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kdonn
06-18-2002, 03:55 PM
This is my first post to the message board, and I have searched the archives.

Basically, what I'm looking for here is someone to provide a sound statistical argument that the scoring in soccer is almost useless in determing which team is better. I don't care whether soccer is a good sport or not, and I don't care whether it's fun or not fun to watch because of the low scores. I'm only interested in whether the scores can be a meaningful indicator of which team is better.

I really know very little about soccer, but my thinking goes basically like this: each scoring drive in soccer has a small chance of success. In order for a team's actual score to represent their ability, there has to be a large number of scoring drives, but in soccer there usually isn't a large number of scoring drives. And this is exacerbated if you further expect the score to indicate the better team. Now, in addition to needing a large number of drives to even accurately represent a team's ability, what you really need is enough drives to reflect one team's slight edge over the other, which dramatically drives up the number of scoring drives needed for an accurate result.

Suppose we had a special coin that would only show heads in 10% of tosses and another that would show heads in 20% of tosses. Believe me, I'm no stat major and I labored over this quite a bit, but my results show that if you flipped each coin 5 times, the 20% coin would have only about a 49% chance of yielding a higher number of heads than the 10% coin. This is to say that the 20% coin would be more likely to lose or tie than to win the game of five tosses.

Now if the two coins were instead two soccer teams, and each team gets to make 5 scoring drives during the game, then we essentially have the coin toss scenario above. We can say that the team that is twice as good as the other team is still not even *likely* to win. A tie or a loss is actually more likely for the vastly better team than a win.

Besides the basic soundness of my coin toss probability math (and I implore people who don't have a solid background in math to resist the urge to throw up some simple calculations because probabilities are beguiling complicated), we'd need to define "scoring drive" and address what the real-world average number of "scoring drives" is in a soccer game, and what the real-world average probabilities are to score before we could really work this out. But all this should be more-or-less available in the annals of soccer stats if they're anything like baseball or basketball stats.

My gut feel is that my assertion will be born out and here's why: soccer is the only international sport. If soccer's scoring more accurately represented the better team, there wouldn't be so many competitive countries. There would be a handful of "superpower" teams and everyone else wouldn't have a chance, ever. But in soccer it seems like any country can have a shot at the big dance. Why? Because it's pretty much a lottery or a crapshoot and the scoring guarantees that. A team has to be enormously better than another team to have a reasonably sure shot of winning.

If soccer's scoring more accurately reflected the better team, we'd see scores more like 15-2 instead of this perpetual (and highly suspicious) 0-1. The little countries wouldn't be able to compete and we'd see a lot less soccer rioting. I mean, who wants to riot when your team loses by 10 or 20 points instead of 1 point?

So, come on stat-boys-and-girls. Enlighten us!

gazpacho
06-18-2002, 04:28 PM
Basically, what I'm looking for here is someone to provide a sound statistical argument that the scoring in soccer is almost useless in determing which team is better. I don't care whether soccer is a good sport or not, and I don't care whether it's fun or not fun to watch because of the low scores. I'm only interested in whether the scores can be a meaningful indicator of which team is better.
By definition scoring in soccer is how to determine which team is better. If you want 15 to 4 scores you need a different sport.

SmackFu
06-18-2002, 04:36 PM
I would tend to think the percentage is much lower than you imply, and that the spread between teams is much higher. For instance, Canada may score .25% of the time and Brazil may be 2%. Over a game (which has much more than 5 scoring chances BTW), it is very likely that Canada will not score. It is likely that Brazil will. Thus 1-0.

London_Calling
06-18-2002, 05:03 PM
I think you're confusing the excitement of a cup competition like the latter stages of the World Cup (a one-match knockout tournament) with a league season lasting 8 plus months.

Cups are about the romance, the excitement, the uncertainty of David's and Goliath's battling for 90 minutes (or however long it takes). That has little in common with a regular season.

stuyguy
06-18-2002, 05:06 PM
kdonn, I know nothing about soccer but I think your premise is sound -- and nicely articulated in you somewhat longish post.

Welcome to the SDMB, BTW.

Sofa King
06-18-2002, 05:18 PM
I don't know if this helps or not, but one of the most hilarious, exasperating matches I ever saw was France v. Paraguay (http://sportsillustrated.cnn.com/soccer/world/events/1998/worldcup/news/1998/06/28/france_update/) in 1998. France was on its way to winning the Cup that year, but Paraguay had an ace in the hole--a penalty-shot kicker who rarely missed.

