Trying to predict football results is a risky business, a cursory look at most of the predictions made before the last World Cup should give anyone enough evidence that it’s not worth the trouble – and the public humiliation that invariably follows – but we’ll give it a shot anyway!

To do so, we’ll talk about the good FIFA rating which is used for women’s football, justify why it might be useful and then predict the group round of the World Cup.

## The TWO FIFA World Rankings

You’ve probably heard about the FIFA World Ranking for men’s national teams, not always in the best possible light. We could argue for hours about the validity of ranking Belgium at 2nd place just above Argentina, or Romania and Switzerland above Italy. Regardless of our opinion, its main quality lies in its simplicity, which is probably one of the reasons it is still in use.

Here is a quick run-down of how it works. For each team and each match it plays, we compute an index:

$$P = outcome\times match\ importance \times opposite\ team\ strength$$

The outcome is 3, 1 or 0 for a win, draw or loss respectively. The importance of the match is a factor between 1 and 4 depending on the nature of the competition. The strength of the opposite team is a combination of the ranking difference between the two teams and a correction factor representing each confederation’s strength. To get the final ranking we take the average of these match indices for each of the last 4 years and sum them up, weighing past years less and less. You can find the precise coefficients used in these computations here.

As mentioned, the good aspect is that it is easy to link a team’s ranking to its recent performances. However, it doesn’t come with a method to predict future results. In fact, it is common knowledge that it might not be the best predictor of future outcomes, which is a question we’ll try to investigate another time.

In 2003, FIFA started releasing a similar index for women’s football. Similar in look at least, its actual computation being quite different. In essence it is a variation on a type of ratings known as Elo ratings. The system was originally developed by Hungarian-born physics professor Arpad Elo in order to create a better rating for his favorite activity: chess. Since then it has been used with some variations in countless settings from American college football to backgamon and competitive League of Legends games.

We won’t go into the details of its computation for now but one of the key features of this rating system is that it is self-correcting. Each match leads to a change in the ratings of both teams involved according to the result. The magnitude of the change depends on the difference between the teams initial ratings. This means that if a high-rated team loses against a low-rated team, its index will drop significantly while the other team’s index will make a large jump. This, in turn, implies that if for some reason we had underestimated a team’s strength (or if it improved significantly), this should be reflected relatively quickly after a couple of games. On the other hand it also relies on previous knowledge, only being updated whenever a team plays, providing more information about its current strength 0. If you want to know more about the women’s ranking method, take a look here.

Here is the ranking for the teams participating in the Women’s World Cup.

This seems reasonable, the relative order of teams corresponds to most people’s assessments, at least near the top. If you’re wondering which team from the top 10 did not qualify for the World Cup… let’s just say it made this man really sad.

You may notice that Canada appears twice in this ranking. The lower one represents its actual rating, while the one above is its theoretical rating considering home advantage. It is a well-documented phenomenon in football (and in competitive sport in general) that playing at home provides a significant advantage. In order to take this into account, we add a 100 points to a team playing at home, and use this updated rating when predicting outcomes.

How do we use this rating to make predictions then? The difference in ranking between teams is not enough to say with certainty that, for example, France ranks higher than England hence it will win whenever they face each other. If this were the case, we could just give Germany the title and call it a day. Instead, we need to think probabilistically.

Luckily, the FIFA Women’s World Ranking (and similiarly all Elo-type ratings) comes with its own method for computing such odds. You can find the formula here for example (the “expected result”). The key point is that it depends uniquely on the difference between the two teams’ ratings (and not rankings!), adjusted in case one of the teams plays at home. The larger the difference the more likely the stronger team is to win. As an example, assuming matches can’t end in a draw (as in the final stage of the World Cup for example), France should prevail over England about 65% of the time, and this is also true of any two teams whose ratings are 100 points apart. If France plays Costa Rica on the other hand, it should win nearly 95% of the time.

You can jump to the probabilities fo all possible match-ups in the Women’s World Cup and the predictions for the group stage now if you want, but we first want to justify why this rating, and the associated match probabilities, are actually meaningful.

## Why it might work

The predictive power of these types of ratings is relatively well-documented, though the specific information for women’s football might be hard to find. Hence we tried to come up with our own basic validation.

We compiled all the matches we found on the FIFA website since January 2012 and used the ratings each team was assigned at the time. We obtained about 400 matches for which both teams had a usable index. We then compared the odds for each match predicted by the FIFA rating with the actual outcomes. Here is what we obtain:

We counted a draw as half a win for each team. Each point corresponds to the average for 15 matches. Though the specific qualities of what a true “good fit” might be is sometimes in the eye of the beholder, the relationship is arguably quite strong.

If we look more closely, we can notice a trend: points are clustered more closely around the line of best fit at the extreme ends, wich corresponds to teams having a large ratings difference (above 500 points). These games are easier to predict with this model. However, if we get closer to the middle the variability increases, meaning that it has more trouble predicting games for teams with ratings that are closer to each other (within 150 points).

Another issue is the dirty little secret of Elo ratings: they were not meant to predict draws ! Here is a plot of the difference in ratings versus actual percentage of draws. Each point now represents 20 games.

