lol man it was a joke. you wrote something wrong i thought id let you know with a little laugh. No hard feeling meant. as to my view on the topic. I think with all these draws in the group so far 14 points should be enough for a top 3 with the USA having qualified in advance and costa rica and mexico to qualify in the last or second last games
Looking at the standings/schedule, we could feasibly clinch qualification against Mexico on September 10th. Currently: USA 10 CR 8 MEX 8 Hon 7 Pan 6 Jamaica toast After next Tuesday, if USA wins and assuming a CR win at home vs Panama: USA 13 CR 11 Mex 8 Hon 7 Panama 6 We'd be 2 games up from 4th with 4 games remaining. September 6th. If we can pull a draw in CR, great, if not it's not a huge deal USA 14 or 13 CR 12 or 14 Panama will beat Jamaica at home giving them 9 points. Mexico v. Honduras will be interesting. A draw and it looks like this USA 14 CR 12 Panama 9 Mex 9 Hond 8 5 points up on 4th with 3 to play. September 10th. We beat Mexico 2-0 at home, HOnduras beats Panama at home, and CR/Jamaica tie in the office. (although CR & Jamaica will almost be a meaningless game at this point for us.) USA 17 CR 13 Honduras 11 Mexico 9 Panama 9 US is qualified. Even if we lose in CR, we're still qualified at this point. With Jamaica at home still to come. Now, for our friends who are fans of the Mexican national team this is where it really gets interesting. October 11th. Most important match day of the hex. Mexico hosts Panama, Honduras host CR with US and Jamaica meaningless. Assuming a Mexico and Honduras win, it will look like: USA 20 Hon 14 CR 13 Mex 12 Pana 9 However, if Mexico and Panama were to tie in Mexico, then it looks like this: USA 20 Hon 14 CR 13 Mex 10 Pan 10 Going into the last game, Mexico is in CR, who will in all likelihood not have qualified yet. USA in Panama. Maybe it would be a good time for a massive amount of experimentation, fall just short of securing a result in a tough place to play like Panama with inexperienced players and then Mexico loses to CR. (not suggesting anything, but we certainly wouldn't want to risk injury to starters having secured qualification.) If we draw/lose in Panama, then Mexico would have to beat CR in CR to get the playoff spot. USA 21 CR 16 Hon 16 Pan 11 Mex 10 Deliciousness.
good thorough analysis MtMike but that made my brain hurt reading all of it. I just look at it as if the US beats Hondouras next week then either Hondouras or Panama will have to win 2 out of 4 while the US also gets 0 points out of those 4 games for us not to qualify.
Thanks. Mainly went through it to say how precarious a position Mexico is in. If we win against Honduras, hard to imagine a scenario where we don't qualify. We'd have to lose our last 4 and that still might be enough given how many points have been dropped.
After the matches of 11 June 2013, it will take 18 points for the USA to clinch direct advancement to the World Cup, and 16 points for the USA to clinch no worse than a playoff with New Zealand. As before, the easiest way to see that 18 points suffice is as follows. There are 14 matches left to play in the hex. For 18 points not to suffice, there must be a possible set of results in those matches that gives three other teams 18 or more points with the USA also earning 18 points. That would mean that four teams, including the USA, would have 72 points among them. The only way for the USA to earn 18 points is to earn two wins and two draws. In the two draws, there are 2 points available. In the other 12 remaining matches in the hex, there are 36 points available. So there would be 38 total points available. The four teams with the most points right now are the USA, Costa Rica, Mexico, and Honduras. Among them, they have 33 points. 