So Paraguay tried like hell to ride out the entire game on defense in order to cash in on the assured one goal in the penalty kick-off. Any time France looked like they had a break, someone would fake an injury or kick the ball out of play. They lasted through all of regulation play and far into the sudden death period, but France finally stuck one in to win it with a few minutes of play remaining.

I mention this because it seems to slightly contradict your theory, kdonn. Paraguay knew that France was the better team, and attempted to compensate by keeping most of their players on the defensive, with the knowledge that the advantage would shift to them once normal play ended. In that single example, Paraguay still lost, 0-1.

But the score belies the complex and insanely boring strategy which was employed to defeat those odds, and which very nearly succeeded. The coins you're tossing are thinking very hard about which way they want to land.

Crusoe
06-18-2002, 05:24 PM
The playing-for-penalties tactic is certainly not unknown. Red Star Belgrade's awful defensive performance against Olympique Marseille in the 1991 European Cup was purely designed to take the game to penalties. Argentina's tactics in the 1990 World Cup final against West Germany were purely designed to bring the game to penalties, where Argentina's penalty-king 'keeper Sergio Goycochea could do his thing.

xicanorex
06-18-2002, 06:03 PM
If soccer's scoring more accurately represented the better team, there wouldn't be so many competitive countries. There would be a handful of "superpower" teams and everyone else wouldn't have a chance, ever. But in soccer it seems like any country can have a shot at the big dance. Why? Because it's pretty much a lottery or a crapshoot and the scoring guarantees that. A team has to be enormously better than another team to have a reasonably sure shot of winning.

The thing is that THERE ARE "super power teams" and not all the teams are on the same level. The teams in the World Cup are not all THE supepowers, but do include the superpower of soccer/football. Can anyone have a shot? No. Look at China, Tunisia, Saudi Arabia, etc. Remember the game between Australia vs. American Samoa (31-0)? The score can reflect the level of game between two countries or teams. Look at the score between Germany vs. Saudi Arabia (8-0) and compare to Germany vs. Ireland (1-1). Of course, a score such as the aforementioned can tell you that Saudi Arabia is a very weak team wheres Ireland is not. Now, there are more stats you have to consider in order to appreciate the level of game and they are: how did the scoring progress (first time vs. secon time? For exampole Senegal vs. Denmark 1:1 (1:0). What was the % of possesion? Shots at goal? Corner Shots? % of possession in the offensive side? etc.

If soccer's scoring more accurately reflected the better team, we'd see scores more like 15-2 instead of this perpetual (and highly suspicious) 0-1. The little countries wouldn't be able to compete and we'd see a lot less soccer rioting. I mean, who wants to riot when your team loses by 10 or 20 points instead of 1 point?

Well, 8-0's do occur ask Saudi Arabia ( I am not sure a riot ensued ;) ). The reason we don't more 15-2 is that more countries are reaching the good level of game vs. the traditional superpowers.

I guess what I am trying to say is that most sports have a certain amount of luck involved, but it is the good teams/athletes that win by skills.

XicanoreX

RealityChuck
06-18-2002, 08:46 PM
Your analysis is flawed. Scoring in soccer is not a random event like a coin toss, and the probabilities are meaningless, since they only represent the results of the past, but not the future.

For example, teams don't have the same number of scoring drives in a game, as in your example. The better team will have more in most games. With more drives, their chances of scoring are better.

And nothing in sport is mathematically certain. You can run simulations in any sport for years and never come up with the same results as real life. I have, for instance, baseball simulation software on my computer. I can run a simulation of the 6th game of the 1986 World Series thousands of times, and it's hardly likely any of the results will ever match the actual game.

When dealing with sports, the math describes the past, but cannot predict the future. A team may usually only convert on .05% of its goal attempts; but in any one game, it will convert on, say, 25%. The probability over the course of a season or tournament is meaningless when applied to any one game.

Finally, all sports have their upsets. While the better team usually wins, there are always times when they're off their game, or run into a streak of bad luck (their best player breaking a leg, for instance, or a ball making a bad bounce).

Shalmanese
06-19-2002, 01:31 AM
His claims do have validity though. What he is essentially saying is that the statisitcal noise is drowning out the signal when it comes to scoring. There is a statisitcally significant chance that a not-so-good team will get a goal while a very-good team will not, thus giving the game to the not-so-good team.

Shalmanese
06-19-2002, 01:46 AM
His claims do have validity though. What he is essentially saying is that the statisitcal noise is drowning out the signal when it comes to scoring. There is a statisitcally significant chance that a not-so-good team will get a goal while a very-good team will not, thus giving the game to the not-so-good team.

BobT
06-19-2002, 02:36 AM
The World Cup, unlike nearly every other major sporting event in the world, just doesn't have surprise winners. That is surprise winner of the championship.

