Latest Hex Simulation and Qualifying Odds

[voros]

Using the power ratings I do for countries, I ran a set of 10,000 sims for the remaining hex matches. Here's the results.

Team Qualify Playoff Out
Mexico 99.80% 0.19% 0.01%
USA 97.73% 1.91% 0.36%
Costa Rica 66.97% 24.25% 8.78%
Guatemala 27.31% 44.13% 28.56%
Panama 7.30% 23.24% 69.46%
T&T 0.89% 6.28% 92.83%

The good news is, when I tested the system previously, it seemed to slightly underrate the favorites in matches, meaning our chances are probably even a little better than the above suggests. Mexico only finished out of the top 4 once in the 10,000 trials.

I also ran 10,000 sims forcing a pair of 1-0 wins for us in the next two matches (the worst scores by whcih you can win by). Here are the results if we assume we beat Costa Rica and Panama (not a safe assumption):

Team Qualify Playoff Out
USA 99.80% 0.20% 0.00%
Mexico 99.73% 0.25% 0.02%
Costa Rica 63.70% 27.86% 8.44%
Guatemala 31.46% 44.09% 24.45%
Panama 4.20% 20.71% 75.09%
T&T 1.11% 6.89% 92.00%

From this we see that, basically, two wins and we can book our tickets to Germany next summer. We wouldn't officially clinch, but with statistically should be the two easiest matches (Panama and T&T at home) still left to play and 12 points already in the bank, the U.S. would pretty much have to implode in the most spectacular fashion imaginable. I believe we would indeed clinch at least 4th and the playoff spot, but I haven't done the full match on that.

[eplkewell]

How did you run the simulations?

[voros]

How did you run the simulations?
I made a power rating system for National Teams (don't ask, it's what I do) and these rankings give me projected final scores for matchups between two teams. I use a poisson distribution (again, don't ask) to run sims, and voila. I can run about 1000 sims a minute, meaning 10,000 sims take sbaout 10 minutes (the miracle of modern computers).

[Anteater10]

Poisson Distribution, Impressive. As long as we get the W.

[CCSC_STRIKER20]

I made a power rating system for National Teams (don't ask, it's what I do) and these rankings give me projected final scores for matchups between two teams. I use a poisson distribution (again, don't ask) to run sims, and voila. I can run about 1000 sims a minute, meaning 10,000 sims take sbaout 10 minutes (the miracle of modern computers).
I don't think I could even begin asking questions.

[DirtyDefender]

Sounds every bit as scientific - and accurate - as the Coca Cola World Rankings model produced by FIFA.

How does your power ranking system differ from theirs?

What programming language/Software do you use to run the model?

[EvanJ]

I'm surprised Costa Rica's chances are that much better than Guatemala's.

[Bootsy Collins]

I made a power rating system for National Teams (don't ask, it's what I do)
But we have to ask, right? I mean, the accuracy of your system is what these predictions are built upon. Put another way, your system is like any other predictive theory: how the matches turn out simply provides feedback on how accurate the system is.

That said, of course I hope you're right w/ your predictions. And I'd have enjoyed seeing the likelihood of the various outcomes if we *lose* the next two matches, simply because at this point in qualifying (only three games in) I never know whether it's worth sticking my head in the oven when something bad happens.

[MarioKempes]

Monte Carlo. You go, girlfriend! Of course, when you play another team they don't care what the power rankings are or who is supposed to win. Power rankings don't take into account matchups, injuries, or the mental states of players. Still, it's a fun exercise.

[DutchFootballRulez]

"He's voros and he approves this message"

I made a power rating system for National Teams (don't ask, it's what I do) and these rankings give me projected final scores for matchups between two teams. I use a poisson distribution (again, don't ask) to run sims, and voila. I can run about 1000 sims a minute, meaning 10,000 sims take sbaout 10 minutes (the miracle of modern computers).

Logically, Arithmetically, and scientifically . Voros, a true football fans choice' for USSF President.

PAID FOR BY THE VOROS FOR PRESIDENT AD FUND.