33 + 38 = 71, which is less than 72. All other sets of four teams have even fewer points. So there is no way for four teams to earn 72 or more points if the USA earns 18 points. So 18 points will suffice for the USA to clinch direct advancement to the World Cup. 17 points do not mathematically guarantee that the USA will clinch direct advancement to the World Cup. The USA can achieve 17 points with two more wins and one more draw; Costa Rica and Mexico can achieve 17 points with three more wins; and Honduras can achieve 17 points with three more wins and one more draw. So there are many possible scenarios in which four teams have 17 or more points. A simple example includes Jamaica and Panama losing all their remaining matches (except against each other), the USA drawing Honduras, the USA losing at home to Mexico, and the home team winning all other matches. That would leave the USA, Mexico, and Honduras with 17 points, and Costa Rica with 20 points. When it comes to guaranteeing no worse than a playoff with New Zealand, the easiest way to see than 17 points suffice is essentially unchanged after this mathcday. There are 14 matches left to play in the hex. For 17 points not to suffice, there must be a possible set of results in those matches that gives four other teams 17 or more points with the USA also earning 17 points. That would mean that five teams, including the USA, would have 85 points among them. But the top five teams only have 39 points, and with 42 points available in the 17 remaining hex matches, 39 + 42 = 81 points are the most that the total among any five teams can be. So 17 points suffice to advance the USA (or any team) to at worst a playoff with New Zealand. The analysis that shows us that 16 points suffice for the USA to guarantee no worse than a playoff with New Zealand is more complicated. There are 14 matches left to play in the hex. For 16 points not to suffice, there must be a possible set of results that gives four other teams 16 or more points with the USA also earning 16 points. Since that would only require 80 total points for the top five teams, and the top five teams can earn as many as 81 total points, such a set of results initially seems possible. The problem comes when we analyze the results that each team needs to achieve 16 or 17 points. Because Costa Rica and Mexico drew, they are both 8 points away from 16. To achieve precisely 16 points, Costa Rica (or Mexico) would need two more draws to go along with two more wins. But that would entail draws as the final result in at least two of the 14 matches left to play in the hex, making available only 40 points in the remaining hex matches, rather than 42. We see that 39 + 40 = 79, which is less than 80, so there is no scenario in which the USA has at least 16 points, either Costa Rica or Mexico has exactly 16 points, and three other teams have at least 16 points. Instead, Costa Rica and Mexico could both achieve 17 points with just three more wins apiece, making available all 42 points in the remaining hex matches. However, 39 + 42 = 81, and USA 16 + Costa Rica 17 + Mexico 17 + Honduras 16 + Panama 16 = 82, which is greater than 81. So there is no way for five teams to earn 16 or more points. 15 points do not mathematically guarantee that the USA advances to a playoff with New Zealand. The USA can achieve exactly 15 points with one more win and two more draws; Costa Rica and Mexico can both achieve exactly 15 points with two more wins and one more draw; Honduras can achieve 16 points with just three more wins; and Panama can achieve exactly 15 points with just three more wins. So there are many possible scenarios in which five teams have 15 or more points. A simple example includes Jamaica losing the rest of its matches, the USA losing to Hondruas, Panama winning in Costa Rica, the USA drawing in Costa Rica and at home against Mexico, and the home team winning all other matches. That would leave the USA, Costa Rica, Mexico, and Panama with 15 points, and Honduras with 19 points. As for realistic possibilities -- no longer concerned with mathematical guarantees -- 17 points will almost certainly advance the USA directly to the World Cup, and I imagine that 16 points would also likely have that result. I would still be suprised to see the USA earn 14 or more points and fail to at least end up in a playoff with New Zealand. For further analysis of realistic possibilities, check with people who run simulations. Analysis of how soon the USA can clinch in my next post.
The problem is that there's no way the USA can get to 17 points without taking points off of and keeping Mexico, Honduras, or CR from getting to 17. If we get 2 more wins and 1 more draw, then both CR and Mexico can't get to 3 more wins since they both play us and each other. One of the two can, but not both.
