 world cups, which were the only ones with more than 3 goals per game. But you can see a tendency, I believe - when England or Italy play, there tend to be rather few goals, in Spains matches probably fewer than you'd expect, while with Germany, France and Brazil there tend to be a lot of goals.
I've done it the way you've suggested for world cups 1950-1974. Overall, the picture doesn't change much and the calculations are more tedious. It is compounded by the fact that the earlier world cups have a 2 point of win scoring system. Simply assuming 3 for a team win (as is the case with later WCs) will not solve the problem. Because back then the teams would have played much more cautiously knowing that the difference between a win and a draw is just 1 point. And also the deviation is lesser if the system is 2-1-0 as against 3-1-0. So the goal difference approach is better suited to answer the question if difficulty.
Since the group stages of the WC 10 are done with, I've updated this thread. This link has the excel with the calculations. Here is how the major teams line up for WC 2010: Overall Goal Difference Average Overall: 1.19 Argentina: 1.17 Brazil: 2.17 England: 0.5 France: 1.17 Germany: 1.33 Italy: 1.00 Netherlands: 1.33 Spain: 1.00 Using this method, Brazil have had a very easy group. Germany and Netherlands have also had moderately easy groups. Argentina and France have groups that were neither easy nor difficult. Italy and Spain have had tough groups. And England has had the toughest group. I'll add the 2010WC results to the graph a little later. PS: The previous page has the description of the method used to classify groups as 'easy' or 'difficult'
I don't think there is such a thing as an easy group or a hard group. It is all about the team under performing. I mean England on paper looks like a freaking tough team, but, in reality, they play with their underwear and have no understanding of the modern game. I guess it really depends on how well your team worked out. For example, the germany that showed up against England was a completely different beast compare to the one that played Ghana.
The fact that both teams from group D advanced to the quarters and non of group C also speaks against C being a tougher group than D. Especially if one compares the two worst teams in the groups.
If both teams advanced from group D to the quarters, wouldn't group D be tougher given the strength of the teams that advanced?
No. That's not what it means. The difficulty of a group is decided only by how tough its to get out of that group. It doesn't matter how the teams do further ahead in the tournament. For example, a group comprising of Albania, Macedonia, Montenegro & Moldova is tougher than a group that consists of Germany, Italy, Liechtenstein and Faroe Islands.
I agree with Homa. It's virtually impossible to determine the strength of a group by the group games alone. As Alex said, you can measure competitiveness, but not strength. The best metric IMHO would be to look how deep the teams that got out of any given group went in the tournament. That's not a perfect system either because it doesn't take into account how strong the team is that kicks you out. But at least it offers a metric to compare the groups of a World Cup in terms of strength, not just competitiveness. For example, any given group could get -2 points for each team that drops out in the round of 16, 1 point for every team that reaches the quarters, 2 points for each team that reaches the semis and 4 points for each team that reaches the final. An example: A: One team reaches semis, the other drops out in Ro16 => 0 points B: One team reaches quarters, the other drops out in Ro16 => -1 point C: both teams drop out in the round of 16 => -4 points D: One team reaches quarters, the other reaches final => 5 points E: One team reaches quarters, the other drops out in Ro16 => -1 point F: One team reaches quarters, the other drops out in Ro16 => -1 point G: One team reaches final, the other drops out in Ro16 => 2 point H: One team reaches semis, the other drops out in Ro16 => 0 points So in this case, Group D would be strong, because the surviving teams were obviously strong. Next we have G, then A and H, then B, E, F, then C. Now, in order to account for the strength of the teams that went out, one could introduce a multiplier. For example, one could give 0.1 points for every point the teams that don't qualify for the second round gathered. One example: A: 0.5 B: 0.4 C: 0.5 D: 0.7 E: 0.3 F: 0.5 G: 0.4 H: 0.5 Let's call the points a Group gets "p", the multiplier "m" and the strength "S". Then we get: S=p*(1+m) for p>0 S=p*(1-m) for p<0 S=0 for p=0 So the final result in this case would be: A: 0 B: -1*(1-0.4)=-0.6 C: -4*(1-0.5)=-2 D: 5*(1+0.7)=8.5 E: -1*(1-0.3)=-0.7 F: -1*(1-0.5)=-0.5 G: 2*(1+0.4)=2.8 H: 0 A group with S=0 would be of average strength. Now I just made this up and of course one could tweak it a little bit here and there. But generally I think this is the kind of thing that gets you closest to a real assessment of the strength of a group.
