A Final-Footballer Rating Look at The World Cup

Perfect game plan, imperfect result

I have precious little free time this week as I am getting married on Saturday. Whenever I am not at work I am working on the last critical items for the wedding. I do feel compelled, however, to comment on what I think is undeserved criticism of the Dutch team's performance in the final.

Let's get one thing straight. Any team in the final has one purpose: to win the match within the confines of the rules of the sport. When a team encounters a finesse/rhythm/passing squad like Spain, they have two options for victory. They can either try to match that team's strategy (if they feel they have the talent to do so), or they do their best to disrupt the other team's strategy and pounce on the mistakes. From the outset of Sunday's match, it was clear the Dutch were pursuing the latter strategy.

To make the latter strategy succeed a team must be relentless and ruthless in their physicality. I am not talking about Ryan Sawcross or Nigel de Jong ruthlessness, but I am talking about fair challenges that push the limits of yellow card territory. You have to make every player think they are about to be hit as soon as they touch the ball. Doing so not only makes them less likely to complete an attacking pass, but it makes it far more likely they'll make a bad pass that sets up a counterattack. I am an Arsenal supporter - this type of tactic is the MO of every lower level squad our team faces in the EPL. I am the most likely to gripe about its application, but as long as the challenges are fair it's part of the game. You can't dictate how the opposition chooses to engage you.

And you know what? The Netherlands' strategy worked perfectly. See Figures 1 and 2 below, which plot each semi-finalists' Footballer-Rating absolute and differential score in each World Cup match they played.

Figure 1: Footballer-Rating score differential by match (dashed line represent three match moving average)

Figure 2: Footballer-Rating score by match (dashed lines represent three match moving average)

Looking at Figures 1 and 2, one clearly sees that Spain had their worst match of the tournament in the final. This is especially true when one looks at the running average, where the only time the Spanish average takes a dive is after they play the Dutch. Passing efficiency for a number of Spanish players was off by 10% or more compared to their match against Germany, and far fewer Spanish players had an efficiency rating of 80% or higher against the Netherlands. The Dutch disrupted the Spanish team's rhythm, and when Spain is winning all their knockout round matches 1-0 such disruption makes a win for the opposition possible.

FIFA, ESPN, and commentators around the world can gripe all they want about the Dutch play in this match. They can call it ugly. They can call it dirty. They can claim it will dull the acceptance of soccer in the US. They can make all the claims they want. What they can't claim is that it was ineffective because the numbers don't support that claim. Quite simply, the Dutch were the most effective at disrupting the Spanish style of play that has shredded the world over the last two to three years. If not for a missed Dutch opportunity or two, we never would have gone to extra time and would instead be talking about how brilliant of a game plan was executed by the Dutch.

The goal of any soccer game is to win within the bounds of the rules. If it produces a beautiful match in the process, that's great. Let's not let our obsession for "the beautiful game" lead us to penalize teams who come up with the best strategy to use against their opponent that doesn't fit within our narrow view of the game. Let us celebrate diversity of tactics, a near perfect game plan to take down a soccer juggernaut, and that juggernaut's impressive patience to score a late goal after nearly two hours of such physicality.

This is how I will choose to remember this World Cup and its final match. How about you?

Update: Only a few hours before I made this post, Soccer Quantified made a similar post that looked at each team's foul count during the tournament and their relative success at winning matches, their total points during group play, and their goals scored. It turns out the Dutch ranked in the top third for fouls/match (although that average was helped out by the 28 fouls in the final), and clearly outperformed all other teams in the metrics vs. their fouls per match. Soccer Quantified found distinct negative correlations for each metric with regards to the number of fouls committed. This implies, clearly, that fouling is no way to win an average match. Deploying the strategy, at the right time, can win a single match. That's the essence of my post above, and I stand by it given the several missed opportunities by the Dutch that would have sewn up their first World Cup in regular time.

World Cup Finals Prediction

What I am hoping to see, but not what I expect to see

I could give you a whole bunch of reasons why the Dutch will win on Sunday. Lord knows I want to - it's not only my personal interest, but my professional one as well.

