I have calculated CONCACAF Power Rankings for the top 12 teams in the region based on the results of the 367 matches between those teams during the past eight years (from 6/12/1996-6/11/2004, inclusive). I plan to update these rankings after each round of 2006 CONCACAF WC qualifying. The ranking scheme assumes goals are Poisson-distributed, and takes into account team strength, home field advantage, and strength of schedule differences. Match results are weighted in time so that more recent results weigh more heavily in the rankings. For example, in these initial rankings, 2004 results to date account for 19% of the total, 2003 results 37%, etc. The rankings are simple and easy to interpret. Teams are ranked based on the predicted percentage of points (PPCT) each would win in a complete home and away round-robin tournament vs. the other eleven teams. Ties, if any, are broken based on the predicted goal differential per game (GD) over the same hypothetical round-robin tournament. Code: [size=2] RANK TEAM PPCT GD 1 USA 0.788 1.09 2 CRC 0.727 0.86 3 MEX 0.697 1.32 4 HON 0.561 0.18 5 GUA 0.439 -0.05 6 JAM 0.409 -0.14 7 PAN 0.394 -0.41 8 CAN 0.379 -0.27 9 TRI 0.333 -0.32 10 CUB 0.258 -0.45 11 HAI 0.197 -0.86 12 SLV 0.167 -0.95 [/size] In the simulated round-robin, USA, MEX, and CRC are all predicted to win all of their home matches, but the US and CRC top MEX in the rankings due to their better predicted away results. MEX, having a huge home team advantage, retain bragging rights as the "best" team in CONCACAF based on goal difference, for what that is worth. Note that this weekend's matches are not yet included in the ratings. I'll update them next following the conclusion of the HAI-JAM and CUB-CRC ties. For those interested, the predicted results for this weekend's matches were HAI 0 JAM 1 and CUB 0 CRC 0. For the return legs, the predictions are JAM 2 HAI 0 and CRC 2 CUB 0.
Thanks for providing these. The surprises, IMO, are that Panama is so high and El Salvador so very low ... although these ratings do fall in line with the weekend results. The above comment begs the question: what are your estimates for the home field advantages of different teams? Also, does Mexico actually have a worse away record than Costa Rica and the US, or is that finding possibly an artifact of the rating system?
VERY cool. Thanks. This weekend's results show that getting the expected result (especially on the road) in CONCACAF is not as easy as it might seem.
why do you assume that goals are poisson distributed? for a sample to be poisson distributed, there are three postulates, one of them being that the numbers of changes in nonoverlapping intervals are independent for all intervals. in soccer, with tactics changing during the game from attacking to defensive with a 1-0 lead or from a 4-4-2 to a bunker with a tie game and 15 mins left in azteca. i just believe the intervals are not independant of each other because after each goal, the probabilities of future goals do not remain constant. poisson is best used in an "arrival" process.
The home goal differences are listed in the table below, both the RAW data over the period and the data ADJusted by time weighting and strength of schedule: Code: [size=2] TEAM RAW ADJ CAN 0.56 0.49 CRC 1.36 1.43 CUB 0.10 0.32 GUA 0.22 0.03 HAI -0.25 -0.22 HON 0.92 0.79 JAM 0.93 0.94 MEX 2.70 2.73 PAN 0.59 0.53 SLV 0.55 -0.26 TRI 0.84 0.46 USA 1.51 2.06 [/size] Their RAW and ADJusted away goal differentials are as follows: Code: [size=2] TEAM RAW ADJ USA -0.06 0.30 MEX -0.17 -0.08 CRC -0.33 0.14 [/size] So the USA are the better road team based on both the raw and adjusted data. I would say that CRC is rated ahead of MEX as a consequence of the adjustments, rather than as an artifact of them. Recall that CRC won the last Hex by going 4-0-1 (W-D-L) on the road, compared to MEX's 1-2-2.
You're welcome. Thanks for posting. That's a fact! Over the 8-yr ranking period, the average (RAW) home goal difference was a whopping 0.98 goals per game. And not a single team had a positive road goal difference, the USA's -0.06 goals per game was the best in the region.
Believe it or not, there are a fair number of studies in the academic literature that conclude soccer goals are Poisson distributed (and one or two that argue as you do that scoring rates vary). For example, see Using Goals to Motivate the Poisson Process
so this only includes matches where these 12 teams played each other, no one outside the confederation?
Thanks for the kind words! Before I forget again, I would be remiss if I failed to acknowledge the use of the World Football Elo Ratings results database by Kirill Shuykin and Advanced Satellite Consulting, Ltd. Also, thanks to tachyon1, for suggesting an exponential time weighting function.
Thx again, #6. As usual, I'll bring up a couple of quibbles, even though in general I like what you've done. The ADJ column has a correlation of 0.94 with the power rating itself. I suspect this means that your version of home field advantage somehow includes the team's power rating. It'd be easier to interpret, IMO, if it didn't. Also, thanks for the away record comments. Count me as still fairly skeptical, since Costa Rica's remarkable Hex was preceded by a semifinal round where they only got one point in three road games.
No, but the adjusted home goal differentials and the adjusted goal differentials are calculated from the same set of match results, so perhaps it is not surprising that the two are correlated.
