With Brian Ruiz back, I can see Costa Rica finishing 3rd or 4th. They took some steps in the right direction with that win in ES.
I think I found a bug in breaking positional ties that favored lower ranked teams. Sigh. Promise I do my day job better than I write programs. Assuming I fixed it, the direct qualifying percentages change to: MEX -- 97% USA -- 69% PAN -- 40% HON --38% CR -- 32% JAM -- 24% Which is much closer to dlokteff's and still looks reasonable. I found the bug trying to re-run using the ESPN rankings (linked by Adam). Those rankings think very highly of Costa Rica and group the US tightly with Honduras. Applying those rankings gives this for direct qualification: MEX -- 96% USA -- 51% PAN -- 29% HON --47% CR -- 63% JAM -- 14% Scary.
O.K. I've used Reccosu's formulas, and spent the rest of the time making my spreadsheet more robust and building in the code (a big pain in the ass for Excel to do...should've stolen a copy of SAS from my previous employer(s)) to deal with ties in the standings. Here are some factoids from what is now 100,000 simulations (in this particular run the sum of the differences in Actual Points vs. Elo predicted points for the USA is 0.0%, and the other 5 nations are +/- 0.3%). Finishing Top 3 (for relevant ties, a random uniform distribution is assumed): Mexico = 98.5% USA = 72.5% Panama = 39.1% Honduras = 37.6% Costa Rica = 30.6% Jamaica = 21.7% Very similar to my earlier run, but with Panama and Honduras' odds improving by about 2% each, primarily at Jamaica's expense (down about 3%), with the small balance coming out of the US's chances (down about 1%). Here is point distribution for the USA from the 100,000 Hex's, and the qualification % given said points: 0 Points = 0 Times (Qual% N/A) 1 = 5 (0%) 2 = 7 (0%) 3 = 21 (0%) 4 = 82 (0%) 5 = 212 (0%) 6 = 449 (0%) 7 = 828 (0%) 8 = 1606 (0%) 9 = 2534 (0.04%) 10 = 3715 (1.15%) 11 = 5401 (5.85%) 12 = 6905 (23.69%) 13 = 8333 (48.86%) 14 = 9714 (76.05%) 15 = 9816 (91.31%) 16 = 10,096 (97.39%) 17 = 9738 (99.56%) 18 = 8068 (99.91%) 19 = 7193 (100%) 20 = 5453 (100%) 21 = 3535 (100%) 22 = 2889 (100%) 23 = 1558 (100%) 24 = 877 (100%) 25 = 603 (100%) 26 = 181 (100%) 27 = 110 (100%) 28 = 62 (100%) 29 = 0 (N/A) 30 = 8 (100%) This is also very similar (and we run the table 0.01% of the time!). We still have 16 points as the most likely scenario for the US, and 97 times out of 100 that gets us through Top 3 (man Costa Rica getting Bornsteined on 16 points was rough, although different Elo's at the time obviously). Spreadsheet is in pretty good shape now, so as the Elo's change it's easy to update the odds. Will add the code to figure out the 4th place %'s and then sim vs. New Zealand to get the complete odds of qualification. After that, I'm going to try to make some home field adjustments based on the results of the last 4 Hex's.
I was going to do this for the ESPN (since the opinion there is significantly different than Elo, and frankly weird. Costa Rica is one of the "big movers" this month...by beating El Salvador and Guyana, whoopdee freakin' do) ratings as well, but didn't know how to interpret the SPIs. How did you do it?
I used the highest team in the CONCACAF region (MEX) and the average of the top ten CONCACAF teams to establish a linear relationship between ELO and SPI for CONCACAF. It gave me these equivalent ELOs for the Hex: MEX: 1894 (the same) USA: 1714 HON: 1703 PAN: 1658 CR: 1745 JAM: 1601 That conversion method is probably a little raw, but it made sense to me and gave results that seem to reflect what the SPI is saying about the teams.
it seems the espn hi rating for costa rica, basically 2nd is the key 2 sets of data project 2 completely set of results the model with cr 5th seems to fit what my eyes tell me, does playing mexico twice give them that bump?? i still have mex, usa, honduras but, i'm wiling to say the panama costa rica battle will be epic and honduras might well mess up a match, which has hurt thme in previous hex's
Continuing... Here's where we were: Finishing Top 3 (for relevant ties, a random uniform distribution is assumed): Mexico = 98.5% USA = 72.5% Panama = 39.1% Honduras = 37.6% Costa Rica = 30.6% Jamaica = 21.7% Here we have the additional percentages for finishing in 4th place: MEX = 1.1% USA = 14.4%% PAN = 21.9% HON = 22.0% CR = 21.6% JAM = 18.6% And here is each teams likelihood to prevail vs. New Zealand in the Home & Home: MEX = 90.4% USA = 74.3% PAN = 62.4% HON = 62.0% CR = 59.1% JAM = 55.3% Multiply it out and you get these odds of getting to Brazil: Mexico = 99.5% USA = 83.2% PAN = 52.8% HON = 51.3% CR = 43.4% JAM = 32.2% Certainly good to play Oceania. Thanks FIFA!
83 is a good number, something we can be comfortable with.. that battle for 3 and 4 is great, i feel honduras has the edge for 3, and panama defense gets them 4 but discouting cr at our danger
Not the same sim as above (I have to refresh formulas a bunch of times), but a similar 100,000 sim where (Elo Pred - actual results) summed to 0.0% for the US, yielded this place distribution for the USA: 1st = 11.738% 2nd = 37.997% 3rd = 22.777% 4th = 14.258% 5th = 8.696% 6th = 4.534%
Exactly. This is just for fun. Who knows what will happen? But this looks to me to be the most difficult final stage of qualifying for the US since 1989.