My upcoming statistical analysis hinges on it (the "he" in the linked tweet being Paul the Octopus who predicted a Spanish win).

Behind US and English soccer, the Dutch are my third love.

Then I look at Figures 1 and 2.

Figure 1: Match-by-Match and 3-Match running average Footballer-Rating score by team - dashed line is three match running average (click to enlarge)

Figure 2: Match-by-Match and 3-Match running average Footballer-Rating score differential by team - dashed line is three match running average (click to enlarge)

And Figures 1 & 2 make me face reality: if Spain and The Netherlands play anywhere near to form, the Spaniards will win the World Cup. With over a 1.2 advantage in the 3 match running average score in the Footballer-Rating system, Spain is a 3:1 favorite to defeat the Netherlands. Even more telling is that while the competition has grown tougher and the final four teams have had their Footballer-Rating scores drop accordingly, Spain is the only team to have both their score and score differential be greater than zero in the last match. They've been the only team to really maintain form, albeit a form that earns them 1-0 wins.

Sure, one could claim that Spain benefits in the Footballer-Rating system by increasing their pass percentages by making a far greater number of inconsequential passes. Then again, that's how they open you up to scoring - pass until they see an opening.

The bottom line is that Spain, statistically, is the best team. They play good possession ball, and they wait for you to make a mistake. They took a German team who was rolling, scared them so much that they changed their game plan, and then they punished them for that.

I am happy that this is the final. These two teams are the ones that steamrolled the competition in the run up to the World Cup. If Holland wins, they will be the first team since the 1970 Brazil team to run the table both in the tournament and pre-tournament. Save for their blemish at last year's Confederation Cup tournament against the US, Spain has been just as good.

Alas, I must follow the numbers. Spain will likely win their first World Cup, and deservedly so. Or you could say the stupid octopus made you pick Spain. Either way, Spain is the favorite today.

It's a shame that both teams can't win their first World Cup. I, however, will be the first person to cheer a Dutch upset if it does happen.

Happy World Cup viewing. It's been a heck of ride. Here's hoping the finish is just as good!

PS - If you're looking for a prediction for the 3rd place match, I don't really have one. The Footballer-Rating scores of the teams are a wash. Miroslav Klose may miss the match. Germany's pretty banged up, but gets Thomas Muller back from his one game suspension. Uruguay's Diego Forlan has been one of the more dangerous men in this tournament, scoring from anywhere on the pitch. I would say go with Zonal-Marking's prediction, but they don't have anything up on their site yet. By a flip of a coin, I say it's going to be Germany. And Paul says so too.

Thoughts and Predictions on the Semifinals

What started with 32 teams nearly four weeks ago has now come down to four teams and four matches over the next six days. I'd like to provide some commentary on the remaining teams, their performance to date, and some predictions for the semifinal round.

Demographics

While I am not using the Soccernomics model to predict outcomes in any of these final knockout rounds, I do find the demographics of each team to be fascinating. Here are the three constituents to the Soccernomics model for each of the four remaining teams (in descending order for each attribute).

Population

1. Germany: 81,757,600
2. Spain: 46,030,109
3. The Netherlands: 16,616,850
4. Uruguay: 3,361,000

In this category we see the Western European nations dominating with their size and population density. It turns out that Uruguay was the second smallest nation to participate in this year's tournament - only tiny Slovenia has fewer people to draw upon for their national team.

GDP per Capita

1. The Netherlands: $48,223
2. Germany: $40,875
3. Spain: $31,946
4. Uruguay: $9,426

Again, the Western Europeans dominate. The Uruguayans come in dead last in both population and GDP per capita, meaning the talent pool they pull from and resources they can dedicate to such a talent pool will be smaller than the other three nations.