[Adam Zebrowski]

while usa does have t&t and panama at home, the away matches at guatemala and costa rica are comparatively difficult as the home matches are "easier"

ruiz missing the mexico match due to cards, and missing next wednesday due to a sprained ankle seems to abnormally affect which projected scenarios would play out...

the aggregate approach, gives a nice big picture view, but a couple upsets tonight and wednesday would throw incredible variability into the next set of projections!!

[CrewDust]

Is your calculations similar to the Math Prof in CR who ran a similar program for the last Qualifing cycle?

[voros]

But we have to ask, right? I mean, the accuracy of your system is what these predictions are built upon. Put another way, your system is like any other predictive theory: how the matches turn out simply provides feedback on how accurate the system is.

From last year's results:

For favorites with an expected win% (chance to win plus chance to draw times .5):

Favorite Win% Wins Draws Loss Win%
0.90 to 1.00 15 1 0 96.9%
0.80 to 0.90 18 4 0 90.9%
0.70 to 0.80 30 10 5 77.8%
0.60 to 0.70 23 12 6 70.7%
0.50 to 0.60 18 17 14 54.1%
Total Favorites 104 44 25 72.8%

As you can see, the system slightly underrates favorites, which is good since we're favorites in every remaining match except the road match against Costa Rica. Also, normally the system would be updated after every match, but for these purposes, the same ratings (the ratings on the day before the first game in the series) were used throughout the 8 month trial, meaning the actual ratings for the matches late in the study would be a little different (and likely more accurate since they'd contain more recent information).

The explanation of the system is on the Statistics and Analysis board. If someone asks nice, I can post a link. No one has come close to asking nice yet.

[voros]

while usa does have t&t and panama at home, the away matches at guatemala and costa rica are comparatively difficult as the home matches are "easier"
Yeah but if we can come up with wins in the next two, reasonable reuslts in the T&T and Panama home games would make the rest of the results irrelevant.

Obviosuly the results we get in the next two are big, but two wins and I think it's pretty much over.

[Serie Zed]

Favorite Win% Wins Draws Loss Win%
0.90 to 1.00 15 1 0 96.9%
0.80 to 0.90 18 4 0 90.9%
0.70 to 0.80 30 10 5 77.8%
0.60 to 0.70 23 12 6 70.7%
0.50 to 0.60 18 17 14 54.1%

Voros, am I reading this right that in none of your deciles (or whatever they'd be called here) was your system off by more than 5.9%? (the .80 - .90 category would leave the favorite with an 85% chance of winning on average, but they actually won 90.9%).

That seems pretty impressive.

[Chicago76]

Voros-
Have you run sims on UEFA qualifiers or posted your world rankings? It would be very interesting to see on the FIFA/Tournaments board...

[mtr8967]

I will add my voice to the chorus. Thanks for the projection. I'd be curious to see the results after today's games. Heck, I'd be curious to see the results after each game going forward.

[voros]

I will add my voice to the chorus. Thanks for the projection. I'd be curious to see the results after today's games. Heck, I'd be curious to see the results after each game going forward.
I'll post tomorrow.

As for Europe, I could run them, but it's a little harder for Europe because you have to keep track of a bunch of groups at once since some 2nd place teams qualify directly and others have to go to a playoff. Running the sims would be easy, but setting them up would be a pain. If things start to materially affect the US (like a potentially seeded team being in deep trouble), maybe i'll try and run the end game. It's always a balancing act between what I want to do, and what I reasonably have time to do and needs to be done. There's all sorts of things I can do for club teams with the system (I still haven't done the Club Rankings of the Americas for example).

I'm definitely planning on doing it well in advance for the World Cup next year, I may even do a special "fake World Cup before the real one" sim.

[Foosinho]

The explanation of the system is on the Statistics and Analysis board. If someone asks nice, I can post a link. No one has come close to asking nice yet.
I'm an EE by training, a software engineer in the modeling and simulation field by trade, and have taken a few graduate level stats courses to make myself more useful to the research scientists in evaluating data from studies we run. Plus, I used to run (many moons ago, when I was an undergrad) a computer ranking for US pro teams. I'd love to see what you've got set up, and a link would save me the trouble of searching for it myself.

Nice enough?

[JBigjake]

I'm an EE by training...Nice enough?
Frankly your avatar looks like a EE by science!