Yes and no. It is fun for me, and there are a lot of variables to decide a soccer game, but... Google "Nate Silver" right now. Same guy who created ESPNs SPI. This has got me worried enough to do the work to run the sims with his rankings and then begin the sleepless nights.
Here are the odds to qualify for 2014 World Cup based on the SPI rankings (using a similar conversion to Elo as Reccossu above, and pretty much says what he said) and 100,000 sims: % Qualify Top 3 + % 4th Place*Defeat New Zealand = % WC Mexico: 99.5% + 0.4%*94.1% = 99.9% Costa Rica: 68.2% + 17.0%*77.9% = 81.4% USA: 51.9% + 22.6%*72.7% = 68.3% Honduras: 44.7% + 24.0%*70.4% = 61.6% Panama: 25.5% + 21.9%*62.9% = 39.2% Jamaica: 10.3% + 14.1%*53.9% = 17.8% Just looking at the SPI it seems a bit more volatile than Elo, more influenced by recent results and more heavily swayed by large goal differentials. That's my impression when looking at their rankings, i.e. Costa Rica's recent thrashing of Guyana 7-0 gets a pretty heavy treatment. The eyeball/gut test tells me Elo "looks better", but the brain knows more work goes into the SPI than the fairly "dumb" Elo. You can read Silver's SPI intro here http://soccernet.espn.go.com/world-...8/ce/us/guide-espn-spi-ratings?cc=5901&ver=us and decide for yourself whether these added complexities should/will make the SPI a superior predictor. For the US's sake I'm hoping not.
Nate did a retrospective on how SPI did relative to Elo, Voros, and FIFA in predicting the order of finish at World Cup 2010. It won (insignificantly) over Elo: The correlation coefficients for the four systems were as follows: SPI -- .58 Elo -- .57 Voros -- .54 FIFA -- .43 http://soccernet.espn.go.com/world-...e/us/soccer-power-index-update?cc=5901&ver=us
The reason is that all six teams are competitive, and the gap between the US and the 3rd team isn't huge, but still significant, while there almost isn't any gap between #3 and #6. According to ELO, the US actually benefits from the strength of the 6th team, and it would be much more difficult to qualify with a true minnow. The US are still favorites against #3-#6 in a virtual two-legged duel (a gap of 76-120 points), but the results of the other teams against each other are almost equally distributed (4 teams within 44 points). ELO's prediction says that the other teams will take more points from each other than from the US. It would be much more difficult to compete against one opponent of almost equal strength for a single spot, with minnows filling up the group, because the opponent will probably win every other game (just like you), and it comes down to a quasi-KO game with a 55-45 chance or so. This is a point many people don't get about UEFA qualifying. Germany loves to get relatively difficult opposition out of pot 3, 4 and 5; give us all the Turkeys, Belgiums and Austrias in the world, because they will drop more points than we do. A group easy to win with something like 20 points from 10 games. The true UEFA group of death for the top seed is a group with a strong #2 and four minnows, where another team might get 8 wins, and you have to get a result in November in Russia or so.
This is really a scary group. I wouldn't be surprised if one of the big 2 misses out on the auto 3 and has to fight for the fourth spot. Goal difference will be crucial.
There's only one big team according to ELO, and one team being the first of the rest of the pack. Mexico today is the highest rated hex team ever; the US are the lowest rated 2nd team ever.
there is no way mexio will miss out and evenb if usa is 4th, usa and new zealand, i like my chances people are running scared heree
True. This also explains why 16 points is a virtual lock in this Hex, and 15 or even 14 points are likely to send us through top 3. There are no weak links to fairly assuredly pick up points on (let alone 2 or 3 as in previous Hex's), and points should be split more evenly among the squads. Here is the distribution of the minimum points (worst team) from a 100,000 sim: 0 Points = 0.099% 1 = 0.636% 2 = 1.507% 3 = 3.110% 4 = 6.534% 5 = 10.591% 6 = 14.548% 7 = 19.115% 8 = 18.787% 9 = 14.076% 10 = 8.097% 11 = 2.459% 12 = 0.414% 13 = 0.027% 14+ = 0% Most likely scenarios are 7 or 8 points for the "doormat". In the previous 4 Hex's last place has been 6, 2, 5, and 6 points. In two of the four Hex's we had a secondary Minnow on 8 points as well. While it looks pretty good for the USA, it's no slam dunk, and there's a nasty battle for the 3rd and 4th spots.
I don't think it's running scared, but for me, at least, it's pretty easy to be glass half empty when the ELOs give the US a 69% chance of direct qualification, Nate Silver effectively gives them a 51% chance, and the US has enjoyed comparitavely easier hexes for the past several cycles.
For this exercise, it's better if he doesn't. It's just math, no bias, no hand-ringing over the results. He takes the available data (admittedly (by Nate, himself) limited for soccer) and uses it as effectively as he can to predict results. You can say garbage in/ garbage out, and to some extent it's true, but his knowledge of the game isn't relevant.
I'd say you are correct in that this is one of several reasons why UEFA qualifying and CONCACAF qualifying are two very different animals. Few people outside this region appreciate the actual differences, but this I'd say nails a portion of it. (The other portion of it has to do with conditions and travel, which tend to be far more diverse and complicated on this continent than in Europe.)