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World Cup Tiebreaker Sudoku

All my life, I have loved trying to figure out sports tiebreakers. They are like sports sudoku puzzles or the impossibly addictive 2048 game which now takes up roughly 18 hour a day for me. Tiebreakers. Magic numbers. NFL playoff possibilities. This stuff has always been fun, and in this way (and in only this way) the shocking (and, grrr, brilliant) last second goal by Portugal Sunday is a gift. Had the U.S. held on for just 30 more seconds, they would be through to the knockout round of the World Cup.

As it stands, the Portugal draw offers the opportunity to unlock the tiebreakers.

Here is the United States group as things currently stand:

Goals Against

OK, that seems pretty simple. Each team only plays three matches so there are not too many possibilities here. Here is how FIFA determines what two teams advance out of each group.

1. Most points (three points for a win, one point for a draw).
2. Goal differential.
3. Most goals scored.
4. Goal difference in game(s) played between the tied teams.

There are a couple of other tiebreakers including the organizing committee “drawing lots,” which is a lot like the coin flip at the bottom of the NFL tiebreaker system. It has never come to that and, you would hope, never will. In the U.S. case, these four tiebreakers shouldl be enough to determine their fate.

We only care about the U.S. chances here but it should be noted that Germany is not quite in yet. It would take the U.S. beating Germany, probably by several goals, to put the Germans at risk, and the chances of that are so small that there’s really no point in discussing it. Germany is almost certainly in. With a draw or better, the Germans will advance as the top team in the group

The United States is about three-quarters of the way in which is more than just about anyone could have expected after the first two games of the Group of Death. Incidentally, I’ve already written this — that whole “Group of Death” thing was pretty ridiculous overkill. The U.S. found itself in a good group, but this was no Group of Death. Group D — with Costa Rica playing absurdly well, and with former World Cup winners Italy, Uruguay and England — THAT is what a Group of Death looks like. Italy, Uruguay and Italy are ALL Top 10 teams in the FIFA World rankings and only one will advance. England, one of the most soccer-loving countries on planet earth, is at risk of losing all three of its matches and sending that great nation into another self-loathing pub crawl. Group D is the Group of Death. The U.S. group is more like the Group of Fairly Severe Back Pain.

OK, to the tiebreakers. First three scenarios are easy.

— With a win, the United States advances as the top team out of the group.

— With a draw, the United States advances as the the second team out of the group.

— If Ghana and Portugal draw, the United States advances no matter what they do against Germany.

So, those are the sure things. The United States has four points, Ghana and Portugal have only one point each. The only way either Ghana or Portugal can match the U.S. point total is to win their game and have the U.S. lose. I appreciate that I’m writing obvious things here but this is the fun of tiebreakers. Some of it is obvious. Some isn’t.

So, now, what if the U.S. loses and Ghana and Portugal do not tie? Well, let’s deal first with the less-likely threat, Portugal.

— If the U.S. loses by one goal, Portugal must win by four goals just to even up the goal differential — that’s what happens when you lose a match 4-0 as Portugal did to Germany. This is obviously very unlikely but to give an example, let’s say the U.S. loses 1-0 to Germany. If Portugal won its match 4-0, I believe Portugal would advance. I’ve seen it written in various places that Portugal would actually need to win by FIVE goals, but I don’t think that’s right.

If U.S. loses 1-0, it will have scored four goals and given up four goals.

If Portugal wins 4-0, it will have scored six goals and given up six goals.

So they would be tied on goal differential. Portugal would then advance on the next tiebreaker, which is most goals scored.

This is highly unlikely. The U.S. could make it harder on itself and lose by two or three goals. That would make the Portugal job a little easier but still not easy. There is actually a scenario that is kind of frightening. Let’s say the U.S. lost 3-0 and Portugal won 2-0. This isn’t going to happen (please!) but if it it did, there would be some madness.

In that scenario:

The U.S. would have 4 points, 4 goals, 6 goals against.

Portugal would have 4 points, 4 goals, 6 goals against.

They tied in their game so that wouldn’t make the difference. Best I can tell from the tiebreaker system I have seen, this would force FIFA to draw lots, as mentioned earlier. But it’s not going to happen so let’s not worry about it.

Bottom line: The goal DIFFERENCE between a U.S. loss to Germany and a Portuguese win over Ghana would need to be five goals to give Portugal a chance — and even that isn’t a sure thing. I have spent too much time going over a very remote possibility.

— Ghana is a whole other matter. The U.S. advantage over Portugal is a massive lead in goal differential. The U.S. advantage over Ghana is their win over Ghana.

So, if the U.S. loses to Germany 1-0, and Ghana wins 1-0, the U.S. still advances. They will have the same number of points, and their goal differential will be the same. But the U.S. victory over Ghana would be the decisive tiebreaker.

For Ghana to win on goal differential, there needs to be a three-goal difference. That part is fairly easy to follow. But what’s tricky — especially in our American mindset where head-to-head play is always the decisive tiebreaker — is that goals scored comes BEFORE head-to-head play in the World Cup. So (as brilliant reader Sean points out) if the U.S. loses 1-0 and Ghana wins 2-1, Ghana will advance NOT the United States.

