Making use of a Poisson model, I have calculated rankings for the top 20 teams in CONCACAF based on the results of all matches (368) among the teams in the past five years. The model takes into account individual team strength, home field advantage (and lack thereof for matches on neutral fields), and results are weighted in time so that more recent results count more heavily in the rankings. The rankings are easy to interpret: each team's ranking is the percentage of points it would win vs. the other 19 teams in a simulated single round-robin tournament played on a neutral field. rank team w d l pf pp pct gd 1 MEX 12.7 4.4 1.9 42.6 57. 0.748 1.31 2 USA 11.6 4.3 3.1 39.1 57. 0.686 1.09 3 CRC 11.5 4.6 3.0 39.0 57. 0.684 1.03 4 PAN 10.1 5.0 3.9 35.4 57. 0.621 0.74 5 HON 9.5 5.2 4.3 33.7 57. 0.591 0.60 6 JAM 7.9 6.0 5.1 29.6 57. 0.519 0.29 7 GLP 8.0 4.8 6.2 28.8 57. 0.506 0.24 8 TRI 7.3 5.5 6.1 27.6 57. 0.484 0.15 9 GUA 7.1 5.2 6.7 26.5 57. 0.464 0.06 10 CAN 6.5 6.1 6.4 25.5 57. 0.447 -0.02 11 DOM 6.7 4.0 8.3 24.2 57. 0.425 -0.20 12 SLV 6.1 5.3 7.6 23.7 57. 0.415 -0.16 13 MQE 5.9 5.6 7.5 23.4 57. 0.410 -0.15 14 HAI 4.9 6.1 8.0 20.7 57. 0.363 -0.32 15 GYF 5.3 3.9 9.8 19.8 57. 0.348 -0.60 16 ATG 4.4 4.5 10.2 17.6 57. 0.308 -0.74 17 CUB 4.0 5.2 9.8 17.2 57. 0.301 -0.64 18 BLZ 3.5 6.5 9.0 16.9 57. 0.297 -0.53 19 NCA 3.9 4.0 11.1 15.8 57. 0.277 -0.96 20 GUY 3.1 3.9 12.0 13.1 57. 0.230 -1.19 Where W, D, L are the expected wins, draws, and losses in the simulated round-robin tournament, PF and PP are points for and points possible, respectively, pct is the percentage of points won (the ranking), and gd is goal difference per match, used as the tie breaker in case of equal pct rankings. Note GLP=Guadeloupe, DOM=Dominican Republic, MQE=Martinique, GYF=French Guiana, ATG=Antigua and Barbuda, BLZ=Belize, NCA=Nicaragua, and GUY=Guyana. Based on past results, MEX are the current kings of CONCACAF, with the top 6 teams being those currently battling it out for WC Qualification in the Hex. Interesting that GLP are ranked as the 7th best team in Concacaf, despite being the only team in the top 20 to not qualify for either the final round of Gold Cup qualifying or the last 12 of CONCACAF WCQ. More to come.