As before, the USA still cannot clinch anything in June. (It should be obvious that because the USA was unable to clinch anything in June even before the results of the last matchday, the results of the last matchday cannot have made the USA suddenly able to clinch anything in June.) The USA can still clinch direct advancement after the first September match day, but it's more complicated than it was before Honduras defeated Jamaica. Suppose these results occur on the next June matchday: the USA wins at home against Honduras, and Costa Rica draws Panama. Suppose that on the first September matchday, the USA wins in Costa Rica, Mexico draws Honduras, and Jamaica wins in Panama. Then the USA would have 16 points, Costa Rica would have 9 points, Mexico would have 9 points, Honduras would have 8 points, Panama would have 7 points, and Jamaica would have 5 points. Initially, this doesn't seem to help much. Jamaica could no longer catch the USA, as an 11-point lead with three matches to play is insurmountable. But any of Costa Rica, Mexico, Honduras, or Panama could catch the USA. Ah, but it would no longer be possible for both Costa Rica and Honduras to catch the USA. To catch the USA, Honduras would have to win all three of its remaining matches, earning 17 points. But then Honduras would have to defeat Costa Rica on the first October matchday, leaving only 6 possible points left for Costa Rica, for a total of 15 points for Costa Rica, not enough to catch the USA. It would also no longer be possible for both Mexico and Panama to catch the USA. To catch the USA, Panama would have to win all three of its remaining matches, earning 16 points (and also, Panama would have to win a tiebreaker over the USA). But then Panama would have to defeat Mexico on the first October matchday, leaving only 6 possible points left for Mexico, for a total of 15 points for Mexico, not enough to catch the USA. So the USA could finish behind Honduras and Mexico. Or the USA could finish behind Costa Rica and Panama. Or the USA could finish behind Costa Rica and Mexico. (The USA could not actually finish behind both Honduras and Panama, by a similar argument.) But the USA could no longer finish behind three teams simultaneously, which therefore would mean that the USA could no longer finish worse than third in the hex. So the USA would clinch a World Cup berth.
Check your logic again. Current standings: USA 10, CR 8, Mex 8, Hon 7 (Panama and Jamaica don't matter.) Hypothetical 18 June 2013 results: USA 0-0 Honduras, Costa Rica 1-0 Panama. Resulting standings: USA 11, CR 11, Mex 8, Hon 8. Hypothetical 6 September 2013 results: Costa Rica 1-0 USA, Mexico 1-0 Honduras (Panama and Jamaica don't matter.) Resulting standings: CR 14, USA 11, Mex 11, Hon 8. Hypothetical 10 September 2013 results: Honduras 1-0 Panama, Jamaica 0-1 Costa Rica, USA 0-1 Mexico. Resulting standings: CR 17, Mex 14, USA 11, Hon 11. Hypothetical 11 October 2013 results: Honduras 1-0 Costa Rica, Mexico 1-0 Panama, USA 1-0 Jamaica. Resulting standings: CR 17, Mex 17, USA 14, Hon 14. Hypothetical 15 October 2013 results: Costa Rica 1-0 Mexico (or whatever), Jamaica 0-1 Honduras, Panama 0-1 USA. Resulting standings: CR 20, Mex 17, USA 17, Hon 17.
It would be fun to be in that scenario and send our U-16 team to play in Panama. HOWEVER, I'll lay down a marker here: It is very good for the USA when Mexico qualifies for the WC Finals. And, as much as our comrades south of the Rio Grande hate to admit it, it's equally good for Mexico when we qualify for the WC Finals. Most of the World thinks that CONCACAF should have 2.5 slots, not 3.5. Looking at our combined ELO and FIFA rankings, there's merit to that argument. However, Mexico consistently advances out of their group and the USA is starting to do the same. Such success at the event (compared to how poorly AFC always performs) helps us keep our extra slot. That can be really important. Imagine the pucker factor in Mexico right now if there were only 2.5 slots. Imagine the shoe on the other foot . . . As much as we hate it, we want Mexico join us in Brazil.
I begrudgingly somewhat agree. can I hope that Mexico has to go through the playoff through New Zealand and advances on a 94th minute own goal in the 2nd leg when it's 0-0 on aggregate? However, most of the world (Europe) thinks they should have 24 spots (including one for the host which is obviously European every time), 4 for SA, and maybe one for each of the other confederations.
Plausible, but extraordinarily unlikely. About a 1% chance of happening. Especially discounting Panama altogether from the equation. They're not going without a point, other than Jamaica, the rest of the hex.
No doubt, and I think they are the only other team in CONCACAF of making a deep run in the WC. But it sure is fun watching them sputter and squirm on the way to Brazil.
Glad that you now agree that 17 points do not mathematically guarantee that the USA will clinch direct advancement to the World Cup.
Yeah, if we're looking now as we sit, yes 17 points don't qualify us. By the time we get to 17 points, it will qualify us.