In order to separate strength of schedule effects from that of the time weighting effects, I re-analyzed the data without any time weighting. The change in each team's total goal difference per game in the "without time-weighted data" compared to the raw data is due entirely to the effect of strength of schedule: Code: [size=2] TEAM SOS MEX 0.34 CUB 0.27 JAM 0.25 HAI 0.24 SLV 0.20 HON 0.19 CRC 0.14 CAN 0.01 GUA -0.04 USA -0.05 PAN -0.11 TRI -0.27 [/size] So MEX played the toughest CONCACAF schedule over the rating period, while TRI played the easiest. The change in each team's total goal difference per game in the "with time-weighted data" compared to the "without time-weighted data" is then due entirely to the time-weighting effect: Code: [size=2] TEAM HOT CUB 0.48 HAI 0.37 PAN 0.20 GUA 0.17 TRI 0.02 CAN -0.02 JAM -0.06 USA -0.12 CRC -0.12 SLV -0.22 MEX -0.41 HON -0.46 [/size] So CUB is the hottest team over the later portions of the rating period relative to the earlier portions, while HON is the coldest.
Rankings updated through matches of 6/20/2004: Code: [size=2] LR RANK TEAM PPCT GD 1 1 USA 0.833 1.18 3 2 MEX 0.682 1.32 2 3 CRC 0.636 0.50 4 4 HON 0.561 0.18 5 5 GUA 0.455 0.00 6 6 JAM 0.394 -0.09 8 7 CAN 0.394 -0.23 10 8 CUB 0.394 -0.27 7 9 PAN 0.394 -0.36 9 10 TRI 0.333 -0.32 11 11 HAI 0.182 -0.95 12 12 SLV 0.152 -0.95 [/size] where LR is Last Ranking. CRC fall one notch to 3rd, and CUB are up two slots to 8th, following their 3-3 series draw. JAM's and HAI's rankings remain unchanged. CUB is the biggest gainer this round, up 0.136 percentage points and 0.18 goal differential. CRC is the biggest loser this round, down -0.091 and -0.36, respectively.
Are you ranking the entire confederation or just those 12 teams? If you're only doing those 12, could you add in the other 2 semifinalists (St. Kitts & Nevis and St. Vincent & the Grenadines) so we can see how they stack up? If you are doing the entire one, can you post below 12th place so we can see how everyone else is by comparison?
I could, but am not sure I should. Let me explain why. I started out ranking the top 24 teams, over the last 4 years, without any time weighting. The problem I ran into is that when some mid-table team like Guatemala thrashes St Elsewhere 14-0 in a home and away series, and none of the other top teams play St Elsewhere over the time period, even with strength of schedule adjustments, Guatemala's ratings become skewed relative to the other top teams. Over eight years and with time weighting, the effect I just described should be less of a problem, but let me check how many of the top 12 teams SKN and VIN have played over the last eight years and get back to you.
Unfortunately, it is as I expected. Of the top 12 teams, over the last eight years, SKN has only played CUB, JAM, HAI, and TRI. VIN has done a little better, playing HON, SLV, JAM, CRC, TRI, and MEX over the same time frame. But the number of matches is too small to make a good estimate of their strength relative to the Big 12. FWIW, the ELO rankings rate SKN 13th and VIN 16th in CONCACAF. I would rate the TRI at SKN match as a toss-up, but otherwise TRI should have little trouble advancing out of this group.
FWIW, here are the system's predictions for the next round: CRC 2 HON 1 SLV 1 PAN 1 CAN 0 GUA 0 JAM 0 USA 0 And bonus predictions for the two matches that don't involve only top 12 teams: VIN 1 TRI 2 SKN 0 MEX 1
In order to better reflect the relative strength of the teams involved, I am making a change to the ranking procedure. Whereas the previous rankings were based on the results predicted to be most likely in a single home and away round-robin tournament, the new rankings are based on the predicted average results over a large number of such tournaments. A more detailed discussion of the new vs. old ranking procedure can be found here. The new rankings: Code: [size=2] OR RANK TEAM PPCT GD 1 1 USA 0.691 1.19 2 2 MEX 0.662 1.34 3 3 CRC 0.574 0.53 4 4 HON 0.521 0.23 6 5 JAM 0.467 0.02 8 6 CUB 0.420 -0.24 5 7 GUA 0.411 -0.19 9 8 PAN 0.409 -0.37 10 9 TRI 0.397 -0.31 7 10 CAN 0.376 -0.39 12 11 SLV 0.308 -0.79 11 12 HAI 0.270 -1.02 [/size] where OR is the old ranking, and as before, PPCT is points percentage and GD is goal difference per game. Since no matches have been played since the last ranking, the changes in the rankings are due entirely to the change in ranking procedure. There is no change in ranking amongst the top 4, although the difference in ratings between those teams is narrower. Interesting to note that CUB makes the top six in the new rankings, even though due to the vagaries of the CONCACAF draw procedures they cannot make the HEX, having already been eliminated from the competition.
Updated rankings, through matches of 7/24/2004: Code: [size=2] RANK TEAM PPCT GD 1 USA 0.691 1.19 2 MEX 0.663 1.34 3 CRC 0.574 0.53 4 HON 0.523 0.24 5 JAM 0.467 0.02 6 CUB 0.419 -0.24 7 GUA 0.418 -0.16 8 PAN 0.399 -0.40 9 TRI 0.397 -0.32 10 CAN 0.376 -0.39 11 SLV 0.310 -0.78 12 HAI 0.270 -1.02 [/size] No changes in the rankings this round, although GUA gain a few percentage points on PAN following their 1-1 away draw at PAN.
Six, Do you know where US and Mex would stand if you threw out the last 10 or so head to head meetings that the US has just dominated? I suspect that Mex would jump ahead if we compared results to the rest of the region. The US just seems to have their number right now. Good job BTW, excellent analysis.
Isn't the ELO system used by Jeff Sagarin in his rankings for college basketball and college football?
The Sagarin ratings have two parts, Predictor and ELO-CHESS. You can look at http://www.usatoday.com/sports/sagarin/fbt03.htm