Before you ask, the USA will get +2 points for the 1:1 draw against Japan. That's because Japan played at home (+100 ranking points) and were expected to get a better result.
Oh, I'm not disagreeing with you on that point - I think if you're predicted to win 4-0 and only get 2-1 or so, that's definitely something to be "penalized" for. I was just pointing out that a 'regular' football Elo system treats any win as a gain in points as any 'win' is a result of '1' while your expected result is always between 0 and 1. btw I think there isn't a time-weighting in the FIFA women's ranking, at least not explicitly. They consider every match all the way back to the first recognized international match, it's just that an Elo-based system naturally emphasizes recent results, to a degree.
Yes, good point. Elo-based systems do indeed naturally emphasise recent results. In the end, that is also a good thing. We want to know how good the teams are based on recent form, not on form 4 or 5 years ago (but we still want older form to have a little say in the final rankings, so that the rankings aren't completely skewed by random form spurts). One problem with FIFA's version of the ELO system involves teams who have not played recently enough or have not played the minimum of 5 matches against ranked teams. They are all tagged on to the bottom of the rankings, but are still given rating points. In many cases, these points are grossly inflated (look at UAE for example, which technically has more points than Nigeria), which means that when they enter the rankings, they will be artificially high, and all teams who play them will get too many points for beating them (and will therefore also be artificially high in the rankings - fellow West Asian teams such as Jordan and Iran are already too high). I've said this somewhere before (many times probably), but one of the key elements is deciding on a start rating for new teams. If this is chosen (or calculated) wrongly, the whole ranking will be affected negatively.
I'm puzzled by what you mean by "to a degree" unless you mean 100% to set of recent results. Very old matches do NOT mathematically meaningfully enter into the rankings. The FIFA/ Elo women's formula only really deals with your current rank and your current result. There is a time weighing ( actually a number of games played weighing ) in the recursive nature of the computational method. The key is understanding what each element does. If a team is brand new( new teams start with 1000 points) and another team has played every game possible in history since results were counted (1972?) and has 1000 rating, they will get the identical rating change for each match they play. And it doesn't matter if you played 30 matches to get to 2000 points or 500 matches to get there. The result for your next match will change your ranking by the same amount in either case. Those extra 470 games don't do anything for you. But the maths makes the old results disappear in a different way. The Fifa/Elo formula would be analogous to what in signal processing is called and IIR filter. ( google Infinite Impulse Response) . A given IIR filter, instead of computing all results forever, which would bog down a computational system, weighs the last result propotionate to K times the previous average. Both the complete average over a fixed time and the IIR filtered average trend to the same number, and the size of K determines how fast the rate of change is. old results in an IIR filter become diluted in proportion to what value you pick for K. If you look at the FIFA formula fact sheet on their website, you will see an arbitrary K value in it ( in the FIFA formula, they call it the Basis Factor and K = 15. You see it where it is multiplied times the game importance). That K value greatly increases the weight of the most recent result, and by extension, decreases the weight the old results. Over time with each iteration, the decrease in old results is cumulative until they trend to zero. There is also a discussion in the fact sheet about how K was changed after 2004 to make the the ranking process reflect what FIFA wanted. What that K number does is regulate the rate of change of the rankings and the rate at which old results die away in importance.You have to tune an IIR filter so it responds quickly enough for a result to be meaningful, but not so quickly that single or few results skew the rankings unduly. That is a decision on usefulness. FIFA made such a change in 2004. The FIFA formula appears to be tuned to about 30 games, after which the number of games played doesn't matter and old results become irrelevant. The actual amount varies on the results of actual matches, but 30 games is a good working number. You can argue about whether the rankings shift quickly or slowly enough, but a discussion about ancient results is just not part of the issue mathematically. A Germany result much past a couple years ago has very little meaning. The note on page 3 of the FIFA fact sheet reads as follows: When you do many iterations and more weight is attached to recent results, the importance of old results becomes less each time a computation is done. Quite quickly, their weight will be less than one rating point and disappear. A second filter type is to declare that only, say, the last X results count and all earlier results don't matter. ( i think this is what you are advocating) This is called a Finite Impulse Response filter. This has it's own problems. If the number of matches varies, that may or may not yield meaningful data. Actually, any system that ranks teams based on a differing number of games will have problems and can potentially be "gamed" This is particularly true at either end of the rankings. It's just the nature of a normal distribution. Whoever makes up a system usually tries to skew the system to wherever they need to extract information, for example, who gets to go to the world cup and how you seed them. In such a system, it is only the top 50 or so teams that matter.