This is my summary of my forcasting... Place Team Point ------ ------- ------ 1. USA 18 2. MX 18 3. HON 16 4. CR 15 I see USA with 2 wins and 3 draws I see Mexico going 3 wins and a draw I see Honduras 3 wins and 2 losses I see Costa Rica 2 wins, 1 draw and 2 losses. These are the most conservative scenarios for us (USA). We win the hex by goal differential. Mexico as always comes up with a late run just like they did in the last Qualifiers, not sure if they would do it with CHEPO or someone else. I just don't see them imploding. The key games are: (home team first) CR vs HON (w) <-- this would be an upset game CR vs MX (w) USA vs MX (D) PAN vs USA (D)
After the matches of 18 June 2013, it will still take 18 points for the USA to clinch direct advancement to the World Cup, and it will still take 16 points for the USA to clinch no worse than a playoff with New Zealand. The argument that 18 points suffice for direct advancement is essentially unchanged. The simple example of the USA failing to qualify with 17 points needs only a few tweaks: USA 13 (+4), CR 11 (+4), Mex 8 (+1), Hon 7 (-1) CR 3-0 USA, Mex 0-1 Hon (Pan-Jam irrelevant) CR 14 (+7), USA 13 (+1), Hon 10 (0), Mex 8 (0) Hon 1-0 Pan, Jam 0-1 CR, USA 0-3 Mex CR 17 (+8), Hon 13 (+1), USA 13 (-2), Mex 11 (+3) Hon 1-0 CR, Mex 1-0 Pan, USA 1-0 Jam CR 17 (+7), Hon 16 (+2), USA 16 (-1), Mex 14 (+4) CR 0-1 Mex, Jam 0-1 Hon, Panama 0-0 USA Hon 19 (+3), CR 17 (+6), Mex 17 (+5), USA 17 (-1) The argument that 16 points suffice to clinch no worse than a playoff with New Zealand is essentially unchanged. A simple example of the USA finishing in fifth place with 15 points is a bit tricky, but still possible in several ways, such as: USA 13 (+4), CR 11 (+4), Mex 8 (+1), Hon 7 (-1), Pan 6 (-2) CR 1-1 USA, Mex 1-0 Hon, Pan 1-0 Jam USA 14 (+4), CR 12 (+4), Mex 11 (+2), Hon 7 (-2), Pan 9 (-1) Hon 1-0 Pan, Jam 0-1 CR, USA 0-3 Mex CR 15 (+5), Mex 14 (+5), USA 14 (+1), Hon 10 (-1), Pan 9 (-2) Hon 1-0 CR, Mex 0-1 Pan, USA 0-0 Jam CR 15 (+4), USA 15 (+1), Mex 14 (+4), Hon 13 (0), Pan 12 (-1) CR 0-0 Mex, Jam 0-1 Hon, Pan 2-0 USA CR 16 (+4), Hon 16 (+1), Mex 15 (+4), Pan 15 (+1), USA 15 (-1) These scenarios point out that there is still some merit to the argument that the USA wants Mexico to win its home matches. Mexico wins in Azteca over both Honduras and Panama would allow the USA to clinch direct advancement with only 17 points, as Honduras would be limited to at most 16 points, and Panama to at most 15 points. Similarly, Mexico wins in Azteca over both Honduras and Panama would allow the USA to clinch no worse than a playoff with New Zealand with only 14 points. Those Mexico wins would limit Honduras and Panama together to a total of at most 28 points, as Honduras hosts Panama on the second September matchday. The loser of the Honduras-Panama match would then be limited to 13 points (if Honduras) or 12 points (if Panama), or if Honduras drew Panama, Panama would then be limited to 13 points. Interestingly, the USA can still mathematically finish in last place in the hex. One simple example: USA 13 (+4), CR 11 (+4), Mex 8 (+1), Hon 7 (-1), Pan 6 (-2), Jam 2 (-6) CR 1-0 USA, Mex 0-1 Hon, Pan 0-1 Jam CR 14 (+5), USA 13 (+3), Hon 10 (0), Mex 8 (0), Pan 6 (-3), Jam 5 (-5) Hon 0-1 Pan, Jam 1-0 CR, USA 0-3 Mex CR 14 (+4), USA 13 (0), Mex 11 (+3), Hon 10 (-1), Pan 9 (-2), Jam 8 (-4) Hon 1-0 CR, Mex 0-1 Pan, USA 0-1 Jam CR 14 (+3), Hon 13 (0), USA 13 (-1), Pan 12 (-1), Mex 11 (+2), Jam 11 (-3) CR 0-1 Mex, Jam 1-0 Hon, Pan 1-0 USA Pan 15 (0), Mex 14 (+3), CR 14 (+2), Jam 14 (-2), Hon 13 (-1), USA 13 (-2) There are many clinching possibilities for the USA on the first September matchday. Obviously, a win in Costa Rica gives the USA 16 points, clinching no worse than a playoff with New Zealand. A win in Costa Rica can still even clinch a World Cup berth for the USA, with help from the results of other matches on the first