Group A Preview: MEX are the clear favorites, followed by PAN. Probability of each team finishing in each position: CAN MEX MQE PAN 1 0.0835 0.5692 0.0434 0.3039 2 0.2049 0.2860 0.1370 0.3721 3 0.3695 0.1103 0.3040 0.2162 4 0.3421 0.0346 0.5156 0.1078 top2 0.2884 0.8552 0.1805 0.6760 top3 0.6579 0.9655 0.4844 0.8922 Probability of each team/each position finishing on a given number of points: CAN MEX MQE PAN 1 2 3 4 9 0.0061 0.1780 0.0019 0.0688 0.2548 0.0000 0.0000 0.0000 8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 7 0.0367 0.3027 0.0133 0.1693 0.4712 0.0508 0.0000 0.0000 6 0.0649 0.1491 0.0366 0.1728 0.1304 0.2819 0.0111 0.0000 5 0.0652 0.1476 0.0356 0.1242 0.1341 0.2335 0.0050 0.0000 4 0.2151 0.1329 0.1532 0.2218 0.0086 0.3861 0.3252 0.0031 3 0.1867 0.0501 0.1670 0.1149 0.0009 0.0395 0.3794 0.0989 2 0.1506 0.0283 0.1527 0.0677 0.0000 0.0082 0.2152 0.1759 1 0.2095 0.0104 0.2912 0.0491 0.0000 0.0000 0.0641 0.4961 0 0.0652 0.0009 0.1485 0.0114 0.0000 0.0000 0.0000 0.2260
Group B Preview: HON are favorites, followed by TRI. Probability of each team finishing in each position: HAI HON SLV TRI 1 0.1099 0.4774 0.1604 0.2522 2 0.1996 0.2688 0.2495 0.2821 3 0.2924 0.1652 0.2799 0.2625 4 0.3981 0.0886 0.3101 0.2032 top2 0.3095 0.7462 0.4099 0.5343 top3 0.6019 0.9114 0.6899 0.7968 Probability of each team/each position finishing on a given number of points: HAI HON SLV TRI 1 2 3 4 9 0.0101 0.1257 0.0188 0.0443 0.1989 0.0000 0.0000 0.0000 8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 7 0.0456 0.2310 0.0700 0.1182 0.4337 0.0311 0.0000 0.0000 6 0.0622 0.1546 0.1069 0.1263 0.1831 0.2548 0.0121 0.0000 5 0.0741 0.1349 0.0821 0.1148 0.1691 0.2309 0.0059 0.0000 4 0.2002 0.1784 0.2222 0.2242 0.0139 0.4359 0.3693 0.0059 3 0.1706 0.0847 0.1631 0.1463 0.0013 0.0403 0.3795 0.1436 2 0.1506 0.0503 0.1213 0.1006 0.0000 0.0070 0.1989 0.2169 1 0.2029 0.0325 0.1560 0.0949 0.0000 0.0000 0.0343 0.4520 0 0.0837 0.0079 0.0596 0.0304 0.0000 0.0000 0.0000 0.1816
Group C Preview: USA are favorites, followed by CRC. Probability of each team finishing in each position: BLZ CRC CUB USA 1 0.0222 0.3504 0.0216 0.6058 2 0.1026 0.4704 0.1096 0.3173 3 0.3867 0.1397 0.4103 0.0633 4 0.4885 0.0395 0.4584 0.0136 top2 0.1248 0.8208 0.1313 0.9231 top3 0.5115 0.9605 0.5416 0.9864 Probability of each team/each position finishing on a given number of points: BLZ CRC CUB USA 1 2 3 4 9 0.0006 0.1059 0.0007 0.2539 0.3611 0.0000 0.0000 0.0000 8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 7 0.0088 0.2428 0.0078 0.3422 0.4905 0.1111 0.0000 0.0000 6 0.0241 0.2186 0.0349 0.1591 0.0753 0.3527 0.0087 0.0000 5 0.0246 0.1260 0.0191 0.1097 0.0710 0.2037 0.0047 0.0000 4 0.1323 0.1816 0.1333 0.0908 0.0017 0.2990 0.2365 0.0008 3 0.1827 0.0682 0.2293 0.0271 0.0004 0.0273 0.4238 0.0558 2 0.1460 0.0363 0.1221 0.0122 0.0000 0.0062 0.2068 0.1036 1 0.3089 0.0174 0.3023 0.0043 0.0000 0.0000 0.1195 0.5134 0 0.1720 0.0032 0.1505 0.0007 0.0000 0.0000 0.0000 0.3264
Match Day 1 Preview: #10 CAN vs #13 MQE Probability of CAN win: 40% Probability of MQE win: 20% Probability of draw: 40% Prediction: CAN 1 MQE 0 #1 MEX vs #4 PAN Probability of MEX win: 44% Probability of PAN win: 23% Probability of draw: 33% Prediction: MEX 1 PAN 0
Match Day 2 Preview: #12 SLV vs #8 TRI Probability of SLV win: 28% Probability of TRI win: 42% Probability of draw: 30% Prediction: SLV 0 TRI 1 #14 HAI vs #5 HON Probability of HAI win: 15% Probability of HON win: 54% Probability of draw: 31% Prediction: HAI 0 HON 1
Match Day 3 Preview: #3 CRC vs #17 CUB Probability of CRC win: 71% Probability of CUB win: 9% Probability of draw: 20% Prediction: CRC 1 CUB 0 #2 USA vs #18 BLZ Probability of USA win: 87% Probability of BLZ win: 2% Probability of draw: 11% Prediction: USA 2 BLZ 0
Great work by NoSix, but those rankings aren't terribly useful because some teams (USA, Pan) have brought significantly stronger sides than others (Mex, Honduras).