@_@ All I meant by the part you bolded was that three or four great results in a row still wouldn't have a massive effect on a team's ranking (unless they were a young team) - as some people thought would've/should've happen to Japan when they won the WWC (beating Germany on home soil, decisively beating Sweden, and drawing the US. Granted, most of said complainers weren't considering Japan's group stage results, but w/e; even if Japan had a better group stage, they likely still wouldn't have passed Brazil just from the WWC). Basically what I meant was that recent results were "more important" based on the recursive nature of the Elo system, but to move significantly you need consistent results over a longer period. But yeah, I know all the math behind Elo in general and FIFA's system. (Just for kicks, I did a straight Elo for WPS in 2009, and then again in 2011. And I've browsed FIFA's docs. And I'm a math major.)
No timescale factors. The actual result is not (1/0.5/0) but it's determined from a table (0.99 for a 6 - 0 win for instance).
We can discuss the ins and outs of various parts of the system all day. The main point is they don't reflect reality for the majority of teams who appear in the rankings. That is surely an issue that has to be tackled. A ranking should be good at ranking the majority of the teams, and at least reasonable at ranking them all. I don't have a mathematics qualification of any kind, nor do I have computing knowledge of any import - but what I can do is study the end result and compare it with reality (in the form of actual results). FIFA's ranking fares poorly.
Well, of course there is no real immovable ranking. But there can be a ranking that has more correspondence to actual results (i.e., a ranking that allows one to predict a greater percentage of match results correctly). The essence of a ranking is that there will be results that go against what the ranking says - hence we have change, which is of course completely necessary. Any ranking will only ever be an estimate of a team's strength at one current point in time - but as we know, a team's strength is not the only factor influencing the result of a game. If a team plays below par, for example, its strength hasn't remarkably dropped - they've just had an off day - which happens. But any one team's strength doesn't tend to go up and down in huge waves - it does tend to gravitate around a certain level, or increase or decrease gradually over time - the ranking attempts to pinpoint the average level of the team (by using results - which, by and large, taken collectively, are the best representative of relative strengths of football teams). This is what I mean when I say "reality". At the moment, FIFA's ranking does not do too great a job in that respect.
Any ranking system can only give you an estimate of the strength of the teams at a certain point in time. Besides multitude of factors that affect how a team performs on a given day that have already been mentioned, there is also a fact that no system can predict: Which players a particular team put on a field that day. Further more, a statistical system can only predict the outcome of an event if that event is repeated many many times .... which soccer is not.
Which is exactly what a ranking system is supposed to do. More exactly, FIFA keeps a ranking system to track past performance for selection and seeding. They have chosen a system. The game is to be the best at FIFA's system. If you want to be at the top, you figure out what it takes to get there and do it. Otherwise you accept what you get. That would be a ranking system for players, not teams. Like it or not, which players you put on the field is totally irrelevant to rankings. And as I stated, FIFA's main purpose for the ranking is not predictive. The ranking system goes back about 6000 games. Adjustments have been made to the system based on that whole body of data. It has meaningful data on a team's current strength back about 30 games, which for most teams is 1-2 years. You are free to play more games if you think it will help your ranking.
And it's really not that hard to figure out. Win many matches, especially those in important competitions against good teams. That's it. The problem is, that people have a very selective memory. So the US fans will remember that one loss against Japan, but will neglect the 30 other matches of which they won 29 or so.
But, as most teams don't win such a high percentage of matches, it's harder to work out for them. The ranking only makes sense at the top (which is the only part a lot of people are interested in). It may be easy to figure out, but that doesn't mean it's good. Anybody could make a simple ranking (2 points for a win, 1 for a draw, 0 for a defeat) and then divide by the number of games played. This would yield a similar result. USA, Germany, Japan, etc. would be at the top. Middle-ranking teams who win and lose an equal number of games are the grey area (and also teams who lose a lot, but against vastly different opponents). I'll leave you with one example which is sufficient reason alone to mock the rankings. Papua New Guinea (who has just lost 15-0 on aggregate to New Zealand in Olympic qualification) is in 49th place, Equatorial Guinea, 2011 World Cup participants, former African champions, are in 66th place. What absolute nonsense!
