After last night. Mexico. Wow. WCQ% = Top3% + 4th%*W(NZ)% (Change) USA = 99.1% + 0.9%*79.7% = 99.8% (No change despite the loss) CRC = 98.2% + 1.8%*67.5% = 99.4% (+2.9%) HON = 71.0% + 21.9%*53.5% = 82.8% (+41.3%, absolutely huge win) MEX = 21.4% + 51.7%*72.9% = 59.0% (-31.9%, enjoy Middle Earth boys) PAN = 10.4% + 23.4%*64.2% = 25.4% (-5.7%, missed opportunity) JAM = 0.01% + 0.2%*34.2% = 0.1% (-0.1%, can't afford draws) USA point totals with Top3%, 100,000 simulations: 13 = 116 (25.43%) 14 = 1,476 ( 66.17%) 15 = 1,740 (94.10%) 16 = 8,244 (97.16%) 17 = 14,445 ( 99.83%) 18 = 6,047 (100%) 19 = 26,950 20 = 20,480 21 = N/A 22 = 20,502 USA Finish: Brazil Bound- 1st Alone = 44,430 2nd Alone = 34,490 Tie for 1st = 11,019 Tie for 2nd = 4,410 3rd Alone = 3,481 3way tie for 1st = 641 Down South, but where to first?- Tie for 3rd = 693 3way tie for 2nd = 288 4 way tie for 1st = 38 Let the god's decide- 3way tie for 3rd = 34 4way tie for 2nd = 4 5way tie for 1st = 2 Hobbit encounter- 4th alone = 445 NZ or bust- Tie for 4th = 19 Suicidal Tendencies- 5th = 6 It wasn't a good night on the field, but it wasn't all that bad in Mathematical Fantasy Land.
By the way, at this point, you should only be doing 19683 = 3 to the 9th power simulations, and weighting them by the product of the likelihoods of each result in each match. There are only 9 matches left in the hex, and for each of them, only three possible results -- win, lose, or draw -- since you don't simulate goal differential. (The playoff with New Zealand complicates this a little bit, but not much.)
Theoretically that would be more efficient. As a practical matter, running 100,000 simulations gives you a reasonable probability of covering all of the remaining permutations, without the necessity of maintaining two different codes. In theory the Monte Carlo approach could "miss" a permutation, but if that permutation fails to occur even once in 100,000 trials, as a practical matter its probability is too low to be relevant anyway.
Can't I just rep this whole thread? I have enjoyed it since the get-go. Then I loved watching the USA numbers pop during the month that will go down as an all-time great one in MNT history. And now, no change following the loss in San Jose. (And watching the trajectory of MEX's probability!) Brilliant! Can we please just earn the 3 points Tuesday and watch things click over to 100%? Please? Thanks to all the great calculations and analysis on this thread--as you can tell, I have really enjoyed it! ~OGx3
I have enjoyed this thread greatly. No one is sure how long Michael Bradley is going to be out. His absence alone, will greatly impact our chances in the remaining Hex matches.
Not as much fun anymore, but I'll play this out: USA = Qualified Costa Rica = Qualified Honduras = 79.95% + 18.18%*57.39% = 90.38% Mexico = 13.37% + 50.72%*73.89% = 50.84% Panama = 6.69% + 31.06%*68.18% = 27.87% Jamaica = 0% + 0.04%*38.48% = 0.02% USA Point Totals: 16 - 0.466% 17 - 5.591% 18 - 3.436% 19 - 30.410% 20 - 25.444% 21 - NA 22 - 34.653% USA Hex Finish: 1st Alone = 76.676% 2nd Alone = 15.229% Tie for 1st = 7.549% Tie for 2nd = 0.514% 3rd = 0.032%
Thanks for posting--do these simulations take into account the possibility that the US and CR might take their foot off the gas?
Back in October when I started this thread Mexico's Elo rating stood at 1894. Now it is 1751. What a tumble. Since Elo takes some time to fully adjust to a change in a team's quality. I wonder if the 1751 might be overstating where Mexico truly stands at the moment.
@dlokteff Thanks for the update. It's still interesting. Especially as you-know-who teeters on the edge of going to NZ and going home.
But by reacting to recent results, Elo also has the potential to over-shoot, and I tend to think that's what's happened to Mexico. If we look at the US, it finished the 2010 group stage with 1785 points. By late 2011, it was down to 1681, and now it's all the way up at 1835. Did its strength really fluctuate that wildly over time? If so, it was only a temporary change in form, not something to hang our hats on. Challenge to anyone who builds future simulations: figure out a way to take Elo's "mood swings" into account.
I have been too busy (sadly) to re-run my sim with the latest results, plus it seemed unnecessary with the good work others were already doing. But if I get a minute I will run the sim for the last two match days with a range of Mexico ELOs to see what difference it makes at this point.
Thought I'd put a wrap on this thread. Elo wasn't real good at predicting this Hex. It had: Mexico USA Panama Costa Rica Honduras Jamaica SPI as it turns out was a bit better, identifying Costa Rica as superior to Panama: Mexico Costa Rica USA Honduras Panama Jamaica Right now, the Elo model says Mexico beats New Zealand 73.23% of the time, while SPI apparently likes Mexico at 85.48%. I had fun. Time to start working on the World Cup spreadsheet.