There are surprises in the early rounds and this year's tournament has four teams in the quarterfinals that have never made it that far before.

Still there have only been seven nations that have won the Cup. And six times the home nation has won (Uruguay 1930, Italy 1934, England 1966, Germany 1974, Argentina 1978, France 1998).

Also in the top leagues in the world, only a few teams win the league championships. Very rarely does a team come from the bottom half of the standings in one season to win the next year.

Another reason why you don't see huge margins in soccer games is that there is often little reason for a team that is ahead by a comfortable margin, say 3-0, to try to score more. It's safer to defend.

Sometimes teams may need to add to their goal difference in which case they will push ahead to score more.

Princhester
06-19-2002, 02:36 AM
Yep, I'm mostly with you on this one,kdonn. I'm not sure your whole analysis is perfect, but the underlying point namely that in a single game of soccer there would seem to be far too much of a chance that the better team will not win, is a point that I have often wondered about.

I'd really like to see someone who is confident on statistics do an analysis of the situation.

However, I have the following comments. Firstly, I think you can throw out the whole concept of "scoring drives" and just do your analysis on the simple fact of how often a team scores a goal in a game.

Secondly, as others have said, your analysis is particularly relevant in competitions where there are few games, and a a large element of knockout. Because then by "fluking" a small number of wins, a poorer team can advance significantly. But most of the big competitions (the English competitions for example) the season is endless and everyone plays everyone else numerous times, and so there is in fact a chance for the laws of chance to make the most of small advantages. And sure enough in those competitions, a handful of clearly better teams do stand out over the course of a season.

Thirdly, one factor that is not accounted for in your statistics is the change in tactics that results from scoring. Soccer is a game in which it is much easier to close down one's defence than it is to successfully attack. Therefore, once a team is in the lead, they will often choose to defend, and not try to score. The result is that scorelines often look very close (0-1, 2-1 etc) but are not necessarily reflective of the winner's real ability advantage: the winner may well have deliberately only attacked hard until they had a one goal advantage.

Welcome to the board, kdonn and I hope your future queries are all as interesting and thoughtful as this one.

Oh, and RealityChuck I think you are seriously missing the point here. I think you would agree that (indeed it seems to be the thrust of your post that) a team may well score more or less in a given game than a past average would predict, right?

The thrust of kdonn's OP is precisely that in soccer, because scoring rates are so low, there is a high chance that a team will win (or lose) in a given game despite what long term past averages would predict. So you are actually in agreement with him.

And further, RealityChuck, your understanding of statistics, and your charming belief that they do nothing to predict the future but are relevant only to the past surely warms the hearts of all casino owners everywhere.

pulykamell
06-19-2002, 04:59 AM
Crap, my last post got lost. I'll try to summarize my arguments:

I understand your points, but I'm not sure they're terribly valid. Soccer, like most sports, has statistical variance. Sometimes favorites lose. Compared to a game like baseball, though, I would argue that soccer has fewer "statistical anamolies."

If you pick a baseball game at random, the result from ONE game is rarely a good indicator of who the better team is. Bad teams win a lot of games in baseball. I'd say the worst team in baseball has a better chance of beating the best team on any given day than the same situation in soccer. (Save for the amazing Senegal win.)

If baseball had the same format as the World Cup, then I can easily envisage the Cubs taking home the title. Or the Red Sox. Or anyone. If soccer had a best-of-5 or best-of-7 structure, then I'd doubt you'd see Senegal taking the series from France. (But you never know.)

As has been explained, there ARE powerhouses in international football. Brazil, France, Germany, Argentina, Spain, to name a few. A couple of them got knocked out (yes, it was surprising,) but you still have most of the usual suspects going through to the quarters. Brazil, Spain, England and perhaps Germany. (OK, England may not be traditionally a World Cup powerhouse, but they play at a fine level.)

It's not neat or statistically accurate, but you can get a ballpark (no pun intended) idea of statistical variance by looking at betting lines. There are clearer favorites in soccer than in baseball. You will generally make more money on an underdog winning in soccer than in baseball because it happens less often. Usually, there's more risk (hence higher reward) in betting Senegal over France than, say, the Brewers over the Red Sox. Hell, look at last year. Statistically the Mariners were the best team, with a significantly higher winning percentage than any other team in baseball. Nobody else was over .600. The Mariners were .716!!!
But no title to them.