International Experience

1. Germany: 709 matches
2. Uruguay: 688 matches
3. The Netherlands: 587 matches
4. Spain: 461 matches

Here's where Uruguay shines. Only four teams - England, Argentina, Brazil, and Germany - have played more international games than Uruguay. Ironically, all five teams are part of the elite group of seven to have won a World Cup (Italy and France being the other two), and four out of those five made it at least to the quarterfinals in this year's tournament (sorry, English fans). Argentina, Brazil, and Uruguay have combined to win half of the World Cups contested to date. Of Uruguay's total international experience, they have played 181 matches against Argentina and 66 against Brazil (only their experience against Paraguay comes close with 63 matches). These matches mean that 36% of Uruguay's international experience comes against perennial World Cup championship contenders. While some may be surprised that CONMEBOL's representative in this year's final rounds is not Brazil or Argentina, they shouldn't be so surprised. Given the right manager and team, Paraguay should do as well as they have due to consistently challenge themselves to play against nations that are much larger than them and who continually challenge for soccer's top prize.

Not that I am counting, but some may be interested in how this adds up for a Soccernomics line. Here you go:

• Netherlands (+0.3) over Uruguay
• Germany (+0.4) over Spain

Regular readers will recall from my previous posts that such small spreads in predicted goal differential mean the model can't accurately predict the outcome of the match. Instead, let's take actual tournament data to understand how each team has performed so far and is trending as the knockout rounds go on.

Play-to-date

As in previous posts, I turn to the Footballer-Rating system for objectively evaluating team's performances in matches. It appears that their website is about a match behind as they have only posted results through the round of 16 (curious US fans should note that the differential between the US and Ghana ratings were 0.4 in favor of the Ghanaians, although both teams recorded negative ratings). Figures 1 and 2 below show the semifinalists' ratings and rating differential by match, with the dashed lines representing the three match running average trendline for each team.

Figure 1: Semifinalist Footballer-Rating score by match with 3 match running average dashed trendline

Figure 2: Semifinalist Footballer-Rating score differential by match with 3 match running dashed average trendline

The figures provide a useful comparison to the results realized so far in the tournament by each team.

Spain is killing the opposition in rating differential and absolute ratings, but this has translated to three narrow onw goal wins and two losses. This is likely due to the fact that Spain has passed the most, had the highest touch differential, been the most accurate passer in these finals, and the Footballer-Rating system rewards passing as well as scoring goals. It's an aberration in an otherwise mediocre performance so far for the second best team in the world according to the FIFA rankings.

Uruguay, on the other hand, has performed erratically and thus has shown relatively small ratings differential versus the competition. It shows in the basic statistics as well - Uruguay ranks at or near the bottom versus the other three semifinalists in every major category. The Footballer-Ratings scores indicate the up-and-down nature of the tournament so far for Uruguay and its fans. It seems that the Uruguayans have been able to make goals (or stop them in the case of the quarterfinal match against Ghana) when they really counted.

Save for their final group play match against Cameroon, the Dutch have completely outclassed their opponents by winning their matches with a Footballer-Rating differential of 0.7 or greater. Their absolute ratings are a bit lower, suffering from tough second and third matches in the Group Play stage. They began to turn things around with a dominant Round of 16 match, nearly equalling their opening match drubbing of Denmark. The Dutch are the only team left to have won all of their matches so far, consistently rank in the middle two spots of the four teams left when it comes to key statistics, but have the highest goals-against average of the four remaining teams.

The German ratings are a bit odd given their performance to date. Something odd happened in the Round of 16 match against England, as Germany dominated the match yet received a -0.9 rating differential. Conversely, their 4-0 opening match win against Australia earned them a +1.5 rating differential. Regardless of the ratings, the German attack has been relentless and has yielded 13 goals with three 4-goal dominating performances. The Germans rank at the top of the shooting categories, and in the middle of the passing ones.

Predictions

Last round I only went 1 for 4 as I picked too many favorites and the wrong upset. I will try not to make that mistake this time.

Figure 3 shows the Footballer rating moving average for the last three matches as scored by the Amaral Lab.

Figure 3: Three match moving average of Footballer-Rating scores

The Spain/Germany semifinal will be interesting to watch. Both squads have been impacted by similar passing/attacking styles originating in The Netherlands - it should make for an exciting match. Outstanding, experienced play is what it will take to beat the young and fast Germans. I think it is too much to ask of the Spaniards to flip the switch at this point in the tournament and go from mediocre play to outstanding play. I see Germany's offense overwhelming Spain for an upset according to Footballer-Rating.