September matchday. Mexico would need to draw Honduras, and Jamaica would need to defeat or draw Panama. No other combination of results clinches a World Cup berth for the USA on the first September matchday. If the USA wins in Costa Rica and Mexico draws Honduras, that would leave the standings at USA 16, CR 11, Mex 9, Hon 8 (ignoring Panama and Jamaica for the moment). In this scenario, Honduras could only catch the USA by running the table, giving Honduras 17 points, but requiring Costa Rica to lose to Honduras. Mexico could only catch the USA with two wins and a result in Costa Rica, giving Mexico 16 or 18 points, but requiring Costa Rica not to defeat Mexico. Costa Rica would have only 4 available points left (3 against Jamaica and at most 1 against Mexico), restricting Costa Rica to at most 15 points, not enough to catch the USA. Therefore, if the USA wins in Costa Rica and Mexico draws Honduras, it is not possible for all of Costa Rica, Mexico, and Honduras to catch the USA. If Jamaica specifically defeats Panama, along with the USA winning in Costa Rica and Mexico drawing Honduras, that would leave the standings at USA 16, CR 11, Mex 9, Hon 8, Pan 6, Jam 5. The USA would have a 10-point lead over Panama and an 11-point lead over Jamaica, both insurmountable with three matches to play. As noted, it would not be possible for all of Costa Rica, Mexico, and Honduras to catch the USA. The USA would therefore clinch direct advancement to the World Cup. Similarly, if the USA wins in Costa Rica, Mexico draws Honduras, and Jamaica draws Panama, that would leave the standings at USA 16, CR 11, Mex 9, Hon 8, Pan 7, Jam 4. As before, the USA's lead over Jamaica would be insurmountable with three mathces to play. As before, it would not be possible for all of Costa Rica, Mexico, and Honduras to catch the USA. Therefore, for the USA not to clinch direct advancement to the World Cup, Panama would have to catch the USA. Panama could only do so by running the table, giving Panama 16 points, but requiring Honduras and Mexico to lose to Panama. Honduras would have only 6 available points left (3 against Costa Rica and 3 against Jamaica), restricting Honduras to at most 14 points, not enough to catch the USA. Mexico would have only 6 available points left (3 against the USA and 3 against Costa Rica), restricting Mexico to at most 15 points, not enough to catch the USA. Therefore, if the USA wins in Costa Rica, Mexico draws Honduras, and Jamaica draws Panama, it would not be possible for Panama and two other teams to catch the USA. As noted, it would also not be possible for all of Costa Rica, Mexico, and Honduras to catch the USA. The USA would therefore clinch direct advancement to the World Cup. Instead, if the USA wins in Costa Rica, Mexico draws Honduras, and Panama defeats Jamaica, that would leave the standings at USA 16, CR 11, Mex 9, Pan 9, Hon 8, Jam 2. Panama could catch the USA with wins against the USA and Honduras and a draw against Mexico; Mexico could catch the USA with wins against the USA and Costa Rica and the aforementioned draw against Panama; and Costa Rica could catch the USA with wins against Jamaica and Honduras. The USA would not mathematically clinch advancement. Similarly, if the USA wins in Costa Rica and Mexico defeats Honduras, that would leave the standings at USA 16, CR 11, Mex 11, Hon 7 (ignoring Panama and Jamaica). Honduras could catch the USA with wins against Panama, Costa Rica, and Jamaica; Mexico could catch the USA with wins against the USA and Panama; and Costa Rica could catch the USA with wins against Jamaica and Mexico. The USA would not mathematically clnch advancement. Similarly, if the USA wins in Costa Rica and Honduras defeats Mexico, that would leave the standings at USA 16, CR 11, Hon 10, Mex 8 (ignoring Panama and Jamaica). Honduras could catch the USA with wins against Panama and Jamaica; Mexico could catch