Tuesday, June 26, 2007

No change

I guess after the U.S. posted an 8-0-1 mark over Mexico in the US since 2000 and a 2-1 Gold Cup final victory, some Mexican fans aren't convinced. Just got this in my SI mailbag.

"The only thing convincing about that win was that 2 is more than 1."

I think I called it a convincing victory for the U.S., which I think it was. And if you want to argue that the win wasn't convincing, perhaps you could also argue how the 8-0-1 isn't convincing either.

But not all fans think like that. I got an excellent response from a Mexican supporter who summed it up eloquently that I'll save for my SI mailbag for tomorrow night's column.

8 comments:

Anonymous said...

I think the crowd of Mexicans saying that the US isn't the better team is shrinking from years past. I've seen some Mexican articles stating that Mexican is no longer the Giant of CONCACAF, and I even read that Carlos Hermosillo stated the same thing. Admitting this isn't a bad thing in my eyes as I think Mexico will only improve if they realize their shortcomings.

I think it has more do than just head to head records this time around too. While the US didn't look good in a few games in this tournament. Mexico by far looked worse until the final. The fact that the US can handle CONCACAF teams easier than Mexico right now shows who the better team is. Mexico might have the better individual players, but as a unit the US is better right now hands down.

Anonymous said...

I really do agree with the above poster.

The 8-0-1 number is not as important to me as it is for others. That's just an arbitrary sportscenter factoid.

However, the quality in the last couple of US victories is important to me due in fact because Mexico played with their A squad and both teams went all out for wins.

Mexico is lacking quality finishers and you can't trot out 34 year olds like Borgetti and Blanco against the US and win. This much we know. Until they develop some quality finishers and a tighter, better back line the results will always be the same.

You can't give up two goals to the US every time you play them and at the same time you can't only score 1 goal against the US and expect that to hold up, given how the US attack has improved under Bradley.

BBSC

Anonymous said...

Agreed that Mexico is slowly beginning to realize that maybe the yanquis can play. However, (I say this as an ardent US fan), Mexico had a far more difficult group stage to contend with in this edition of the Gold Cup than the US. So while it is clear we have Mexico's number when matches are played out of the Azteca, I'm not sure this tournament gave us sufficient evidence to conclude that Mexico has more difficulty with other CONCACAF foes. Switch groups and we might be commenting on how much difficulty the US had with Honduras and Panama.

ryan said...

Here's a look at the US's record v. Mexico from a statistical standpoint. If we assume the outcomes are independent (a reasonable enough assumption, given that no games were played on the same day or anything like that) then we can statistically test whether or not the two teams are equal.

If we throw out the tied matches (because they're uninformative about who's better), then the probability that one team beats another team 8 out of 8 times (this only includes the games in the US, but since games in the US outside of Columbus are essentially home games for Mexico it's rather reasonable), assuming the two teams are equally good, is 2*(.5^8) = .008. In other words, the same team winning eight out of eight games against an equally good opponent would only happen 8 out of 1000 times. From a statistical standpoint we can reject the hypothesis that the two teams are equal.

And of course, the idea that "the better team lost" eight out of eight games to an inferior team would happen even less than .008 of the time.

Nick said...

Ryan,
That is an excellent analysis. Is there any way to factor in the US's losses in Mexico during that time period? I believe we played there twice, once during each eliminatorias. So, obviously the sample size is not good, but i wonder if there would be a way to analyze the results objectively to factor in the games in Mexico...

ryan said...

Nick,
One way to get at this is to use a binomial distribution. Basically, it can tell you what the probability is of getting something like 8 heads in a row, or, in this case, 8 heads out of 10 coin flips.

So, the probability that two teams are equal, and that one of them wins 8 or more out of 10 games is .0547 (and this can be multiplied by 2 as I did before to test both tails of the hypothesis that the teams are equal, but this is not really necessary, it would be reasonable to just test one direction - that the US is better than Mexico - since we already know the US has won more games). This means that if two equal teams played each other ten times, one team would win 8 or more of those games 55 out of 1000 times.

Of course what would be most fair is if all the games were held on neutral territory, or half were home games for one team the other half were away games. Games in the US at best are neutral, if not home games for Mexico. So, I believe it is fair to only consider games played in the US (but of course I am biased). There are more complicated analyses we could do to account for these things, but this should suffice.

Anonymous said...

Is this a soccer blog or third period stats?

Anonymous said...

You don't need to develop an algorithm or bust out with regression analysis to show that the US has been better than Mexico head to head since 2000.