New and Improved User Inputs

From Sukhdev

Well, I guess it's about time that I chimed in. Javier and I don't always agree and that is evident from our views on football. I've run the simulator using 50% model and 50% user inputs. My user inputs are a little less "exact" than Javier's.

I have concentrated on batching teams. As Javier is Spanish, I guess he is being modest about Spain's chances, and with Xavi's supposedly playing with a calf injury and Torres' operation, maybe Javier is just being prudent or does not want to tempt fate. However, I think they should be favourites followed by Brazil, who also look fabulous.

Next I have batched England, France, Germany, Italy and Holland. All great teams, which on their day can win, so I think they should be equally weighted and the model can look towards history to sort them out. Next I add Argentina followed by Portugal. I would expect Argentina to be strong, but Maradona was definitely a better player than he is a manager. How can a team with such talent only barely qualify for the finals?

My surprise team is Ivory Coast who, with the likes of Drogba, Kalou and Toure, should do really well. So my simulation looks like:

World Cup Statistics

From Javier

We are asked frequently what is the most "probable" path in the World Cup according to the Isthmus Partners World Cup Simulator. People want us to boldly predict the pairings that will take place in the first round of the knockout stages and then in quarterfinals, semifinals and finals.

What needs to be realised is how difficult it is to predict the World Cup. Let's just take the Group Stage games. There are 8 groups and in each group there will be 6 games, so a total of 8 x 6 = 48 games just in the Group Stage. How easy would it be to predict the winner or draw of each game (Team A wins, Team A&B draw, Team B wins)? Well, the number of possibilities (possible combinations of results) is huge, beyond comprehension. It is 3^48, which is 79,766,443,076,872,500,000,000. That is 79.77 billion trillion. I know that in each game there are favourites and that you fancy that your chances of prediction are better than a 33.3% chance of getting it right in each game. But even if you 75% confident, the probability that you will get all 48 games right is 0.000101% (about one in a million, calculated from 0.75^48). Do one thing, look at the 48 games now and write down your prediction for those game just in terms of which team wins or if it is a draw. Then on June 26 after the Group Stages compare the actual results against your prediction (may be a humbling experience). And we have not even considered the different possibilities in terms of actual scorelines in those 48 games. The combinations are simply staggering.

Some have told us that the possible combinations in the knockout rounds are much smaller. Well, yes the combinations are much smaller, but the numbers are still huge. Let's look at potential pairings of first round of knockout stages. The tournament organizers have already determined the following pairings:
Winner Group A - Second Group B
Winner Group B - Second Group A
Winner Group C - Second Group D
Winner Group D - Second Group C
Winner Group E - Second Group F
Winner Group F - Second Group E
Winner Group H - Second Group G
Winner Group G - Second Group H

How many pairings of Groups A & B are possible? In each Group there are 12 different combinations of First/Second. So in total there are 144 combinations (=12 x 12). What about across all Groups? There are in total 4 sets (A/B, C/D, E/F, H/G). In total that is 144^4, which is 429,981,696. And then in the knockout stages there are 15 games to the final (we exclude the game for 3/4 place as it is the only one not relevant to determine which team wins the World Cup). That is 2^15 = 32,768 combinations in the knockout stage once we now the first round pairings of the knockout stage. So we multiply 32,768 x 429,981,696 and that is equal to 14.09 trillion combinations. That is a lot of combinations.

So how can we dare to represent that the World Cup Simulator has any degree of accuracy with only a maximum of 9999 iterations? Once we have modelled the probability distributions of the head-to-head pairings of all the teams and the structure of the World Cup, with a few hundred or thousand iterations (each iteration being a whole tournament played out by the model) we can have good estimations of what the model is predicting. Big teams will have higher probabilities of winning, but from time to time the simulator plays out a World Cup where a big surprise happens (Algeria or Korea Republic wins). But the probability of a Honduras - Korea DPR final is zero, it just will not happen. This is the strength of Monte Carlo simulation, that with the brute force of computers running simulations we can have an idea of the distribution of outcomes. It is also the weakness, as the human tendency to have blind faith in models could lead to models that predict too narrow a distribution range. More about this in future posts.

Running Simulation with User Inputs

From Javier

Its easy to run the Isthmus Partners World Cup Simulator using your own inputs for team weightings. These are the steps:


(1) Go to the 'Setup' worksheet and change under the heading "Model Weighting" the cell next to "Model" from 100% to 0%


(2) In the range under "User Team Weightings" change the numbers for each team according to your own criteria. You need to make sure the total is 1000. One trick is to give your favourite team 80 or 100 and the weakest teams a score of 5, and then fill in between. Remember the average score per team is 31/32, so for each team scored above 32 you need you will need to put below average scores for other teams.


(3) In the table below are the estimated probabilities for each team of reaching different stages of the World Cup resulting from a 9999 iteration run using my own User Team Weightings and with 100% User Input weighting. The first column in the table below reflects my own input weighting for each team.




I have given Brazil the highest score, 100. I have assumed for Spain the second highest score with 78 and Germany third with 65. Between Brazil, Spain and Germany those three teams have an almost 50% chance of winning the World Cup, which to me seems fair, as I personally believe this World Cup is more open than previous tournaments.


I have given South Africa a relatively high score compared to its football history and rankings because of the home country advantage. I know that no home team has ever failed to progress to the second stage of a World Cup. South Africa has about a 1 in 40 chance of winning according to my inputs.