That's a risk I am taking, but to a greater or lesser extent, all of the Hex teams have sent B squads, so perhaps it will even out over the course of the tournament. A monkey throwing darts would be expected to predict 33% of matches correctly, so if I can do better than that, the rankings will be useful (the monkey's 33-0 lead after match day 1 notwithstanding).
The three possible outcomes of any game (Team A win, draw, and Team B win) don't have to be equally likely. If you made a round-robin group of Spain, Germany, Netherlands, and Moldova (three of the top countries in UEFA and one much weaker one) and predicted two out of six outcomes correctly you would have done poorly assuming Moldova lost all three games.
In general, the three outcomes are not equally likely, but they do have to sum to a total probability of 1. Therefore, a monkey choosing randomly among the three outcomes in the long run does so with a probability of ((pW+pD+pL)=1)/3 or 33% (rounded to the nearest whole percentage). My ability to choose the most likely outcome is what gives me an advantage over the monkey (in theory!).
Match Day 4 Preview: PAN vs MQE Probability of PAN win: 50% Probability of MQE win: 20% Probability of draw: 30% Prediction: PAN 1 MQE 0 (18% probability) MEX vs CAN Probability of MEX win: 57% Probability of CAN win: 12% Probability of draw: 31% Prediction: MEX 1 CAN 0 (24% probability)
Match Day 5 Preview: TRI vs HAI Probability of TRI win: 45% Probability of HAI win: 21% Probability of draw: 34% Prediction: TRI 1 HAI 0 (20% probability) HON vs SLV Probability of HON win: 49% Probability of SLV win: 22% Probability of draw: 29% Prediction: HON 1 SLV 0 (17% probability)
Match Day 6 Preview: USA vs CUB Probability of USA win: 90% Probability of CUB win: 2% Probability of draw: 8% Prediction: USA 2 CUB 0 (20% probability) CRC vs BLZ Probability of CRC win: 76% Probability of BLZ win: 5% Probability of draw: 19% Prediction: CRC 1 BLZ 0 (22% probability)
Match Day 7 Preview: PAN vs CAN Probability of PAN win: 61% Probability of CAN win: 12% Probability of draw: 27% Prediction: PAN 1 CAN 0 (21% probability) MQE vs MEX Probability of MQE win: 8% Probability of MEX win: 69% Probability of draw: 23% Prediction: MQE 0 MEX 1 (23% probability)
Match Day 8 Preview: SLV vs HAI Probability of SLV win: 34% Probability of HAI win: 32% Probability of draw: 34% Prediction: SLV 1 HAI 0 (16% probability) HON vs TRI Probability of HON win: 54% Probability of TRI win: 18% Probability of draw: 28% Prediction: HON 1 TRI 0 (19% probability)
Match Day 9 Preview: CUB vs BLZ Probability of CUB win: 31% Probability of BLZ win: 32% Probability of draw: 37% Prediction: CUB 0 BLZ 0 (23% probability) USA vs CRC Probability of USA win: 51% Probability of CRC win: 21% Probability of draw: 28% Prediction: USA 1 CRC 0 (17% probability)
My analysis indicates that BLZ and CUB each have a 0.4% probability of beating the other by the requisite 4+ goals in order to qualify for the quarterfinals. The other 99.2% of the time, the USA with a win or draw vs. CRC will face MQE in the quarterfinals, or with a loss vs. CRC will face HON.