Shalmanese
06-19-2002, 05:47 AM
Having a look at the betting merel tells you what the betting public thinks the chances of a team winning is. It is in no way an indication of the actual probability. The way bets work is that they are structured so that no matter who wins, the guy who takes the bet makes money.

pulykamell
06-19-2002, 06:18 AM
Yes, Shalmanese, I know. That's why I qualified my statement saying it's not a statistically accurate way to look at the question, but, in my opinion, a decent general assumption. I would reckon that it IS indeed at good general indicator of actual probablity. Sports that are known for having unpredictable results in the long run tend to have closer betting lines than sports where favorites tend to win significantly more often than they lose.

pulykamell
06-19-2002, 06:23 AM

Vegas oddsmakers are probably one of the better ways to figure out who is statistically the better team.

muttrox
06-19-2002, 08:15 AM
I don't know where you get 5 scoring drives from. As much as you can break down a "continuous" sport like soccer, I would say there are a few dozen drives a game.

There is some soundness to your basic premise, I've thought of it myself. If the bad team gets lucky scores in the first 10 minutes, it is compartively easy for them to pack the defense and play for a 1-0 win.

Note that all your criticisms apply almost as well, maybe even better, to american football, where there are a distinct, small, number of scoring chances. In football, the better thea usually wins, but there's plenty of upsets. Were my beloved Patriots really the best team, or did we just get lucky? No one can say for sure, that's part of the fun of sports.

muttrox
06-19-2002, 08:30 AM
Originally posted by kdonn
Suppose we had a special coin that would only show heads in 10% of tosses and another that would show heads in 20% of tosses. Believe me, I'm no stat major and I labored over this quite a bit, but my results show that if you flipped each coin 5 times, the 20% coin would have only about a 49% chance of yielding a higher number of heads than the 10% coin. This is to say that the 20% coin would be more likely to lose or tie than to win the game of five tosses.

Here's the math my friend the high power statistical consultant came up with (took him all of 2 minutes, the jerk). :

I got a probability of 0.83067 (83%) -- subject to typos in Excel, but it seems
right.

Basically, I did it by brute force. That is, I figured out the probability distribution of getting 0 through 5 heads for coin A, and then the same for B:

# Heads Coin A Coin B
5 0.00001 0.00032
4 0.00045 0.00640
3 0.00810 0.05120
2 0.07290 0.20480
1 0.32805 0.40960
0 0.59049 0.32768

Then, since the results for Coin A and Coin B are independent events, you
can multiply probabilities to find out the probability of various
combinations.

e.g. P(5 heads for B, 5 heads for A) = 0.00001*0.00032.

Then add up all of the probabilities for the events that B has equal or more heads than A!

muttrox
06-19-2002, 08:34 AM
So even in your example with only 5 scoring chances, the better team wins 83% of the time.

nicky
06-19-2002, 11:18 AM
A soccer team's attacks are not independent events. A team will play differently leading 2-0 than losing 2-0.

And a scoring chance isnt due to the attackers' skills, but the complex interplay between the attackers' skills and the defenders' skills.

Senegal's defeat of France was not as much of a upset as you might think. Senegal were runners-up in the African Championship, and almost all the Senegalese squad play in the French soccer league in the top division.

andrew dupont
06-19-2002, 11:47 AM
There's only one objective way to judge the better soccer team, and that's goal scoring. If the US beats Germany 1-0, then they were the better team that day, no matter what anyone says. It doesn't mean that Germany won't slaughter them the next time the two teams play, but that for those ninety minutes they were outplayed.

Soccer does not reward scoring opportunities. If it did, Mexico would've killed us, and we'd have beaten Poland.

Michael Davies, special columnist for ESPN, is keeping a diary at the tournament and remarks at how little respect US soccer gets from the traditional powers (South America and Europe). After the Mexico win he was told by a British journalist that the US were lucky to have beaten Portugal...Portugal "deserved to win."

Deserving to win seems to be a concept that only applies at the World Cup. It's certainly the only place I ever hear it. Argentina deserved to win against England, Portugal deserved to win against the United States, Italy deserved to beat Croatia. The rules of this game are very simple: The team that scores the most goals wins. Beautiful play is beautiful to watch, and we can all appreciate it, but goals win games, conceding them loses games. It's as simple as that.

xicanorex
06-19-2002, 11:49 AM
Originally posted by BobT

Also in the top leagues in the world, only a few teams win the league championships. Very rarely does a team come from the bottom half of the standings in one season to win the next year.

EXACTLY!

If scoring was a matter of luck such as a toin coss, then the top world leagues would not see the results that we have. Rather, what we see are leagues where a couple of teams dominate for example Argentina= River Plate or Boca Juniors, Spain= Real Madrid or Barcelona, England= Manchester or Liverpool, etc., etc. This does not arise out of cheer luck, but due to teams being able to acquire players with high degree playing skill for large amounts of
[/B]\$\$\$ whereas "poorer" teams have to do with less skilled players and hope to G-d they won't go to a lower division.