In The Netherlands/Uruguay match I am going to take the favorite. I think the Dutch are playing too well, too consistently to not make it through to the final. Along with the Germans, they seem to have been the best TEAMS of the tournament - each player knowing their role and supporting the team accordingly. While I know my Dutch friends approach each match with apprehension waiting for the classic Dutch breakdown, this team has seemed very focused on the matter at hand and resilient when presented with a challenge (i.e. being down 1-0 to Brazil). I think they're simply too good, and they will eliminate an Uruguayan team that has fed off luck and bucking the statistics in this tournament.

If my predictions turn out correct, it'll make for a repeat of the 1974 World Cup final match. If that is the case, it would be an exciting match to watch. It would be a shame to have to see such a gifted German team lose, but I think much of the world would be pulling for the scrappy Dutch to finally deliver the world championship they have come close to winning several times before.

Short- and Long-Term Statistics: World Cup Quarterfinal Predictions

Soccer Dad at Soccer Quantified provides a nice cautionary tale about the over reliance on statistics in trying to predict the outcome of individual matches like those in the World Cup. He provides a nice link to my "Statistics Are Just Numbers" post, and after reading his post I feel compelled to comment on the subtle difference in some of the statistics I have used during this World Cup.

There are two types of statistics that I have used to predict performance in this tournament - longer term demographic data within the Soccernomics model and shorter term team performance data within the Footballer-Rating.com model. They both serve good purposes at
different stages of the tournament. Let me explain.

Socceromics Model In Group Play

The Soccernomics regression uses demographic data and match results over decades to predict the most likely outcome of a match between two teams. That is to say that it will tend to make better predictions in larger sample sizes where individual matches have less
impact (i.e. not win-or-go-home). Team adrenalin and short term boost have less of an impact in group play matches than knock out round matches, both in the many games that must be played and in the fact that each team knows that they must perform over those many games. This makes the Soccernomics model better suited for group play, although many statisticians might argue that three group play matches per team and 48 total matches might still be a smaller-than-ideal sample size for such a model. I will let my last post be the judge of that.

There is an additional benefit of using the Soccernomics model in the group play rounds. It will not only provide a reasonable prediction over time, but it also plugs a gaping hole - no player rating data exists for such matches. As much as we'd like to have a more direct method to compare the teams in their group play matches, there is very little short term data available to make such comparisons. The high pressure qualifying matches that might be the closest environment to that faced by World Cup teams are completed six months prior to the start of the final tournament. Team composition, chemistry, and momentum have changed greatly in those six months. The friendlies that most teams play as warm ups to the tournament are just that - they are good warm up matches, but they are not anywhere as competitive as a World Cup match. Thus, we must turn to longer term demographic data at the outset of the tournament to get a reasonable idea of which teams are going to make it out of group play and which teams aren't.

Footballer-Rating Model in Knockout Rounds

The knockout rounds are a different matter. After three matches of group play action, we can quantify how well a team did against World Cup caliber teams in a World Cup setting. We can begin to understand which teams are lucky to be in the knockout rounds based upon their play to date, and which ones got into them by dominating their competition. At this point, a player or team-based metric that evaluates actual performance should provide a better judge of future near term performance than a long-term demographics based model. Enter Footballer-Rating's player metric model, which got seven out of the eight Round of 16 matches correct compared to the Soccernomics model that got five out of the eight matches correct. Statistically, the chances that the Soccernomics model is more accurately predicting the outcome of the knockout matches versus simply flipping a coin is only 16%, while the Footballer-Rating method's chances are 76%. Why is that?

Recall from my last post where I showed that the ability of the Soccernomics model to accurately predict a "not lose" situation greatly increases once predicted goal differentials rise above 0.5. The problem is that most of the disparity in team performance based upon demographics is gone by the time the knockout rounds start. There were only two matches in the Round of 16 where Soccernomics predicted goal differentials larger than 0.5, and in both cases the predicted winner actually lost the match. In one case the Footballer-Rating prediction greatly favored the opposite team, and in the other case it predicted a virtual draw (which did occur during regulation and extra time). Combine these low goal differentials with the fact that the knockout rounds cannot produce a tie, and we see that the Soccernomics model is not a good fit for knockout round predictions. The Footballer-Rating model, which looks at recent play at the same tournament, naturally provides better predictions.