If U.S. loses 1-0, they will have scored four goals and given up four goals.

If Ghana wins 2-1, they will have scored FIVE goals and given up five goals.

That means Ghana advances even though the U.S. beat Ghana.

To put it another way, for Ghana to advance over the U.S.

1. Ghana must win.
2. The U.S. must lose.
3. The goal differential in the two games needs to be three OR Ghana simply needs to score two more goals than the U.S. scores.

Anyway, I THINK that’s how it goes.

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35 Responses to World Cup Tiebreaker Sudoku

  1. If we lose 1-0 and Ghana wins 2-1, we’re out. Because they’ll have scored five goals and we’ll only have four.

  2. Jay Shumsky says:

    Hard to believe head to head record is the third tiebreaker to be used and not first.

    • Marco says:

      It’s because of the three way ties that happen all the time where A beat B, B beat C, and C beat A.

    • A lot of tie breaker scenarios occur with three ways when A beats B, B beats C and C beats A and everyone either has the same result against D.

      • Jay Shumsky says:

        I realize there can be 3 way ties, but head to head can still be the first tie breaker so if it applies, it is used and if not, then you move on to the next tiebreaker. For a tie between 2 teams, head to head should be the deciding factor if 1 team beat the other team.

        • Other Scott says:

          I’ve never liked head-to-head much as a tiebreaker. It lessens the sample size to games between those teams, rather than taking a whole sample like point/goal differential.

        • Phillip Murphy says:

          It’s not b/c of three way ties. The NFL has rules w/ dealing w/ three way ties where you pick a winner, and then start the process over again with the remaining two teams, if you need to. The argument for doing it the way FIFA does it goes something like this: You have a pool of 4 teams, and you take the best 2 of the 4…in the entire pool. So, while the US may be better against Ghana, head to head, Ghana would’ve been better against the pool. Any scenario that has Ghana advancing on ties, would mean that the US tied Portugal and lost to Germany, whereas the Ghana would’ve beaten one and tied the other (as they’ve already tied Germany). So in the non-USA-Ghana match ups, the US would’ve been 0-1-1, where Ghana would’ve been 1-1-0 (the tie being the head to head victory that results in both teams being 1-1-1); so you then break it but goal differential against the entire pool. The idea is to get the best team against the entire pool. I say this being a proponent of using head to head as the first tiebreaker. I’m just giving the logic for doing it the other way- I reiterate that I don’t agree with it.

          • Jay Shumsky says:

            If that is the reasoning behind it, I guess it makes some sense, but to me, it still seems like if you beat another team head to head, that should count for more than how you do against common opponents which is really what the other tie breakers take into account. Can you think of any other sporting event where head to head record isn’t the first tie breaker?

          • Jay Shumsky says:

            In the NFL, there are 4 teams in each division (same as the World Cup pools), but head to head is still the first tie breaker to win the division.

      • Jarid says:

        But… that just means that the tiebreaker result is a tie, and you then move on to the next tiebreaker. The fact that a tiebreaker result might be a tie does not mean that it’s always invalid.

        • Jay Shumsky says:

          I’m not saying it’s invalid because it might be a tie. I’m saying that I think head to head should be the first tie breaker. If you can’t decide based on that (2 teams tied each other, 3 teams where each one beat someone else, etc), then you need to use a second tie breaker. is there any other sporting event where head to head record isn’t the first tie breaker?

          • Jarid says:

            No disagreement here – I wasn’t replying to you, but rather in parallel to you. I simply left the page open for too long and didn’t refresh before posting to see if someone else had already the same argument as I did (which you had done). We both are making the same point.

    • David says:

      The reason goals scored is such a good tie breaker is that it offers a very strong incentive to keep scoring goals. In my opinion ii makes the games more exciting when there is still an incentive to go for goals even if you have a 2-0 lead. All teams know that it is better to win 3-2 than to win 1-0, and this should encourage teams to play more aggressively making the sport more entertaining for fans.

  3. Brent says:

    I agree that Ghana is the greater threat, but unless Portugal has zero pride, they are still the better team (by quite a lot) and SHOULD win that match

    • Jake Bucsko says:

      Brent, I don’t know. Small sample and all that, but based on what we’ve seen…Portugal was embarrassed by Germany and were also outplayed by us, and they are certainly the better team by quite a lot over us as well.

      Meanwhile, Ghana were the better team in our game with them, we were a bit fortunate to escape with the win. Two defensive lapses, one early and one late, and in between Ghana controlled much of the match. And against Germany, Ghana more than held their own. That was a well earned draw. The USA absolutely need a result against Germany, I’m very wary of Ghana swooping in and stealing our spot.

    • Martín says:

      A healthy Portugal is better than Ghana on paper, but they have had numerous injuries and they don’t have much depth (or so I’m told).

      The US found a lot of success against Portugal running up the right flank (Fabian Johnson!), and Ghana is well-equipped to do the same.

