There was much good cheer and happiness when FIFA revealed the first edition of the Women's World Rankings on WED 16 JUL 2003. This gives us a chance to compare women's sides objectively all across the world, and it offers a bit of insight in advance of the 2003 Women's World Cup.

But what do the rankings really mean? To determine just how much we can glean from the rankings, let's start by looking at the top thirty two of the first edition:

Notice that of the top sixteen, only four are missing out on USA 2003. By comparison, seven of the 32 top ranked nations in the men's table [as of MAY 2002] failed to qualify for the 2002 Men's World Cup.

Looking through the list also provides a good reality check. The easiest comparisons are within confederations. Looking only at UEFA nations, we have Norway, Germany, Sweden, Denmark, France, Italy, Russia, England, and so on. Seven of these eight nations finished in the top two of their UEFA qualifying groups, and Italy missed their chance on the last day.

Turning our attention to confederational comparisons, we see a number of UEFA teams here - twenty in fact. This should be no surprise, since UEFA have more nations participating in their women's tournaments [34 in the Women's World Cup qualifiers] than any other confederation. CAF and CONMEBOL have only one team each, and not coincidentally, these are the only teams from their respective continents to have reached the quarterfinals in any of the first three Women's World Cups.

THE FORMULA
The rankings are determined by assuming each team has some initial stash of points. Then, for each match, there is some "expected result" based upon the number of points the teams already have. Whichever team betters this expectation earns points [rounded to the next higher integer], and the other team loses points. A better result means more points. The precise formula is:

If you're ready, let's examine these various values.

T: POINT TOTAL
Teams are supposed to start with 1000 points or so. But if you look at the historical tables at [R], you'll see that such isn't the case. Nobody knows how the initial values came to be; this is a mystery best left for future generations.

P(d): PREDICTED RESULT COEFFICIENT
The difference in the two teams' rankings [disregarding H for the moment; we'll talk about that later] gives us a coefficient reflecting what we expect the result to be. If the ranking difference is d, we have:

This gives a result between 0 and 1. As you'd guess, P(0) = .5, and P(-d) = 1 - P(d). It flattens out at each end, so that you gain a lot by playing an opponent who's, say, 30 points below you as opposed to one 20 points below you, but you don't gain much by playing someone who's 230 below compared with 220 below. Note that P(800) = .99. Keep that in mind for later.

A: ACTUAL RESULT COEFFICIENT
The match result is converted into a coefficient according to the table on page 4 of [M]. In short: A is the same for both sides in the case of draws, and it rises slightly from .475 for a 1-1 draw to .53 for a 5-5 draw. For any other result, we have A + a = 1. That is, the losing team's coefficient is 1 minus the winning team's coefficient.

If you plug that into the formula for T above, you'll see that for these matches, the teams' point carries are negatives of one another. However many ranking points one team gets in a non-drawn match, the other team loses that many points.

Draws, though, are weird. For example, consider two teams with identical point totals. If they play to a goalless draw, they both will lose points. But if they draw at 2-2 or higher, they'll both gain points. [Subject to roundoff errors, of course.]

We talked about the expected coefficient for teams separated by 800 points. That .99 value corresponds to a 6-0 win. Hence, the expected result in a United States [2169] - Panama [1367] match would be 6-0 to the US, and Panama would actually earn points for a 4-0 loss.

H: HOME/AWAY COEFFICIENT
Teams get a 100 point hike in the calculation of P if they're playing at home. That means that if you host a team that's tied with you, you've got to beat them to get any points. If you visit someone who's already seven hundred points ahead of you, you can rest easy - you'll pick up some points even if you lose 8-2.

M: MATCH IMPORTANCE FACTOR
Sometimes players and/or coaches say that once you step on the pitch, it doesn't matter if it's the World Cup final or a silly little friendly - they want to win. Of course, if you've had to shell out for World Cup final tickets, you can definitively tell them otherwise.

The difference between A and P is multiplied by some factor depending upon what type of match it is. Friendlies are at minimum, but not if they're between the top five in the rankings:

Hence, M is the absolute maximum that a team can ever get for a match. That's only possible if they were expected to lose heavily but win heavily instead; for instance, winning 5-0 when you were supposed to lose 6-0 would score you 97% of the possible points. In an Olympic or World Cup match, that would be 39. In a more realistic case, winning 2-0 when you were supposed to lose 2-0 bags you 84%, or 34 points at the World Cup or Olympics.

Ready for some examples? First, take a look at [R]. That's where you can go for the updated rankings, plus listings of all women's international matches factored into the teams' rankings. Click a team, and you'll get their match list, with the results, points awarded, and new total for each match. You'll also see the type code, as given above, under Class..

EXAMPLES
On SAT 18 MAY 2002, Yugoslavia visited the Republic of Ireland in Longford. Rep Ireland, three points behind Yugoslavia on the final matchday, needed a win to have any hope of winning UEFA Group 6. But Vesna SMILKOVIC scored in the 76th minute to give the visitors a deserved 1-0 win. So what happened to the rankings?

This match was a UEFA Women's Championship qualifier. Yugoslavia started with 1710 points, Rep Ireland with 1624. But Rep Ireland were at home, which is good for a 100 point bonus. So the effective ranking difference for Yugoslavia was -14. That corresponded to a predicted coefficient of .48, which would be right around a 1-1 draw or so.

Note that Rep Ireland lost only seven points for this match, whereas Yugoslavia earned eight. That's because of the ceil() in the formula. It's the ceiling function, which means round up. So +7.4 goes to +8, and -7.4 goes to -7.

Anyway, moving on to our next example. This time we go to the second matchday in Group A of the 2002 African Women's Championship and the big match between tournament favourites Nigeria and Ghana on TUE 10 DEC 2002 in Warri, and Black Queens captain Albertha SACKEY made it one to remember for the visitors. Or should it be "one-nil" to remember?

This particular confederation championship was also used for Women's World Cup qualifying. Conveniently, both types of matches have the same M of 30. Nigeria entered the day with 1751 points, Ghana with 1461. Add in Nigeria's home field, and they're at +390, equivalent to a 4-2 win.

As it turned out, Nigeria got their revenge in a 2-0 win in the tournament final. But still, they lost sixteen points in that tournament.

Ready to make things complicated? No? Tough. Let's go to the Four Nations Tournament in China PR, where the hosts faced Norway on WED 29 JAN 2003 in Shanghai. The Steel Roses earned a 1-1 draw to finish second in the annual tournament, which routinely draws some of the world's best sides. It's a friendly tournament, but China PR and Norway are both elite nations, so that hikes M up to 20. The ranking table showed China PR at 2129 points and Norway at 2162. China were at home, so they were ahead by +67, which is about equal to a ½ goal win.

Draws are asymmetric results in the rankings. The exact values were -2.4 for China PR and +1.4 for Norway, but with the ceil() function, it was two points each way.

STUDENT EXERCISES
Hint: I don't know the answers either.

1. How in blazes did the US beat Panama 9-0 at the 2002 CONCACAF Women's Gold Cup and still lose a point?
2. What are 0-0 draws worth?
3. What are penalty shootout wins worth? Shootout losses?
4. What the hell is a "provisional" ranking? What is the threshold for turning a provisional ranking into a real one?
5. Which makes more sense, the Men's or Women's World Rankings? Discuss.

REFERENCES
[M]: InfoPlus: FIFA Women's World Ranking.
[R]: FIFA.com: FIFA Women's World Ranking.