the USA with wins against the USA, Panama, and Costa Rica; and Costa Rica could catch the USA with wins against Jamaica and Honduras. The USA would not mathematically clinch advancement. If the USA draws or loses in Costa Rica, the USA cannot mathematically clinch anything on the first September matchday, not even fourth place or better. (Well, a draw would give the USA 14 points, and 14 points clinches no worse than fifth in the hex, because the maximum total points in the hex is 47 + 36 = 83, which is less than 6 times 14, but who cares.) We'll see that the USA can finish in fifth place after a draw in Costa Rica, considering Jamaica either defeating Panama or failing to defeat Panama, and ignoring the Mexico-Honduras result (which turns out to be irrelevant to the USA trying to mathematically clinch fourth place with a draw.) Of course, if the USA can finish in fifth place after a draw in Costa Rica regardless of the results of the other two matches on the same day, the USA can certainly finish in fifth place after a loss in Costa Rica regardless of the results of the other two matches on the same day. If the USA draws in Costa Rica and Jamaica defeats Panama, the USA could still finish in fifth place. That scenario would leave the standings at USA 14, Costa Rica 12, Mexico at least 8, Panama 6, Jamaica 5 (ignoring Honduras). Jamaica could catch the USA with wins against Costa Rica, the USA, and Honduras; Panama could catch the USA with wins against Honduras, Mexico, and the USA; Mexico could catch the USA with wins against the USA and Costa Rica; and Costa Rica could catch the USA with a win against Honduras. The USA would not mathematically clinch fourth place or better. If the USA draws in Costa Rica and Panama defeats or draws Jamaica, the USA could still finish in fifth place. That scenario would leave the standings at USA 14, Costa Rica 12, Mexico at least 8, Panama at least 7, Honduras 7 (ignoring Jamaica). Panama could catch the USA with wins against Mexico and the USA and a draw against Honduras; Honduras could catch the USA with wins against Costa Rica and Jamaica and the aforementioned draw against Panama; Mexico could catch the USA with wins against the USA and Costa Rica; and Costa Rica could catch the USA with a win against Jamaica. The USA would not mathematically clinch fourth place or better. As for realistic possibilities -- no longer concerned with mathematical guarantees -- they don't appear to have changed much. 17 points will still almost certainly advance the USA directly to the World Cup, and I still imagine that 16 points would also likely have that result. I would still be suprised to see the USA earn 14 or more points and fail to at least end up in a playoff with New Zealand. For further analysis of realistic possibilities, check with people who run simulations.
Great work from the Dr. G, but let's keep it simple: Matchday 7 clinching scenarios: USA win in Costa Rica AND Mex/Hon DRAW + Jam win/draw at Panama. Then we are in and can have a party in Columbus against Mexico, if that scenario plays out, we'd go into Columbus with the table looking like this: USA: 16; CR: 11; Mex: 9; Hon: 8; Pan: 7; Jam: 3 A USA win, with Honduras besting Panama in SPS and CR winning at Jamaica would give us this: USA: 19, CR: 14, Hon: 11: Mex 9, Pan 7, Jam 3. Mexico would host Panama next and travel to Costa Rica for the finale. Tons of pressure to win at home, else rely on an already qualified USA to do them a favor and win Panama, and that would only likely get El Tri 4th. Even juicier scenario: Matchday 7: CR/USA = Draw. Pan/Jam = Pan win; Mex/Hon = draw. Hex Standings: USA = 14, CR = 12, Mex = 9, Pan = 9; Hon = 8, Jam = 2. A USA win in Columbus, CR wins at home over Jamaica, and the table would look like frightening for El Tri if Honduras beats Panama. Hex Standings: USA = 17, CR = 15, Hon = 11, Mex = 9 (Pan, @CR), Pan = 9 (@Mex, USA).