[B]Another reason why you don't see huge margins in soccer games is that there is often little reason for a team that is ahead by a comfortable margin, say 3-0, to try to score more. It's safer to defend.

Sometimes teams may need to add to their goal difference in which case they will push ahead to score more.

True!

Let me add that weaker team may acquire a goal for the following three reasons:

1) It played better. Scored one goal and clogged their lower part with defense by using a 4-4-2 or even 5-4-1. It happens. Even the New York Yankees lose! ;)

2) Penalty. Spain nearly lost it due to a stupid move by Hierro agains Ireland with a penalty. Stronger teams can "give" a goal to a weaker team via this way.

3) Human error. It occurs in any sport. Example, Italian player against Korea. Italy leads 1-0. Italian player stops a ball in their own penalty area, is not able to stop it properly, inadvertantly plops the ball in front of the Korean player, who proceeds to kick it to the goal. Game goes 1-1. Of course, if the Korean player did not have the skills nor the expertise, he could have kicked the ball no where near the goal.

Let me reiterate, yes, there is always a degree of luck involved in any sport, but it is the great player with skills that win the games. Soccer is no different.

xicanorex

casdave
06-19-2002, 11:56 AM
I think that if you were to devise some sort of wargame that would reflect more accurately the chances of each team that you would have to apply a goddly number of factor, before finally applying the random factor genrator such as a dice.

You would need to take into account the individual 'quality of each player, then another on how well the interacted with each other and then include things such as tactical ability of the manager, leadership of the team captain, wether the ground is neutral or which team is at home or away.

The number of scoring attempts is not as relevant as might appear, you would need to asses the quality of each scoring chance, and the quality of the person making the attempt, thus one team with a superb midfield might generate plenty of chances but their strikers might not be good enough to make the goal, and vice-versa.

It is no accident that the best players command the highest wages, and so end up playing for the wealthiest clubs in the world, and you will not be surprised to note that these same clubs win just about every trophy there is, especially in regional competitions such as the UEFA champions league.

You could do an analysis of the wage bill for each team, it would reflect pretty nearly the the actual outcome.

muttrox
06-19-2002, 12:03 PM
It certainly is different.

World cup: a few pool games (pool is randomly seeded), and 4 more games to win it all. If you start off at least good enough to get out of pool, you only need 4 games.
(Analogy: New England Patriots. Obviously at least a competent team, had 3 arguably lucky games to win the super bowl.)

NBA Basketball: 82 reg season games determine playoff seeding. In any game, there are ~100 possession per team. In playoffs, each round is a multiple game format, so luck is lessened. You must survive 4 rounds of multiple games. Vastly more difficult to beat the good teams.

panamajack
06-19-2002, 12:23 PM
muttrox, your (or your friend's) analysis is correct, but the conclusion of your next post is flawed (that the second team wins 83% of the time). Just above that, you said Then add up all of the probabilities for the events that B has equal or more heads than A!

This is 83%, but it's the cases of a win or draw. The OP refers to wins alone, which is 49% (confirmed by the numbers you provided). Perhaps it was a bit slippery of the OP to rule out draws there, since one could just as easily say that B is more than twice as likely to win as A (49:17).

Whether this actually applies to soccer scoring may be a moot point, though in my opinion (and from the looks of this thread) it probably doesn't.

muttrox
06-19-2002, 12:31 PM
Originally posted by panamajack
This is 83%, but it's the cases of a win or draw. The OP refers to wins alone, which is 49% (confirmed by the numbers you provided). Perhaps it was a bit slippery of the OP to rule out draws there, since one could just as easily say that B is more than twice as likely to win as A (49:17).

Good catch -- it's my fault for having phrased the problem badly to my friend. I believe your 49:17 would be the correct figure then, or 74%.

I also agree the coin analogy has serious problems, but it was part of the OP, and seemed to drive the poster's thinking, so I felt obliged to speak to it.

This is definitely the thread of the day IMO.

BobT
06-19-2002, 03:09 PM
How about if we examine a sport that has the most scoring chances, i.e. basketball.

In an individual basketball game, a team may have anywhere from 80-100 possessions. Does this high number of scoring chances make it impossible for a less talented team to beat a more talented team? Not really. The best NBA teams will usually end up with a better winning percentage than the best MLB teams, but the poor teams still have a decent shot at winning a game.

This year's Lakers team lost to several last place teams. They even lost to the Bulls TWICE, including the matchup in Los Angeles.