Toughness is difficult to assess because it depends on the thing you compare to. A group of two extremly good teams and two really bad teams is very tough for the bad teams but easy for the good ones. So Benztown is right in saying that inside a group you can only assess relative competitiveness which doesnt say anything about the absolute strength of the group (or rather the teams in the group). Assessing the strenght of the group by the success the teams have which topped it is also not a good way because you ignore half of the group's teams. Again you could have two really strong teams which could advance pretty fat and two really crappy ones which go home after the group phase. Is such a group strong? Guess the strength of a group would probably best assess by combining those two things. a) competitiveness inside the group b) strength relative to other groups (success of the two top teams after group stage). The whole thing nonetheless isn't more than guess work because the sample sizes are far too small.
That's what I tried to do...as I said, one might tweak it a little, like increasing the multiplier or something like that, but ultimately, that's the direction you wanna go...
@ benztown: What you have come up with is indeed a very ingenious method to ascertaining the strength of the groups.HOWEVER, what I tried to determine was competitiveness and not strength. When I made this thread, it was a few days after the groups for WC10 were announced. And people were all saying that group x is easier than y and country xyz always has it easier than country abc etc. That is why, I came up with a method to determine the how easy and difficult groups have been. Historically. I'll be a devil's advocate and examine your method of strength assessment: 1) Let us take 2 groups. A - which has teams a1,a2,a3,a4 and E - which has team e1,e2,e3,e4. Suppose a1 and a2 both reach the WC quarter finals finals. e1 and e2 too reach the quarters In group stages, this is how the teams lined up: a1= 7 pts a2 = 7 pts a3 = 1 pt a4 = 1 pt e1= 4 pts e2 = 4 pts e3 = 4 pts e4 = 4 pts So, applying your formula for strength of a team S= p*(1+m) for p>0 S= P*(1-m) for p<0 S=0 for p=0 For group A m=0.2, p = 4 S= 4*1.2 = 4.8 For group E m=0.8, p = 4 S=4*1.8 = 7.2 So, this makes group E stronger than group A, simply because the teams that DIDN'T qualify have gathered more points. Since a1,a2,e1,e2 are all losing quarterfinalists, it is evident that they didn't play each other. We don't have an objective way of saying if a1,a2 > or = or < than e1,e2. But we are already declaring group E > group A? I find this slightly flawed. 2) Why have you used -ve points for R16 exit? Just use a 0. Keep it Simple, Silly principle. 3) Your formulae do not take into account the goal difference. Goal difference is a better differentiator of teams than merely points. a1 and a2 could have won their games 5-0, 5-0 or 1-0 , 1-0 against a3 and a4, and it wouldn't impact S of the group at all. Intuitively, that doesn't feel right. @ Homa: You said That is what I tried to do. I took the overall average of the goal differences in all the group stages. That tells me on an average, how close games have been in a given tournament. Then I compared that with the average of the goal differences in one particular group (which is a sub set of the overall). That way, I am measuring competitiveness inside a group to performance of every one on an overall level during group games.