Quarterfinal Predictions

Based upon the accuracy of the two models in the two different phases of the tournament, I will be using the Footballer-Ratings model for the rest of the tournament. However, it must be said that their is one shortcoming with that model - the authors of the website that compiles the team ratings are not updating it with knockout round match data. I would have liked to have seen such updates, as team performance can change throughout the knockout rounds as the quality of opponents continues to rise. Nonetheless, Figure 1 shows the Footballer-Rating team average scores from the group play stage.

Figure 1: Footballer-Rating average team scores from group play matches

From a previous post we know that a gap of 0.7 or greater means that the favored team's chance of winning that match is 75%. With each match exceeding this threshold, we're likely looking at a semifinals round with Brazil, Ghana, Argentina, and Paraguay. Given that Ghana's predicted gap is the smallest and Uruguay's stiff defense, I would expect that the most likely upset might come from that match. I think Germany has a reasonable shot at slowing down Argentina. The Argentines are flying so high right now that they simply must regress to the mean at some point, and teams that perform so well and all of the sudden hit their first serious challenge often choke up a little bit. However, while I think the Argentina/Germany match may be close, I don't think the Germans have enough to beat Argentina.

So, here's my prediction for semifinalists: Brazil, Uruguay, Argentina, Spain. It's been a CONMEBOL dominated World Cup. Why stop now?

Evaluating Group Play Against the Soccernomics Model

I've spent a number of posts talking about the Soccernomics predictions for World Cup group play outcomes. Now that group play is complete, it's time to evaluate how the model did at predicting outcomes and which teams greatly over- and underachieved versus their Soccernomics predictions.

Ability of the Model to Predict Group Play Match Outcome

One way to judge the accuracy of the model is to look at its overall count of correct and incorrect predictions of outcomes. I have added a third category, "D" for draw, to capture when a push might occur in a situation where a wager is made on a specific match. Figure 1 captures this count.

Figure 1: Count of matches where Soccernomics predicted outcome of win/loss was correct (1), incorrect (-1), and when a draw occurred.

As one can see, the Soccernomics model correctly predicted the winner of 24 group play matches, or 50% of the matches played. The next likely outcome was a draw, with the least likely outcome being an incorrect prediction. This suggests that if wagers were involved in the matches, one could stand to make a good bit of money in wagers without spreads that also utilized pushes.

Of greater interest, however, is under what predictions the Soccernomics model is most accurate. How big does the predicted goal differential need to be to ensure a higher likelihood of predicting the correct outcome of the match? Figure 2 answers this question by using a cumulative distribution function (CDF). A CDF is used to show the likelihood (y-axis) of finding a value equal to or less than the one of interest (x-axis). In this case, I have plotted (1-CDF) to more clearly show the separation of the accuracy of predicted outcomes based upon predicted goal differential.

Figure 2: (1-CDF) for the Soccernomics model's ability to correctly and incorrectly predict a match outcome, as well as a draw.

Two observations can be made about the Soccernomics model's ability to predict outcomes in World Cup group play:

• By a goal differential of 0.5, the model's ability to predict a "not loss" outcome is about 2:1. This gap grows as the goal differential progresses to 1.0. Any predicted goal differential greater than 1.1 means that the superior team will either draw or win the match with virtual certainty.
• The closeness of the "correct" and "draw" lines indicates that the model's accuracy is not good enough to differentiate between a win or a tie. This makes the push all the more critical in a situation involving wagers.

The importance of a win in group play is even higher than expected given the roughly equally likelihood of drawing or winning with such high goal differentials. As SoccerQuantified.com points out, the number of draws in this year's group play was completely normal compared to previous competitions (although an abnormally high percentage came in the first matches).

Performance vs. the Model

Given the model's predictions, I have also quantified which teams have over- and underperformed the most versus the model. One measure of this is the average residual from the model - see Figure 3 for a plot of these average residuals in descending order.