Even the most talented basketball team may just have a day when it can't shoot well, just as the most talented soccer team may have trouble getting the ball in the net. Also, the best basketball team may have a hard time playing on a poor team's home court (and in the World Cup ask Portugal and Italy about playing Korea in Korea). And, basketball is also subject to highly subjective officiating that can greatly affect the outcome of the game (ask Italy about playing Croatia or Korea).

muttrox
06-19-2002, 03:12 PM
However, the best basketball team (or at least one of the top few) almost always wins the championship.

BobT
06-19-2002, 03:14 PM
Actually, I was going to add that point.

I meant to draw a parallel between basketball and soccer's penchant for one-shot upsets, yet overall dominance by a few teams.

muttrox
06-19-2002, 03:18 PM
But note the difference in what it takes to win. In Soccer, you can get a lucky pool seed. Or you can have one lucky game and make it out of pool play. Then 4 games... certainly a lot of luck is required, but it's certainly conceivable for an underdog to make it pretty far. Like the USA

In basketball, the regular season does help your seeding. And each round of the playoffs is multiple games, it's much harder to be that lucky for so long.

So I hypothesize (you can argue the evidence forever), that there will be many less upsets near the end of basketball playoffs than near the end of The World Cup.. that is, who's left standing.

BobT
06-19-2002, 03:25 PM
Yes, when it comes to the NBA playoffs or the World Cup, it is a bit easier for an underdog team to win it all.

However, there still hasn't been a real underdog team that has won a World Cup, with the possible exception of Uruguay in 1950.

What we're debating now is whether or not a single elimination tournament is the best way to determine a champion, not whether or not the ultimate outcome of a soccer match is more the result of chance or skill.

kdonn
06-19-2002, 05:05 PM
I'd like to thank everyone for their input (well, almost everyone...). I've learned a bit about soccer, but mostly I've changed my understanding of how an answer must be framed. It seems like if we develop a model and then try to show that the model yields a lot of error or noise, the model will always be assailable as inaccurate.

Perhaps the only way to unequivocally state something about soccer scoring is to review the history and analyze the distribution of actual scores for particular teams over time and then to compare this to a corresponding analysis of another sport. Then we could say something certain like "soccer scores are more or less noisy than baseball scores". But even so, a critic could claim that because soccer has more injuries or whatever, that this still is not a valid comparison.

One friend of mine put it this way, "I don't think there's any real argument against the central issue: that low scoringness constitutes coarser granularity of sampling, which should be less desirable than higher scoringness if you expect scoringness to somehow estimate some goodness metric for soccer playing." My thesis in a nutshell - soccer scoring is not a reliable metric for goodness in soccer playing.

We discussed what one of the earlier posters had said about my estimate of number of "scoring drives" being too low. I asserted that however you define "scoring drive" doesn't really matter and I left it open. Regardless of what granularity you use to define "scoring drive" you'll then have to hit the real-world stats to correlate a percentage chance to score during that interval. The smaller the granularity on "scoring drive", the correspondingly smaller the probability of scoring must go.

I pointed out to him that even in the model the respondent suggested (i.e. 100 "scoring drives" with Canada having a .25% chance to score and Brazil having a 2% chance to score) we still have a team that is *eight times* better than another team barely winning by only one point at the buzzer! If anything, this supports my thesis rather than refutes it.

My friend did a little MATLAB program to simulate this more quasi-continuous model. Results:

Brazil = 2%, Canada = .25% ==> P(Brazil wins) = 80% after 100 intervals
Brazil = 2%, Canada = 1% ==> P(Brazil wins) = 60% after 100 intervals

I think my original assertion that a team has to be enormously better than another team to have a reliable chance at winning stands. I don't dispute that we have some "superpower" teams. In order to have teams that win reliably, they would *have* to be superpowers, but because of the randomness in the scoring, a group of teams that really have a wide disparity in actual ability to put the ball in the goal will still manage to form a league in which each has a shot at winning. That's really all I'm saying. If dominant teams emerge, it's not because they're somewhat better than the others, it's because they're greatly better than the others.

Well, in all honesty, I was hoping the Big Man would step in and give us the final, compelling answer. It seems all we can do is teem and hope...

Manduck
06-19-2002, 06:39 PM
Originally posted by pulykamell
Compared to a game like baseball, though, I would argue that soccer has fewer "statistical anamolies."

I think that baseball is something of a special case, because so much depends on the starting pitcher. A relatively poor team might have one really good pitcher, and stand a good chance of winning in the one game out of 4 or 5 where he is pitching. That would lead to higher variance in baseball outcomes.