First of all, p=2 in your example, not 4. And I still think that this makes sense. If a1, a2, e1, e2 all go equally deep into the tournament, we have to conclude that they are roughly of the same strength. So if they're all of the same strength, yet e3 and e4 managed to win 8 points against them while a3 and a4 only got 2 points, we also have to conclude that e3 and e4 are better than a3 and a4. Therefore overall, E > A. At first I was experimenting with 0 points for an R16 exit. It does cause some undesired effects though, because it leads to overestimating the strength of a group in which only one team performs well. You might be able to circumvent that by having a big drop-off between r16 and the quarters (maybe 0,6,7,9 points) but I didn't think that through so much, as I think the negative numbers work perfectly IMHO. The problems with the big drop-off is that you don't get awarded much more for going deeper. In my example you get twice as many points for reaching the semis compared to the quarters and twice as much again for reaching the final. The drop-off leads to this not making much of a difference once you reach the quarters. If however you'd increase the differences (i.e. 0,6,12,24) then again the overall strength of a group gets overestimated when one team does well. The negative numbers are a good compromise. I can give a team that reaches the semis twice as many points compared to the one that reaches the quarters and still make sure that a group with only one good team isn't outperforming the others... Maybe something in between (like 0,6,9,15) also works, but again, I think this would need a lot of thinking through and I was lazy. Why try to tweak it when I already have a great solution with the negative points? Personally, I don't think that GD is a particularly good metric, because they have a lot to do with the styles of different teams and how they work out once these teams meet. For example, Ghana at this WC plays very defensively. Once they have a 1-0 lead, they happily defend that. Historically, Italy has done the same. So teams like these might always come up with close results, but that doesn't mean that they'r not comfortably winning. Another example: Look at North Korea and their results. They got a very close result vs. Brazil, while getting hammered by Portugal and to a degree Ivory Coast. I think we'd all agree that Brazil was the best team in that group. Imagine a group with 3 Brazil like teams and one North Korea: NK would get zero points, but the GD would be very close still. Now imagine a group with 3 Portugals and one North Korea: NK would still get zero points and have a historically bad GD. According to your system, the group with the 3 Brazilian teams is more competitive, because of GD. But we know that it's not true. It's just that Brazil's style prevents them from blowing NK out of the water. Ultimately, what counts is the points, not the goals. It might make sense to include goals as an additional (small) factor, but the focus should be on whom wins.
First of all, thanks for the detailed reply. Yes, that was my mistake. I took it as 2 points per quarterfinals appearance. But since both groups have teams reaching the same stage, the quarters, it doesn't make any difference to the point that I am making. Instead of the multiplier 4, we use the multiplier 2 in both the scenarios. And, no, just because two teams are eliminated at the same stage of the tournament, you cannot assume that they are roughly of the same strength. That is a very wide generalization. In a tournament like the WC, 16 teams play 3 games only, 8 play 4 games only, 4 play 5 games only and 4 play more than 7 games ( as all the semifinalsist play 7 games). Most of the time, the teams that have been knocked out at a certain 'step' haven't played each other. So, we just cannot conclude that they are of equal strength. To do that, we have to assume that the groups that they came from are similar. But the entire point of this exercise is to find out the strength of the groups. YOU ARE IN A SENSE MAKING ASSUMPTIONS ON WHAT YOU SET OUT TO CALCULATE In our example, a1,a2,e1,e2 are all quarter final losers. They haven't played each other. It could very well be that a1 and a2 lost to the two finalists on penalties in the quarters. e1 and e2 lost to the other two losing semi finalists by a large margin. But your method, does not take that into account. It puts E>A simply because e3,e4 managed more points than a3,a4 even though a1, and a2 are stronger than e1 and e2. I am looking for exceptions to your model. If they exist, then the model should be tweaked. I understand what you are trying to do, but I think that the premise that teams which reach the same stage in a WC are of nearly equal strength is slightly shaky. Excellent thinking. Good point. I'm convinced here. Here I completely disagree. winning or losing is a function of your goal difference. So when you say that focus should be on who wins, you are in effect treating all GD> 1 as win, GD = 0 as draw and GD< 1 as loss. While you club all GD =1, GD =2 , GD = 3 etc under one bracket, i.e win. I am treating each as a separate case. I'll address the points that you have raised point wise: So Ghana and Italy play cattenacio/defense and win comfortably, but it doesn't show in the GD. Fair point. But there are three more games in the group, where the teams know that they have to win big to get a +ve goal difference because they would have all had a minor -ve goal difference against Italy. This thinngs will always offset and correct one another. You are focusing only on one end of the spectrum. On the other side, suppose you have a Saudi vs Germany scenario. There treating a 8-0 win as a 1-0 is unfair as both are categorized as wins, but that in itself is not indicative of the strength of the teams in the groups. For eg, in 2006, group H comprised of: Spain Ukraine Tunisia Saudi Arabia Let me demonstrate my point further by using both your and my methods: by my method: Over all means of the GD in WC 2006 was 1.48 Mean of GD in this group was 2.00 So, clearly this group is easier than the average group in the 2006 tournament. If I were to use your method, both Spain and Ukraine were knocked out in R 16. There fore p = -4. Saudi and Tunisia finished with 1 pt each. So m = 0.2 S = p*(1-m) = -4*(0.8) = -3.2, which should classify as easy. So far so good. Now let us compare this with Germany's group on the same WC. That group too had an average GD of 2.00. So, it qualifies as easy from my methodology. Using your technique, Sweden were out in R16 and Germany were semi finalists. So p=0 implying S=0. So its an average group. ???? And this is where, I beg to differ. Because Spain's and Germany's groups both were very easy for the top two teams, where they've finished on 9,6 points in their respective groups. To the Brazil & Portugal example: Yes, this is a flaw with the GD system. But my reasoning is that no big team likes to win by a small margin against a minnow. Even defensive teams want to win comfortably against minnows. Brazil tried, but couldn't do it. It had more to do with their form that day and not Brazil's style of play. France weren't an offense minded team in 1998. But they beat Saudi 4-0.