There’s a trend here, but there’s also quite a bit of noise. Since a point represents 20 games and draws occur at most 30% of the time, even a variation of 1 draw has a visible effect. We used the curve added on top to estimate the probability of each match ending in a draw. We played around with several formulas for this curve which we think fits the data best. Though we do not have a perfect rationale for our choice, here are the features we were looking for:

• It should peak at 25%: two teams of equal strength should draw about a quarter of the time and that’s the maximum likelihood! This might go against common sense but draws are never the most likely outcome.
• It should be perfectly symmetric for obvious reasons.
• It must tapper off quickly at the extremes. When the difference of indices is above 300, the probability of a draw falls below 5%, and it nears 0% above 600. Admitedly, we may have been overdoing it, but we decided to use the actual data as our guide.

## Predicting the Women’s World Cup group stage

Now that we know that the FIFA index historically does a fine job at predicting outcomes we can move on to making our own bets.

As a first step, we can use the recipes described above to predict the odds of a win, a draw or loss for any possible match-ups between teams participating to the Women’s World Cup. You can also look up combinations which will not occur during the group stage, if for example you’re interested in knowing the odds of Costa Rica winning against Thailand in that fantastic final you’ve been dreaming about.

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We then combined these odds to obtain a probability for each possible final ranking in each group. We had to make some simplifying assumptions in case of ties, since we didn’t try to predict the number of goals scored in each match. Here are our predictions.

One thing we were not able to predict (without making this writer’s computer melt), are the odds of finishing as one of the four best 3rd place teams, which are also qualified to the next round. To get a rough estimate you can suppose that a team at 3rd place should advance to the next round about 2/3 of the time, but this is of course an oversimplification.

### Group A

Canada Netherlands China PR New Zealand

This is one of the most unpredictible groups. Behind Canada which, partly thanks to its home advantage, has more than 80% chance of making it to the next round, China, The Netherlands and New Zealand all have a fair chance of qualifying too. How China and New Zealand each fare against the Netherlands is going to be decisive here.

### Group B

Germany Norway Thailand Côte d'Ivoire

Here we have the opposite situation. Germany is essentially certain to qualify, and most likely at first place. Behind, Norway’s chances are also above 80% to move on to the next round. Interestingly our model gives Thailand a high chance of finishing at 3rd place. If they manage to polish their goal difference against Côte d’Ivoire and give a good show against the top dogs, they may have a chance of moving on too.

### Group C

The situation is similar to Group B. Japan and Switzerland should qualify easily in that order, while Ecuador and Cameroon are in a tough spot. The fact that they are of roughly equal strength may actually make things worse for them, preventing a blow-out when they meet which could have helped their cause.

### Group D

USA Sweden Australia Nigeria

Each World Cup has its “Group of Death” and here it is. Though the U.S.A. team is without a doubt one of the top contenders for making it to the final (together with Germany), they will have a much tougher go during the group stage with only a 54% chance of coming out on top 2. In total they have more than 80% chance of making it to the next round but their position will have a large effect on who they meet next. Behind Australia and Sweden each have a good chance of qualifying, with Sweden having the edge. All the matches between these three teams are going to be important.

### Group E

Brazil Spain Korea Republic Costa Rica

The situation is quite similar to Group D. Behind Brazil which is likely to qualify but not sure to finish at 1st place, Both Spain and Korea have a good chance (above 60%) of making it too. In fact it’s almost a perfect toss-up between the two. Again, many interesting matches to pay attention to here.

### Group F

France England Mexico Colombia

This group shares one thing in common with Group B: There’s a gap between England and France’s chances and Mexico and Colombia’s. However knowing which one of the two will come out on top is a different story. Their face-off should be one of the highlights of this stage, the outcome probably deciding who will come out on top of the group.

## Want to bet ?

You think giving probabilities is a cop-out? That real men and women tell you what WILL happen, and bet their lives on it? Well here we go then. The teams qualified at the end of the group stage WILL be:

• A
2. Netherlands
3. China
• B
1. Germany
2. Norway
• C
1. Japan
2. Switzerland
• D
1. USA
2. Sweden
3. Australia
• E
1. Brazil
2. Korea
3. Spain
• F
1. France
2. England
3. Mexico

We are so sure of our prediction that we’ll be betting 1000 1 buck/quid/euro on it.

Come back at the end of the group stage, when we’ll evaluate how awfully wrong we were and yet make more predictions for the final stage. Meanwhile, if you want to tell us how wrong we already are please comment below!

Photo by IQRemix shared under CC BY-SA 2.0 license.

1. In fact this is one of the issues of this type of ratings: by carefully choosing who to play against and limiting the number of matches, it is possible to keep one’s ranking artificially high. However this is usually not an issue in football.

2. If you find these probabilities to be on the low side, an alternative is to consider that the U.S. will have almost as much of a home advantage as Canada (except if they ever meet of course). If we add 100 points to their rating, their probability of finishing in first place jumps to a healthier 69%, and they would have more than 90% chance of qualifying to the next round.