Papua New Guinea played mostly with countries in their own association and won most matches, hence they won the points. Even when they lost to NZ badly, you can only deduct so many points from them, you can not give them 0 total points just because of that or somehow decide those 2 losses put them below EG! Equatorial Guinea hadn't done that well in Africa until recently and they still lost to many countries from other associations, hence they did not win as many points. They did move up from a year ago. What do you propose?
In short - a better ranking system. Equatorial Guinea are likely 4 or 5 goals better than Papua New Guinea. They are certainly not worse. Equatorial Guinea's 'many' losses to teams from other confederations have all (all 3 of them) come in the World Cup, and were all to Top 15 teams - and the losses weren't that bad (0-1 v Norway, 2-3 v Australia, 0-3 v Brazil). The last time Papua New Guinea played Australia, they lost 10-0 (in 2004), and before that 13-0. It's quite likely a similar result would happen if they were to play again. Papua New Guinea's wins have come against very weak opponents (Tonga, Solomon Islands, American Samoa, etc.), so they should not be valued so highly (incidentally, they're also ranked above Ghana, who are used to appearing in World Cups and have a long history of winning many matches and being the 2nd team in Africa). Equatorial Guinea's wins have come against much higher calibre opponents (Nigeria, South Africa, etc.) Again - the problem may be down to the start ratings. If you start Oceania and Africa teams at the same level, of course PNG will end up higher due to the fact they win more often, and due to the limited number of inter-confederational matches at that level. Especially in women's football, where inter-confederational matches are rare outside the World Cup and Olympics, and almost non-existent outside the Top 20 or so teams, this factor is very important.
And what is a better ranking system? You suggest the problem is with the start rating, what do you propose? You have to have a start rating to plug into the formula. It does not matter what number you use, if teams A and B start with the same points, Team A loses more, while team B wins more. It may win against bad opponents but it will keep gaining points and end up with higher ranking. What else can do you? I know with Chess, the start rating is 1500 and before you play 20 games, your rating is provisional. The thing that helps Chess rating is that players play a whole lot more games than soccer and after hundreds of games, the rating is pretty accurate. Also the rating is about you only. Soccer rating is for a team and over time, your roster changes.
Put up or shut up. Come up with a system we can critique. "a better ranking system" means nothing. Propose how you would do it. You do understand that nobody cares if a team is 47th or 66th - right? The truth is that the rankings are only really concerned about the top 20-30 teams in the world, because knowing who they are is what seeds the major tournaments. And the only way to get in that group is to beat those teams. Beating up on #128 will not get you there. So they are reasonably accurate in figuring out who THOSE teams are. That's all that matters. You sound like you have lost money betting on teams based on the rankings. THE RANKINGS ARE NOT SUPPOSED TO BE PREDICTIVE. Their purpose is to show what teams did, not what they will do. If they were good at the latter, there would be no point in playing the matches.
Well, up until this point, this was a friendly debate. But you appear to have gone on the rampage. Never mind. Seedings are not only concerned with the top teams. Seedings, in Europe, for example, are done all the way down (there are groups of seeds, which encompass the WHOLE spectrum of teams). "Nobody cares if a team is 47th or 66th." By "nobody", are you talking about yourself? "That's all that matters" Again, to you maybe. Don't go assuming that we all think like you. In fact, think yourself lucky that we don't. "Their purpose is to show what teams did, not what they will do." So what did Papua New Guinea do that was so miraculous to put them in the Top 50? Beat Tonga a few times? Don't make me laugh. To the question of the start rating - you give the team the start rating based on the result of their first match (not giving the same start rating to EVERY team). That way, a team who loses 20-0 to Jordan (à la Iraq) does not start in the same place as a team like Montenegro (who is clearly at a much higher level). It shouldn't have to take 20 or 30 matches to get them to the level that everybody with half a brain knows they are at. I have used this system, and it works. Perhaps not perfectly, but it works. I don't need to justify anything here, and I don't need to propose anything. What would help is if people would just see that the system is not that great and could be improved. Knee-jerk reactions like that to criticism are just extremely childish and help nobody. I'd advise you to compose your next response a little more carefully, and perhaps rephrase "put up or shut up" - it's downright offensive.