Figure 3: Average residual from Soccernomics model by nation

One can see that four out of the top five teams made the knockout rounds (Slovenia being the exception), and eleven of the fifteen teams with positive average residuals made the round of sixteen. This left only five spots for the remaining teams, meaning teams with a positive goal differential residual to the Soccernomics model were twice as likely to make the knockout rounds than those who did not.

Another way to understand which nations performed most consistently against their Soccernomics prediction is to look at the standard deviation of their residuals to the Soccernomics model. Figure 4 summarizes this data.

Figure 4: Standard deviation of residuals from Soccernomics model by nation

Nations with the smallest standard deviation of performance to the Soccernomics model present a mixed bag of overall performance. New Zealand and Slovenia ranked high on both lists, indicating they consistently outperformed their Soccernomics predictions. Cameroon pretty much conformed to their Soccernomics prediction given their average -0.1 residual and low standard deviation. England and Italy, by ranking low in average goal differential and with a low standard deviation, consistently underperformed against their Soccernomics predictions. Also note that Portugal has the highest standard deviation, which indicates their top spot on the average residual list is likely due to the outlier of the seven goal barrage against North Korea. This means Slovenia's performance was likely the most consistent overperformance in the tournament.

If there is a Tom Thumb award to be handed out, it's a toss up between Slovenia and Uruguay. Slovenia deserves special consideration due to how small and new their country is. They have only two million people, with a much smaller population base of 20-30 year olds that could play in the World Cup. Uruguay deserves consideration for their high score on the average differential scale, and their win in the Round of 16. To win that match they had to overcome both the Soccernomics prediction and Footballer-Rating.com prediction that both favored Japan. They will face a challenge similar to what the US faced in the first round - a Soccernomics prediction that favors them but a Footballer prediction that favors Ghana. If they make it through that match into the semi-finals, they will truly be a Tom Thumb winner. Until then, Slovenia's high average residual and low standard deviation make them the winner.

Notes About the Round of 16

As I stated here, the Soccernomics model predicted smaller goal differentials for the Round of 16 - only one match had a projected goal differential higher than 0.6. In fact, the one game that did have a projected goal differential higher than 0.6 ended up being an incorrect prediction, although it did fall into the second most likely outcome for regulation time score (a 1-1 draw) based upon group play matches with a predicted goal differential of 1.0 or more. On the other hand, the Footballer-Rating.com method of looking at group play performance of the two teams to determine likely match outcome predicted the correct result in seven of the eight matches (Paraguay's win against Japan was the one outlier). This model seems to be a much better predictor of outcome in the early stages of the knock out round. It will be interesting to see if this trend holds. The statistics team at Footballer-Rating.com does not seem to be updating team performances based upon knockout round matches, which will force me to rely upon the group play data. I would have preferred to do a three match running average to capture the effects of playing against tougher opposition as the competition goes on.

Observations on the Round of 16

This time it will be much closer

It's been an exciting two weeks of group play, but now we know who is in the knock out rounds. We start things off early Saturday morning with the Uruguay/South Korea match and finish things up on Tuesday with a clash of the Iberian Peninsula.

In commenting on Round of 16, I will rely on two statistical methods for quantifying performance: the Soccernomics model for international matches that relies exclusively on demographic data, and the Footballer-Rating.com method that judges past performance in the tournament. The projected goal differential (Soccernomics) and average player rating by team (Footballer-Rating.com) are shown in the figure below.

Figure 1: Soccernomics and Footballer-Rating.com predictions for the Round of 16. Both scores are differences between the two teams expressed as (Left hand team - Right hand team)

As I mentioned in my last blog post, the United States/Ghana match is the only one where a team has at least a 1.0 goal differential advantage according to the Soccernomics model. Based upon matches with similar projected gaps, the US stands a good chance (11.5/16) to advance. Interestingly enough, the US/Ghana match also shows the biggest gap between the Soccernomics and Footballer predicted performances.

Per the original study that produced the Footballer statistical method, a differential of 0.75 or greater meant that the favored team had 3:1 odds of winning the match. This would mean that Ghana, Argentina, The Netherlands, and Spain are heavy favorites to win their first knockout round matches if they can maintain their group play form.

On the demographic front, there are some interesting points to be made.

