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The full version of SPI's methodology is here and here, but the short version of the differences between SPI and the FIFA rankings is this. SPI is a predictive, forward-looking rating system. It is designed to tell you which team will win tomorrow, not which one has been better in the past. It measures a team's strength offensively and defensively by analyzing the numbers of goals it scores and concedes and adjusts it based on the strength of its opponents. Perhaps most importantly it analyzes whether each team is actually fielding its best lineup in the match and weighs the importance of that match accordingly. More on that later.
Overall, we believe SPI is a better way to rank international countries because of its predictive nature. Most pub chatter centers on which team is better right now and which one will win tomorrow if my team X played your team Y. We want to know how the USMNT will do in World Cup qualifying or how will England will perform in the Euros. We don't care as much about ranking our team's successes against others over the past several years. SPI is deliberately set up to answer the question, "If two teams played their best squads in a match on a neutral field, which one would win?
By contrast, FIFA's rankings are intended to sort previous accomplishments. It is a backwards-looking system that ranks squads based on achievements in the past.
With that in mind let's take a quick look at a few countries where SPI diverges from the FIFA rankings.
Germany (No. 1 in SPI, No. 3 in FIFA rankings)
The Germans are number 1 in SPI largely because of their incredible goal differential in recent play. Their form was impeccable in qualifying, winning all ten matches with a plus-27 goal differential. During its qualifying run, Germany surpassed Spain as the number one team in SPI. This may throw some people off, but keep this in mind. During Spain's World Cup triumph last summer, Germany faced tougher competition, yet its plus-11 goal differential far outpaced Spain's plus-6. Even if we include Spain's 2008 Euro victory, it is only one goal better than Germany across the two tournaments.
Greece (No. 45 in SPI, No. 14 in FIFA rankings)
Greece may be the best example of the different ways FIFA and SPI rate teams. The Greeks have qualified for the past three major tournaments (Euro 2008, World Cup 2010 and Euro 2012), which has heavily boosted its FIFA ranking. However, Greece has been less than convincing in these qualification rounds and even worse in the actual tournaments. It finished Euro 2012 qualifying with a plus-9 goal differential in 10 matches, tied for the worst scoring margin among automatic qualifiers and worse than three group runners-up. In the 2010 World Cup, only North Korea finished the tournament with a worse goal differential. In the 2008 Euros, only France was worse. To put it simply, Greece has accomplished quite a bit in the past five years, but given its less than dominating performance, it is not expected to accomplish as much in the next five.
Mexico (No. 9 in SPI, No. 21 in FIFA rankings)
Mexico is a great example of SPI's weight on the importance of matches as well as its predictive nature.
Entering the 2010 World Cup, Mexico was had roughly the same ranking in SPI and FIFA. Right after the tournament, Mexico's ranking fell sharply in FIFA thanks to El Tri winning one of its four matches. However, SPI saw that a minus-1 goal differential against Uruguay (another country SPI predicted success for against Argentina, France and host nation South Africa is actually a good result and in turn it moved Mexico inside the top 15 in the world. Being a predictive system, SPI anticipated Mexico's stellar play to continue coming out of the World Cup -- which it did. It wasn't until Mexico won the 2011 Gold Cup that the FIFA rankings caught up with SPI on Mexico's ranking.
Fast forward one week and you see El Tri immediately falling in FIFA after the Gold Cup triumph. This is because it lost all three of its matches in Copa America. But as we all remember that was a Mexican team without any of its A-squad players on the roster. SPI recognized this was the case and kept Mexico static throughout the tournament, as we really didn't learn anything new about the quality of the team because of the absence of its top players. FIFA, however, dropped El Tri significantly following its subpar performance.