Now, Now, Don't do the "knickers all in a twist" act. It just an attempt to deflect from the fact that you have no alternative. Just come up with something that makes sense statistically. The FIFA ranking does as good a job as anything anyone has tried( and lots of people have tried) it gets the best teams in the world in the knockout rounds. I'm talking about the folks who have to decide how many teams each confederation gets, how they are selected and how they are seeded. I'm clearly not making the mistake that I think you think like me your comprehension is poor. You missed the part where nobody- not me, or not FIFA cares about PNG being 47. They need to get top 25 to get anywhere, and to do it they must beat good teams. Until they do, they are a footnote. You must not be referring to me, now. I don't think the start rating matters at all after a few matches. I think giving everyone the same start is better than having Sepp Blatter or one of his henchmen decide. So, your one concrete solution is to rank teams on the worst statistical sample possible? One game? Great, then they will fail to gain as many points in their second win, should that ever occur. It will only take one extra game for them to settle in where they belong. With their higher ranking, they would have earned zero points for their 20 point win. Just curious- what happens when two new teams play against each other? One gets a last place ranking and one gets the top spot? Sorry, if your feelings are hurt, your proposal is so ludicrous it just can't gain a whole lot of respect. " I don't like it" is just annoying if you have no better method - probably as annoying as me telling you to produce. I like a lot of the things you post, but you just won't convince many statisticians on your one game ranking proposal as the grand solution.
If Papua New Guinea continue to beat the likes of Tonga regularly, they will end up in the Top 25 - then will they matter to you? They've certainly managed to move up the rankings by doing just that (59th in 2003 to 49th today). So, my comprehension is fine, thank you. I'm also not interested in convincing statisticians of anything. I'm interesting in creating as accurate a ranking as possible, insofar as that is possible (all the way from 1-200, not just the top 20-30). Surely a commendable enterprise? Rankings should show the current strength of teams relative to each other. Unfortunately, this doesn't seem to be taken seriously by most people. Historical "what we did" lists are called league tables. When 2 new teams play each other - then they cannot be ranked until one of them plays a ranked team, then they can both be ranked. All rankings can be thought of as provisional until a certain number of games are played (from experience, 5-10 is adequate). Simple concept really. Not all of us only care about or think that the Top 25-30 teams are important. Everybody must start somewhere, and it's beneficial for teams to know where they stand and to judge their development over time. With the FIFA ranking, only the top 20 or 30 teams (who already know where they stand) can judge their development. The rest are left clueless (another example I will throw in is Tanzania - who are almost rock bottom despite many wins recently, and finals appearances at the African Championship and All-Africa Games). What does that do for their confidence when they find they are permanently unseeded despite winning matches? What makes this whole conversation even funnier is that FIFA agree that they need to be changed.
The problem is that probably more than 90% of the national teams don't play teams from other confederations. So obviously we can't rank all those OFC, AFC and CAF teams properly, because they're completely separated from each other. However the ranking inside each confederation should be fine.
That is a problem. But there are ways around it. If the top 2 or 3 teams from each confederation are ranked properly, then the teams below them in their confederations will naturally find their places in the ranking. If we know that Team (AX) is ranked 20 in the world, and Team (AY) from the same confederation consistently loses by 2 goals to Team X (but doesn't get the chances to play teams from other confederations), we can say that Team Y is probably somewhere around 40th. Let's then take another team from a different confederation (BX) - ranked 21st in the world (and therefore pretty much equal to team (AX) above). If another team (Team BY) consistently loses by an average of 4 goals to Team BX, we can then rank team BY relatively to Team AY (team BY would be ranked lower), even though the two teams are from different confederations and never play outside of their confederations.
In July 2003, Papua New Guinea ranked 59 with 1412 total points. In May 2012, Papua New Guinea ranks 49 with 1491 total points. That is a gain of 79 points in 9 years. In May 2012 Czech ranks the 25th with 1730 total points. So Papua New Guinea needs to gain 239 points. My Math tells me it will take ... a long time ... for Papua New Guinea to get to 25th place. Just saying.
This is actually a good input to help solve the problem. (Note I say help, there are other things you need to solve.)