• Only 6 of the 16 teams has a GDP per capita less than $10,000, and all but one of those 6 are from Central or South America. Ghana, the poorest country in this year's tournament, is the one sub-$10,000 country not on the American continents.
• At the opposite end, there are 6 teams with a GDP per capita greater than $30,000. This group consists of the four European teams left in the tournament, the US, and Japan.
• Every team in the knockout rounds has played 400 matches or more of international soccer competition. This meant most of the African teams were doomed from the outset, with Ghana being one of the few African teams with the requisite experience to get through group play.

Finally, some commentary on the Germany/England match. This might be the most even match of the Round of 16. Soccernomics says it is dead even, while Footballer-Rating.com has the Germans coring 0.3 points higher on their scale during group play. Perhaps we should just be listening to this octopus after all, because the statistics are clearly a wash on this match.

Happy World Cup watching over the next four days, and go Team USA!

That's Why They Play The Games, Part IV

Time for some revenge for 2006, boys!

They were the richest of nations, they were the poorest of nations...

A description of tomorrow's USA/Ghana knockout round match might as well begin with a twist on that classic beginning to A Tale of Two Cities. Demographically the two nations couldn't be more different. Not only does the US hold a sizable advantage in wealth, but it also holds a huge advantage in terms of population. Let's dive into the numbers to see what Soccernomics can tell us about this match.

Population

• Ghana: 23,837,000
  
• United States: 309,488,00
  

GDP per capita

• Ghana: $671
  
• United States: $46,381
  

International Experience

• Ghana: 389 matches
  
• United States: 403 matches
  

These advantages translate to a predicted 1.0 goal differential in favor of the United States. In fact, this will likely be the largest projected goal differential of any match if the first round of the knockout stages. In the Soccernomics model at World Cup 2010, a projected goal differential of 1.0 is huge. Only 15 matches in group play, or less than one third, have been projected to have a goal differential greater than or equal to 1.0. Fourteen of those matches have been played so far, with today's Switzerland/Honduras match being the fifteenth. In the 14 matches so far, the record of the teams favored by one goal or more has been:

• Wins: 9
• Draws: 4
• Loss: 1 (those plucky Slovenians over Algeria)

I don't have the statistics of how well the US and Ghana do at extra time or penalty kicks, but let's call it 50/50 so that the draws are split evenly. This means the US has at least an 11/15 chance of moving on if World Cup group play is any guide, and possibly as high as 12/15 if the Swiss meet their Soccernomics prediction and win today's match.

The one caveat to all of this is that Ghana is playing great soccer right now. As I noted in my last post, they have outplayed their opponents in group play to a greater degree than the US, but the gap is much smaller when you look at their absolute average team ratings (Ghana's 1.2 vs. US's 1.0). This should be a great match, and a great tuneup for whoever moves on to face the winner of the Uruguay/South Korea match.

There was a time late in the match on Wednesday when I thought I would never be posting a fourth installment of my series of posts. Anyone who tells you they felt differently, that somehow they hadn't given up hope in the closing minutes of that match, is either a liar or delusional about soccer. Landon Donovan's goal not only saved the US's run in the Cup, but validated what many of us believed to be true - this team is a world beater that deserves to be in the knockout rounds. Informed pundits and players around the world know this is a special team for the US, and they have got a good draw in the knockout rounds. They have accomplished goal #1, and can now pay lose and without fear. If they can beat Ghana, they have a good shot at running through to the semifinals. And if this team gets up a head of steam, they can be VERY dangerous. Just ask Spain and Brazil. I'm not saying they can win the Cup, but I am saying they can make a deep run and make the knock out rounds very interesting.

US Men's National Team, you've already made you nation proud and provided us with some of the most dramatic games of the cup. Thank you so much. Now it's all about continuing to shock the world. Let's go boys!

Another (statistical) way to look at World Cup performance

The best player in World Cup group play as of June 24th.

I am always on the lookout for good statistical measures of individual soccer players' contributions to overall team success. This has been elusive for a number of years, whether it's due to the pace of the game or the desire of many to not sterilize the beautiful game with a (largely American) obsession with statistics. One of the more popular methods for looking at individual players' overall performance is the Castrol Index, but this metric is a much better measure of individual, and not team, performance.