Sloppy, sloppy work. I reached the right conclusion, but my argument had a flaw. The only way for the USA to have earned 18 points at that time was to earn two further wins and two further draws. In the two draws, there are 2 points available each, for a total of 4 points available. In the other 12 remaining matches in the hex at that time, there were 36 points available. So there would have been 40 total points available. 33 + 40 = 73, which is greater than 72. The reason that 18 points would have sufficed is more complicated than in my first explanation. Costa Rica, Mexico, and Honduras could not have all caught the USA at 18 points at that time. At that time, the USA had 10 points. At that time, Costa Rica had 8 points. At that time, Mexico had 8 points. At that time, Honduras had 7 points. Among them, Costa Rica, Mexico, and Honduras had 23 points. Among them, Costa Rica, Mexico, and Honduras had 11 matches remaining. Of those 11 matches remaining, 3 were against the USA. If the USA were to get to 18 points, of its five remaining matches, it would have needed to win two and draw two. It could win the two matches against teams other than Costa Rica, Mexico, and Honduras, but in two of the three matches against Costa Rica, Mexico, and Honduras, the USA would need to at least draw. So in the 11 matches remaining, Costa Rica, Mexico, and Honduras would have 24 points available in the 8 non-USA matches, but only 5 points available in the 3 USA matches. 24 + 5 = 29, and 23 + 29 = 52, which is less than 18 + 18 + 18. So there was no way for the USA to end up on exactly 18 points and have Costa Rica, Mexico, and Honduras all also end up with 18 or more points. Costa Rica, Mexico, and Panama could not have all caught the USA at 18 points at that time either. Among them, they had 11 matches remaining, of which 3 were against the USA. As before, that would leave only 29 points available for Costa Rica, Mexico, and Panama. Among them, Costa Rica, Mexico, and Panama had 22 points. 22 + 29 = 51, which is less than 18 + 18 + 18. So there was no way for the USA to end up on exactly 18 points and have Costa Rica, Mexico, and Panama all also end up with 18 or more points. No other group of three teams could catch the USA at 18 points. All other groups of three non-USA teams had at most 21 points among them (Costa Rica's 10, Honduras's 7, and Panama's 6 were the most available). 21 + the USA's 10 + 40 = 71, which is less than 72. So there was no way for any other group of three teams, plus the USA, to earn 72 or more points if the USA earned 18 points. So 18 points did indeed suffice for the USA to clinch direct advancement to the World Cup (and 18 points still suffice), but for a more complicated reason.
A BigSoccer poster, who is also well-known outside BigSoccer, made an interesting point on Twitter that hadn't previously occurred to me: Way to go USA.Now we need only 5 points to qualify for Brazil. Or 4 points if they are all earned by draws.— Mix Diskerud (@MixDiskerud) June 19, 2013 miklagard (as he's known at BigSoccer) is correct; with four more draws, the USA will mathematically clinch direct advancement to the World Cup. (He's also correct about needing only 5 more points, as 13 + 5 = 18, which, as noted above, always suffices.) With four more draws, the USA would have 17 points. Costa Rica would have 12 points plus the points it earns from the three non-USA matches. Mexico would have 9 points plus the points it earns from the three non-USA matches. Honduras would have 7 points plus the points it earns from its four remaining matches, none of which involve the USA. Panama would have 7 points plus the points it earns from the three non-USA matches. (Jamaica, which can only earn 14 points at most at this point anyway, would be irrelevant.) Panama would no longer be able to catch the USA, because 7 + 9 = 16, which is less than 17. Mexico and Honduras would not both be able to catch the USA, because Honduras would need at least three wins plus a draw to catch the USA, leaving only 7 more points for Mexico (the draw with Honduras plus wins in the other two non-USA matches.) 9 + 7 = 16, which is less than 17, so there would be no way for both Mexico and Honduras to catch the USA. So only Costa Rica plus either Mexico or Honduras -- but not both -- could catch the USA. So the USA would mathematically clinch advancement with four more draws.