Updated Probability Estimates (June 22)

From Javier...

Its worth updating the Simulator's updated probabilities as we enter the final stage of round 1 of the World Cup. The table reflects the fact that some teams are already qualified for the play-offs, evidenced by their 100% chance of reaching the 2nd round.

Brazil is favoured to win. The most devastated team from the ex-ante estimates is France. It would have to take a miracle for Argentina not to qualify today.

Remember to click on "Keep User Input Scores in the Model" in the Dialog Box within the Simulator to simulate the rest of the tournament while keeping scores to date intact.

The estimates below are generated 50% model weighting (ex-ante estimates) and 50% user inputs (our updated subjective views).

Simulating Group Stage Final Positions

From Javier...

Well, well, well....Serbia 1, Germany 0. The final games of Group D are going to be very interesting. Its time to use the simulating capabilities of the Simulator. Not the Monte Carlo simulation engine, rather testing the impact on Group classifications of different outcomes in the last two games.

To do this go to the workbook 'Group Stages'; put the actual results to date in the right boxes and then start playing around with different results of the last two games, hitting the "Update Tables" button. An example of an outcome for Group A is below.

Group A is really interesting. First, a tie between Mexico and Uruguay will automatically qualify both of them (Uruguay first, Mexico second) for next round. Will the two teams accept this? I doubt it, the second team has to play in all probability Argentina in the next round and I don't think the Mexicans will be conformed with that. They should, and will, come out to win to have an easier match-up in the second round.

Even if Mexico and Uruguay do not tie, France will not qualify automatically even with a victory over South Africa, as illustrated in the table. France would need a big victory over South Africa to be able to pass to second round.

So do not discount the French. The French players should assume that Uruguayans and Mexicans will go out for a win. And if the French have any pride left in them they should go for a big win by four or five goals. The coach should bring Henry out and go for broke. But the South Africans will also want to redeem themselves in front of their fans, so this will be a potentially great match.

What about Group B? Nigeria is not out, as the simulation illustrates. I think it is fair to assume that Argentina will beat Greece, so Nigeria has its destiny in its hands. And the Koreans will also want to win, so that match-up will be great to see.

Updated Simulator June 17

From Javier...

So now that each team has played at least one game it is time to update the Simulator.

The first step is in the worksheet 'Group Stages': put in the results to date in the right input boxes reserved for scores.

The second step is to back to worksheet 'Setup' and hit the "Run Simulator" button. Now in the Simulator dialog box the key thing to remember is to check the box next to "Keep User Input Scores in the Model". This will keep the scores to date when the simulation is run and will not overwrite them.

What we have also done is to run the Simulator on 50% Model weighting and 50% User Input. And we have updated the User Team Weightings to reflect our subjective estimates of the strength of each team after having seen them play.

Below is the results of the Simulator with updated estimated probabilities of a 9999 iteration run. Compare this to out previous blog entry of Results of a 9999 Iteration Run to be able to observe the impact on estimated probabilities of games to date and user inputs.




South Africa now is estimated to have very low chances of making it to the second round after last night's match. Uruguay on the other hand has high chances (have increased to 86% from Simulator's previous estimate of 44%).

Spain, in spite of our generosity in the user inputs, has taken a considerable beating in probabilities both to pass to second round and to win the World Cup. This is just a reflection that last night's result has put Spain in harm's way of random/adverse events in the next two games; it is on precipice and does not have room for error. Switzerland has improved dramatically its chances of going to the second round and even of winning the World Cup (still low, but at 1.6% much higher than the previous estimate of 0.4%).

Greece suffers a dramatic drop in probabilities of success (15% chance of passing versus previous estimate of 64.5%), while Slovenia (now 47% from 16%), Japan (now 53% from 17%) and Korea Republic (now 63% from 18%) have increased considerably their chances of making it to second round.

Germany, Netherlands and Argentina's probabilities of winning the World Cup have been revised upwards, with Germany now the second most probable team to win after Brazil.

Also to note is that the model gives a Brazil - Spain cross in the first round of the playoff stages a 30.7% estimate (use the "Analysis of Heads to Heads" utility within the Simulator dialog box to check this out).

Please update the results in your Simulators and use your own inputs.

Number of Iterations

From Javier


The Isthmus Partners World Cup Simulator allows to run simulations with a range of iterations of 500 - 9,999. Each iteration is the simulation of one World Cup, with the model simulating results of all games in the first round and second round, with the play-off games reflecting the outcomes of the results in the first round and previous play-off matches. Each tournament is simulated up to the final and the 'Probabilities' worksheet reflects the number of times out of 100 iterations that each team has reached a certain stage of the tournament including being champion.


If the user runs successive simulations with 500 iterations, the user can observe that the probabilities of each team winning changes, for example for 5 runs of 500 iterations (using 100% model inputs) the estimated probabilities of Brazil winning are successively 21.4%, 19.2%, 17.8%, 17.4%, 20.4%. What is the usefulness of running more iterations? Although one is tempted to say that more iterations mean more accurate estimations, the correct interpretation is rather more technical: if one compares a similar number of simulation runs using different iterations, the simulation runs with more iterations will tend to show less variance and smaller ranges (distance between maximum and minimum). This is a mouthful, so lets repeat this with an example to clarify what this means.


We complete the following:

- Group 1: 20 runs of simulations with 500 iterations
- Group 2: 20 runs of simulations with 1000 iterations
- Group 3: 20 runs of simulations with 2500 iterations
- For each run we estimate the probabilities of Spain and Brazil winning the World Cup
- Within each Group we estimate the average probability of winning for each team, the variance (standard deviation using STDEV function) of the probability of winning and the range between maximum and minimum in each Group.


Below is a table comparing the results for each Group.









Remember that each column represents the results of running the simulation exercise 20 times with the respective number of iterations. The table shows that with more iterations, the standard deviation of the distribution of estimates of winning the World Cup around the average result is tighter and the range (difference between maximum and minimum) is narrower.

What this means also is that with more iterations for the same confidence level (i.e. 90%) we can assume that the average probability is within a tighter band around the estimated average probability. For example for 2500 iterations we can say that we are 90% confident that Spain's chances of winning are between 17.00% and 19.48%, while for 500 iterations the same range will be 14.83% to 20.97%. With more iterations and more degrees of freedom (which means running more instances of the simulator) for the same level of confidence we can estimate a narrower range. There is a subtle but important difference between that statement and saying that at more iterations the estimated probability is more accurate.

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:

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!

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.