Over the last several weeks I have read tweets that proclaim "New Statistical Method Quantifies Soccer Player's Performance" that often linked to a summary of the study from a news organization (like Forbes). Very few of the tweets link to the original study, likely due to its relatively deep mathematical and statistical theory. I've read several of the articles and the original study, and can tell you the news articles leave out much of the very powerful details of the study that can provide us some great insight into World Cup 2010.

Before I go into explaining the power of the study, I must comment on its methodology and approach to provide proper background. The study is completed from the standpoint of asking, "What do individuals do to make teams succeed?" Soccer offers a good method for evaluating such theories because it provides a quantifiable outcome (goal differential), yet many of the player's contributions are hidden by the few traditional stats available and the few goals made in a match. This forced the authors to examine players' contributions in ways other than scoring - namely successful passing and assists given the choices each player was presented with. This allows every player, except for goal keepers, to be evaluated for their effectiveness in contributing to the team's success. By creating their own scoring system for such passes and shots on goal the authors have developed a way to evaluate each player's contribution to the team's success or failure, as well as a correlated method for translating the average of the player's scores to a positive or negative goal differential. A more detailed reading, for those interested in the statistical theory, is available here.

The statistical method manifests itself in the graphical representation in Figure 1. The thickness of the lines defines the frequency with which such passes are made, the color the score of the pass or shot path, and the size of the player circles the overall player score. One can see in each of the 2008 Euro knockout matches that not only do Spain's players provide more accurate passing, but they also have a greater proportion of their players executing accurate passing.

Figure 1: Graphical representation of Spain's Performance in Euro 2008 knockout matches.

The studies findings are fascinating, as the authors demonstrate their new test statistic correlates well with actual match results. Those findings include:

• The test statistic is defined as the difference between two team average scores in the study's new player score method. The authors are able to prove a statistically significant mean player score differential between teams where a win occurs versus a loss.
• When testing for sensitivity of the test statistic in predicting match outcome, the authors find a statistically significant difference between win and not win or lose outcomes. This proves that the test statistic, as conceived, accurately predicts the team's likelihood of having won the match based upon the observed behavior.
• In looking at the sensitivity of the test statistic, the authors found that Euro 2008 team performance could be accurately predicted by using the two highest scoring players on a team for the team average. This greatly simplifies any quick calculations one wants to make, and proves that most teams are only as good as their two best players.
• The sensitivity analysis also showed that when the test statistic is greater than 0.75, the odds that the higher performing team wins the match are 3:1.

It remains to be seen if such a model is as accurate at quantifying World Cup performance as Euro 2008. The authors of this study are working to assess this attribute, and their real time scoring can be found here. Assuming that it does, there are a couple of interesting conclusions to be drawn from World Cup play so far.

• Argentina, Spain, and Chile have been the best teams in group play so far as ranked by average rating difference. This is important, because the model showed that teams that played the best in group play tended to also play the best soccer in the knockout rounds of Euro 2008.
• Lionel Messi tops the list of highest scoring players, but Brazil has five of the top ten spots.
• As a preview of this coming Saturday's knockout round play, Ghana averaged a 0.7 team differential score vs. 0.3 average differential score for the US.
• Portugal's 7-0 drubbing of North Korea only yielded a 1.4 average score differential.
• The England/US match showed a 1.0 average score differential for England, which indicates the US was lucky to get out of the match with a goal.
• Conversely, the US had a 1.2 average score differential benefit vs. Slovenia. Remember, the odds say that the US should have won that match three times out of four. Further rationale for why the outcome didn't truly represent the team's effort.
• The US turned in their best performance of group play with an average player score of 2 for a differential of 0.6 vs. Algeria.
• Finally, Clint Dempsey is the US player with the highest average player score.

If you're interested in further statistics, the Amaral Lab's Footballer-Rating.Com website allows anyone to look at team, player, or match statistics. I recommend you check it out, if for no other reason than to see how your favorite team might stack up against their first knockout round opponent based upon group play scores. It will certainly be interesting to see how this model works within the data generated at the World Cup, the findings of which will be published at a later date by the study's authors.