So Cuba cashes in on their 1/250 chance of making the quarterfinals, MQE are out, and USA will face SLV in the quarterfinals instead. Before looking forward to the quarterfinals, a quick summary of the preliminary round results: Out of 18 matches, 11 results were predicted correctly (61%), including 5 exact scores predicted correctly (28%). The probability of predicting 11 or more out of 18 matches correctly by chance alone is only 1.4%, so TrueCrew's concern regarding the usefulness of the model has proved to be unwarranted.
Updated rankings, based on match results through 2013/7/16: rank team w d l pf pp pct gd 1 MEX 13.3 3.7 2.0 43.5 57. 0.764 1.53 2 USA 13.1 3.3 2.6 42.5 57. 0.745 1.55 3 CRC 11.5 4.6 2.8 39.3 57. 0.689 1.04 4 PAN 10.9 4.7 3.4 37.4 57. 0.655 0.90 5 HON 9.6 5.1 4.3 33.8 57. 0.594 0.61 6 JAM 8.2 5.8 5.0 30.3 57. 0.532 0.32 7 GLP 8.2 4.6 6.2 29.1 57. 0.511 0.25 8 TRI 7.7 5.0 6.3 28.0 57. 0.491 0.17 9 MQE 6.7 5.4 6.9 25.4 57. 0.446 -0.01 10 DOM 6.9 3.9 8.3 24.5 57. 0.429 -0.23 11 SLV 6.4 5.2 7.4 24.3 57. 0.426 -0.12 12 GUA 6.3 5.0 7.7 23.9 57. 0.418 -0.18 13 CAN 5.4 6.2 7.4 22.3 57. 0.392 -0.24 14 HAI 4.8 6.0 8.2 20.3 57. 0.357 -0.36 15 GYF 5.3 3.7 10.0 19.6 57. 0.344 -0.68 16 CUB 4.6 4.9 9.5 18.7 57. 0.327 -0.59 17 ATG 4.6 4.4 10.0 18.1 57. 0.318 -0.75 18 NCA 4.0 3.9 11.1 15.9 57. 0.279 -1.00 19 GUY 3.2 3.8 11.9 13.5 57. 0.236 -1.20 20 BLZ 2.5 5.0 11.5 12.5 57. 0.220 -1.01 As the only perfect team through the group stage, USA close the gap on MEX at the top. The eight gold cup quarterfinalists rank 1st-5th, 8th, 11th, and 16th. Biggest gainers are USA, up 59 pct points and 0.46 gd, MQE, up 36 pct points and 0.14 gd, and PAN, up 34 pct points and 0.16 gd. Biggest losers are BLZ, down 77 pct points and 0.48 gd, and CAN, down 55 pct points and 0.22 gd.
Quarterfinal Day 1 Preview: #4 PAN vs #16 CUB Probability of PAN win: 69% Probability of CAN win: 10% Probability of draw after regulation: 21% Prediction: PAN 1 CUB 0 (18% probability) #1 MEX vs #8 TRI Probability of MEX win: 68% Probability of TRI win: 11% Probability of draw after regulation: 21% Prediction: MEX 1 TRI 0 (16% probability)
Quarterfinal Day 2 Preview: #2 USA vs #11 SLV Probability of USA win: 75% Probability of SLV win: 7% Probability of draw after regulation: 18% Prediction: USA 1 SLV 0 (18% probability) (Note that a 2-o result (18.1% probability) is almost as likely as a 1-0 result (18.4% probability)) #5 HON vs #3 CRC Probability of HON win: 23% Probability of CRC win: 43% Probability of draw after regulation: 34% Prediction: HON 0 CRC 1 (19% probability)
So the US has a 38.5% (75 - 18.1 - 18.4) chance of winning by 3 or more goals? Or am I interpreting your numbers wrong?
The probabilities listed (18.1, 18.4) are for those exact scores; there are other results such as 2-1, 3-2, 3-1, etc. where the USA would win by 1 or 2 goals. My calculations indicate that the USA have a 14.4% probability of winning by exactly 3 goals, and a 25.0% probability of winning by 3+ goals.