JaxBeachBoy
06-19-2002, 11:00 PM
This entire thread is based on the false assumption that score is used to determine which team or individual is better.

Although in most cases the assumption is true, there are games in every sport where one team completely outplays another, yet loses.

Princhester
06-20-2002, 02:20 AM
Originally posted by kdonn
If dominant teams emerge, it's not because they're somewhat better than the others, it's because they're greatly better than the others.

Or because while a single game is not a good metric, a whole season is. The granularity of a single game then becomes less relevant, no?

muttrox
06-20-2002, 08:35 AM
Originally posted by kdonn
One friend of mine put it this way, "I don't think there's any real argument against the central issue: that low scoringness constitutes coarser granularity of sampling, which should be less desirable than higher scoringness if you expect scoringness to somehow estimate some goodness metric for soccer playing." My thesis in a nutshell - soccer scoring is not a reliable metric for goodness in soccer playing.

I think your friend has stated the issue very well.

But note that while you can compare various sports to each other, and say which should be better than another at determining who is best (as I've been doing with soccer, american football, and basketball), this doesn't tell you whether or not any of them are reliable metrics at all. There is some threshold of reliability. Maybe all sports easily meet that threshold, maybe none do. Maybe some do, and some don't. I don't see anyway to know this unless you get a real precise mathematical model of how the games works, which is next to impossible.

So all you can say is: Soccer is not as good at determinng the better team as sport [x]. You can't make the added jump that soccer doesn't meet some arbitrary poorly defined threshold of it's reliable or it isn't.

erislover
06-20-2002, 09:27 AM
Originally posted by JaxBeachBoy
[B]This entire thread is based on the false assumption that score is used to determine which team or individual is better.Score is used to determine who wins. In theory that should line up with who is better.
Although in most cases the assumption is true, there are games in every sport where one team completely outplays another, yet loses.That doesn't seem very complete to me, but whatever. I don't think using scoring as a test of "betterness" is crazy in any way, shape, or form.

Almost all player stats in all sports are based off of their ability to get their team a point, either through assist measures or direct scoring.

xicanorex
06-20-2002, 12:59 PM
Originally posted by kdonn
I'd like to thank everyone for their input (well, almost everyone...). I've learned a bit about soccer, but mostly I've changed my understanding of how an answer must be framed. It seems like if we develop a model and then try to show that the model yields a lot of error or noise, the model will always be assailable as inaccurate.

My thesis in a nutshell - soccer scoring is not a reliable metric for goodness in soccer playing.

Well, is not a 100% perfect reliable measurement system since you model of "flipping coins" is a very linear and does not lend itself to a more complex set of real life events.

And that is why I love soccer. It may seem simple, but it has it's complexity of team play.

....
...but because of the randomness in the scoring, a group of teams that really have a wide disparity in actual ability to put the ball in the goal will still manage to form a league in which each has a shot at winning. That's really all I'm saying.

Well, in ANY sport, at the beginning of the season, ALL have chance of winning. Yet, in real soccer examples, based on a single-table, such as English Premier League, it is only those with better teams that remain on the top flight whereas those with lesser ability teams end up on the bottom table.

If dominant teams emerge, it's not because they're somewhat better than the others, it's because they're greatly better than the others.

Sorry, semantics, but it is because they are just better not greatly better.

XicanoreX

JaxBeachBoy
06-20-2002, 02:20 PM
I agree with your points Eris, as score generally will show the better team. However, there are instances where the team or individual who performs best do not win.

Score is used to determine a winner, not to determine who played the game better.

For lack of any better way to do this, I will give you an example from American football.

Team A drives into Team B's territory, and scores a field goal. They later do this again. Team A leads 6-0. Team A, late in the game, drives again deep into B's territory. Team A throws an interception, returned by Team B for a touchdown. Team B now leads 7-6. Team A again drives into team B's territory with time running out, only to miss the game winning FG.

Team A outgains Team B in total yardage 450-125. Team A has one turnover to Team B's 3. Team B was completely outplayed in every aspect of the game, yet emerges victorious 7-6.

I fabricated the above scenario, but anyone who watches or participates in team sports can vouch that these situations occurr. There is nothing more frustrating than knowing you completely outperformed your opponent, yet when the final bell/buzzer sounds, the score is not in your favor.

I think this is one of the great allures of team sport. Victory seems certain for the vastly superior team, until one play changes the final outcome of the contest.

Basically--the best team does not always win.

erislover
06-20-2002, 02:49 PM
But my question is why would anyone ever feel the need to distinguish the better players from the winners. That seems counter-intuitive and insulting, IMO.