Well, I admitted as much in my initial post. The point is, shaky as it may be, it's still the best data we could possibly get. It can lead to a group looking weaker than it really is (but hardly the opposite). Let me draw it out so that I can make clear why it's not that big a problem: Team A wins the World Cup. On its way, it beats team B in the round of 16, team C in the quarters, team D in the semis and team E in the final. Theoretically, team B could be the second best team which just happens to have the bad luck of meeting team A first. However, in the round of 16, group winners always meet the runners up. So if team B is indeed so good, one would expect it to win its group and never meet team A before the final. If it doesn't, there's no reason to complain. So it doesn't really get shaky before the quarters which makes things much better (no negative points). Now one could think about a metric to balance this out a bit. For example: You get p=0.5 if you drop out in the quarters against a team that goes on to lose the semis. For example: a1 drops out in the semis => p=2 a2 drops out in the quarters against a team that went out in the semis => p=0.5 Although that skews the balance a little bit...so I guess we'd have to rework the points given for each stage...maybe -1.5 (out in r16) 0.5 (out in the quarters against a semi finalist) 1 (out in the quarters against a finalist) 1.5 (out in the semis) 2.5 (finalist) or in order to get even numbers: -3 (out in r16) 1 (out in the quarters against a semi finalist) 2 (out in the quarters against a finalist) 3 (out in the semis) 5 (finalist) You could always break it down more...like going out in the semis against the champ vs. against the runner up, or you could distinguish between the winning and the losing finalist. You could go one level deeper and also look at how well the team does which kicked out the team that kicked you out and so on... But ultimately, I think that's not needed, I think not much actual information is gained, and it could lead to a weak team that drops out against a strong team to be overrated. So I still think that my original system is simple and good enough: -2 (r16) 1 (q) 2 (s) 4 (f) Yes, a strong team could end up being underrated, but the effect isn't all that bad and frankly you'll always have inaccuracies. I simply see no better metric. Great I don't know, I still think that goals are not that important and only bring in an element which can skew the whole thing. For example: Lets say Teams a1, a2, a3 are world class, absolutely great, on top of everybody else, by far the best teams in the entire World Cup. Team a4 however is absolute crap and the worst of the lot. Now, teams a1, a2, a3 draw all their games, but each of them blasts a4 away with 10-0. So the average goal difference in this group is 5. According to your system, it would be an easy group, when in reality it's just a very unbalanced group. I think the problem is that you look at the groups from the perspective of the individual team. But that approach is flawed as the individual team is a part of that group. I look at the group as a whole. With your approach, you can say that in group X, the games were very close. But that doesn't make the group "difficult" in itself, it makes it difficult for the individual team in that particular group. With my approach, look at group X as a whole, not just from the perspective of the individual teams, but also how the group fared in the tournament overall. I think that constitutes a large part of what makes a group difficult. Maybe I should define how I understand "difficult group". To me a group is difficult when you can take out any team x from that group and put in any other team y and no matter which team it is you take out or put in, it will be difficult for team y to qualify.