Please be mindful that the chances of winning the World Cup are not only dependent on a team's strength, but it is also influenced by "path dependency". Path dependency is one of those technical words that modellers like to use to look smart. But all it means in this context is that the chances of a team progressing are determined by the other teams it meets along its way to the final. So for example although Argentina and France have similar weightings, Argentina has a significantly higher chance of winning the World Cup because it has a theoretically easier Group Stage, which is why Argentina has a 83.7% chance of reaching the 2nd round compared to France's 74.8%. Observing France's group in the first stage it is not unreasonable to assume it has a 1 in 4 chance of being kicked out of the tournament in the first stage, like it was in World Cup 2002.


Another way to check the reasonableness of your estimates is to check head-to-head pairings using the "Score Generator" in the Isthmus Partners World Cup Simulator Dialog Box. The results of Brazil to Spain pairings are:
Brazil wins: 46%
Draw: 25%
Spain wins: 29%


I am comfortable with those probabilities of Brazil vs Spain. If I pair Brazil vs Australia then Brazil has a 65% chance of winning, 25% chance of drawing and 10% chance of losing. I am also OK with that. Spain vs Germany results in Spain having a 44% chance of winning, 24% chance of drawing and 32% chance of losing.


Play around with the user weightings and the Score Generator until you get results that are in your comfort zone. Remember each time you change User Inputs to "Run Distributions" in the Dialog Box.

Please post your assumptions and results as a comment, we want to see what you are coming out with!

Five Mythical World Cup Games

From Javier:

What a simulator cannot do is to model the drama of a great football game. These are five great World Cup games:

World Cup 1950: Brazil 1, Uruguay 2
The famous (infamous for Brazil) "maracanazo". Arguably the biggest sporting upset in history. This match has acquired mythical status in spite of no live television broadcast. The game was not actually the final, rather the last match of a round robin of four finalists. All Brazil needed to do was tie to win the tournament, and early in the second half Brazil scored first. But two Uruguayan goals upset the host nation’s firm belief that they would win. According to FIFA President and World Cup founder Jules Rimet, in the stadium “the silence was morbid, sometimes too difficult to bear”.

YouTube Maracanazo

World Cup 1970: Italy 4, W. Germany 3
In this semi-final match, Italy scored early in the first half. The West Germans tied 1-1 in the last second of ordinary play. In extra time West Germany scored first, followed by two goals by the Italians, followed by an equaliser by the West Germans. At 3-3, the Italians scored their fourth goal through an uninterrupted passing movement straight from the kick-off. Five goals in extra time. West German legend Beckenbauer played extra-time with a dislocated shoulder. The Italians even made a movie where the game is played continuously in background for the duration of the film.

YouTube Game of the Century

World Cup 1970: Brazil 4, Italy 1
The Brazilian team and its offensive play have acquired legendary status. Pele played and scored in his second World Cup final. Brazil’s fourth goal scorcher by Carlos Alberto from a perfect pass by Pele is arguably the best goal in a World Cup final ever.

YouTube Best Final Ever

World Cup 1982: W. Germany 3, France 3
West Germany won this semi-final game on penalties. At 1-1 by the end of ordinary time the French took a 3-1 advantage in extra-time only to see the West Germans come back and tie. The game is infamous and still polemic due to the West German goalkeeper Schumacher’s vicious foul on French player Battiston.

YouTube 1982 Semifinal

World Cup 1986: Argentina 2, England 1
This high tension quarter-final game between two countries recently at war is not mythical for the quality of play (rather boring for those of us old enough to remember), but for two moments that would forever be etched in a fan’s memory: the “Hand of God” and “the Goal of the Century”, both played out by legendary Argentine player Maradona. With Maradona returning to the 2010 World Cup as Argentine coach, expect the memories of this game to be rekindled.

YouTube Hand and Goal of the Century

YouTube Goal of the Century with mythical commentary by Victor Hugo (Spanish)

Will there be any mythical games in 2010? Time needs to pass for a game to be considered mythical. Perhaps the 2006 semi-final between Germany and Italy or the final between Italy and France may acquire mythical status, but time will tell.

Results of a 9999 Iteration Run

From Javier:

Below are the probabilities estimated from a 9,999 iteration run of the Isthmus Partners World Cup Simulator, using the Model Weightings 100% and without any results hardcoded for any game. Brazil is most likely to win the World Cup with an 18.8%, followed by Spain with an 18.2%, and third Italy with a 9.5% chance. Ghana, Honduras, Japan, Korea DPR, New Zealand and South Africa have neglible chances of winning.

Getting Started with Isthmus Partners Simulator

From Javier:

Hi, getting started with the Isthmus Partners World Cup Simulator is easy. Just follow these steps:

1. Go to the following web page: http://www.isthmuspartners.ae/display.php?page_id=77&page_tagline=true

2. Scroll down until you see the Excel icon in the "Isthmus Partners World Cup Simulator April 2010" row.

3. Right click on the Excel icon and then select "Save Target As....."

4. Save the Excel file to the destination in your computer that you prefer.

5. Save and close any other Excel files you might have open. Open the simulator spreadsheet. You will need to enable macros to run for the model to be operational.

6. Right cick on the pdf icon next to the Excel Icon and save the pdf file. It is a quick guide to using the simulator.

7. You can also download the pdf report titled "Modelling and Simulation - World Cup Simulator". It is a report about modelling, simulation, the World Cup and how the Isthmus Partners World Cup Simulator was built.

Cheers.

Post comments if you have any issues setting up the model.