Score should reflect the better player (in principle, I think "winner" should be the better platyer, and winner is based off score). A "game" isn't an event, it is a series of events. If it is unlikely for even good teams against bad teams to score more than a goal or two, then there is a problem there IMO.

Of course there couldn't be a 100% guaranteed system... even in games without any chance at all like chess players can still have bad days. But then it is clear in such a case that they really were the worse team.

I am suspicious of any behavior where competency doesn't guarantee championship (however those terms are applied for the behavior in question).

djbdjb
06-20-2002, 08:35 PM
I am an American. I don't like soccer as much as some other sports played in the U.S., and when I mention the reasons why this is so to non-American soccer fans, they usually respond with a statement to the effect that "you just don't understand the game".

I agree with the original poster's point, and think that soccer could be improved by decreasing the difficulty of scoring. The goal area is currently 8 yds. by 8 feet (7.32 m x 2.44 m). I would start increasing this. How about 2.9 m high ( 9ft 6 in: most athletic men would be able to touch the cross bar) and 9 m wide.
We keep twiddling with this till the occurance of a 0-0 tie after 90 min of play is 1%.

If this sounds blasphemous to you, what is so sacred about 7.32m by 2.44? Why not play with a goal 71cm x 71cm (1 cm more than the diameter of the ball) Would complaining about the low scores in this version of soccer be just an "American desire for constant action" or a realization that there is not an unlimited amount of time to see who has more skill in kicking a ball at a target?

(Continuing on with the If-I-Ran-FIFA tirade: Increase net size, move pentaly shot location back (22 m?) to compensate for larger net, add more referees to be closer to fouls, add instant replay, move the area where offsides can not occur from the midfield line, to another line that is closer to the opponent's goal)

Maybe with these modifications Christian Vieri's wide-open shot in the Korea-Italy game would have gone in and the world would be spared a lot of Italian whining.

heresiarch
06-20-2002, 08:45 PM
This is an interesting question.

Here's another point in favor of the OP: Look at the numbers we've used in our simplified models. We single out "chance to score on a scoring drive" as the main statistic and then compare numbers like 10% vs 20%. Or 1% vs 2%. It seems unlikely that teams at this level of competition would have skill levels that vary so much.

I'd expect the teams' "chance to score" to be closer - maybe we should compare 18% vs 20%. That would create more opportunity for the noise to drown out the signal.

And one point against the OP: As others have already said, it's an oversimplification to single out that one factor in a game. The better team will initiate more scoring drives, get further with each drive, and maintain control of the ball longer than the weaker team.

Here's the bottom line, in my own humble opinion. The low number of scoring drives is a bigger problem than the low scores. Each goal results from a combination of skill and chance. Fewer scoring drives makes it more likely that chance will decide the game.

KillerFig
06-20-2002, 10:13 PM
I'm neither a soccer fan nor a statistician, so this may seem quite ignorant, but it seems like an important point is being missed: that the number of scoring drives is not predetermined, but rather determined by the abilities of the players.

Scoring goals and defending against goals are important aspects of gameplay, but attempting to maximize one's own opportunities to score while minimizing the opportunities of the opponent is significant as well.

Take the coin analogy and extend it--imagine that the number of times each coin is tossed is determined by rolling a die; and imagine that one of the coins is associated with a die that comes up as six 20% of the time, while the other coin's die only comes up as a six 10% of the time.

I'm sure the probability stuff gets more tricky now (and I realize that for this to work I'd have to define the probabilities for each other number on the dice as well), but it seems like this would be a more useful analogy than the simple coin-tossing one.

Let me know if I'm wrong (or, since I'm sure I'm wrong about something here, let me know how wrong I am about what).

-KillerFig

BobT
06-20-2002, 11:10 PM
Soccer, and to a certain extent hockey, are sports where the most scoring opportunities don't frequently correspond with the most goals scored.

Many teams, such as the US team, don't try to push forward often for scoring opportunities, but rather wait to make counterattacks. This usually is a result of a team thinking that it has a good defense, but only an adequate offense. You try to frustrate the team that attacks more and hope that it sends too many players forward and then gets caught outnumbered on a counterattack.

So, one could make the case that the US team was not as skilled as the Mexican team, but it was more disciplined and made better use of its infrequent scoring opportunities.

In hockey, this happens although in a different way. A team like Carolina would hope to get an early score and then play a style that would make it nearly impossible for the other team to catch up. Unless you were a team that was much more skilled, such as Detroit.

muttrox
06-21-2002, 07:23 AM
As I said previously, and the last 4 or 5 posts have illustrated, coming up with an accurate mathematical model of the individual soccer game is near impossible.