  4. Jay Stevens says:

    Before we complain too much about head-to-head match ups being the tiebreaker, it’s important to note that the current setup encourages teams to score goals.

    I’d have to look it up, but I believe these rules are fairly recent, after some especially lifeless games where teams just kicked a ball around for a tie.

    So, yeah, while head-to-head matchups as tiebreaker may be an American ideal, so, too, is scoring as much as possible…

  5. agmonaco says:

    Drawing of lots has never been used to eliminate a team, but at Italia ’90 it was used to separate the Republic of Ireland and Netherlands, both of whom had 3 draws, 3 points, 2 goals for, and 2 against.

    Sepp Blatter picked Ireland’s ball, so Ireland advanced as the 2nd placed team in the group and Netherlands advanced as the 3rd placed team (this was back when, with only 24 teams in the competition, several third-placed teams made it to the knockout stages).

    It turned out to have a big impact – as a result of winning the draw, Ireland faced Romania in the round of 16 (and won) while Netherlands had to face the eventual champions West Germany.

  6. Martín says:

    The important question here is … what’s the largest numbered tile that you’ve achieved at 2048, Joe?

    That game really is amazingly addictive. My girlfriend observed that, just as there are no clocks in casinos, 2048 doesn’t display the current time. You play for a game or three for a little while, then look up and realize that you’ve grown a beard, your dog has died, and your loyalty to King George III is strangely out of fashion.

    • adam says:

      The trick is – only move 3 directions, never a 4th. Just eliminate one direction, and you’ll win.

      • flyingdonut says:

        I’ve gotten the 8192 tile once. It was a superhuman effort that required me to sacrifice a goat. The 4096 tile is green and the 8192 tile is black, just FYI. I’ve never gotten past 2048 since.

  7. Standard tiebreakers in the US in almost every case starts with head to head. If that were the case, Ghana would have no chance of beating out the US, since the best they could hope for would be a win and a US loss, where they would lose the head to head tiebreaker. So, then the US would only need to worry about a Portugal win & US loss. The win would have to be big and the US would need to have to lose by several goals. Very unlikely. So, that “little” difference could have a huge impact. Would it make sense to the international soccer community that the US would lose out, in a tiebreaker, to a team that they had beaten? I know it makes no sense here.

    Watching the games, it is not clear that the Germans are the best team in the group since Ghana came very close to the upset and probably outplayed the Germans overall. So, Ghana hanging a number on Portugal, I think, is pretty likely. Portugal’s goals agains the US came off what the commentators called a “catastrophic” collapse of the US defense… probably the worst clear I’ve ever seen. And a perfect pass by Renaldo following yet another Bradley giveaway at midfield and a general lack of hustle by the US on the play to get back quickly (given that this was in the last minute, you’d think the US would have been a lot better at protecting the goal).

    So anyway, this is very concerning. The US needs to get at least a tie against Germany, or I think it’s quite possible that Ghana will beat Portugal like a drum & the US will be out.

  8. mark says:

    I’ve never liked head-to-head as a tie-beaker. I understand its appeal, but I look at it backwards from most. To me, It means deciding an entire season on a minority of games. And by virtue of logic and definition, if two teams are tied and one of them wins the head-to-head, then the other MUST have outperformed them on the majority of the season. I don’t expect anyone to change their mind because of this, but it is another way of seeing things.

    BUT:Ignoring our personal preconceptions for a moment, Jay Stephens has it exactly right up above. This tie-breaker system rewards teams for scoring goals. Score early; score late. Score when you have no chance of losing the current game. Score when you have no chance of winning the current game. One thing we Americans always hated about soccer was the INTENTIONAL lack of action in too many games. 0-0 ties used to be much more common, in part because of the incentive structure. And if a team was winning 3-0 with 10 minutes left both teams used to just stop bothering and listlessly kick the ball around. But now they try to score when the result of the game is not in doubt. This is all for the better.

  9. Richard Aronson says:

    These are bad conditions of contest, and “The Bridge World” magazine has discussed many of these since they, too, have numerous round robin matches where multiple teams advance. Basically, Germany and the USA could both leave the ball untouched the entire game, risk no injuries, conserve energy, hide their strategies, and both advance. In soccer, any time you push an attack you are at greater risk of a counter attack and enemy goal (as well as a greater chance of your scoring). Yes, Germany would be the first qualifier, U.S.A. the second, but we’d take that. Given the heat down there, the chance of cramps and dehydration related injuries, I think Germany would take that. If soccer changed the rules to force a winner in the third game of qualifying, then this could not happen. If they also changed the timing so the weaker game played first, it would reward the better teams in the third game by letting them know what they needed to do to advance before their game started. If Portugal and Germany are both up by one goal late, i bet the USA doesn’t risk a big loss by pushing too hard.

  10. SoDak Tony says:

    All very interesting comments, but what about the elephant in the room–the fact that Germany has absolutely nothing to play for and that a draw for sure keeps out a Portugal team that is clearly better than the U.S., and a Ghana team that is probably playing better than the U.S., if not outright superior?

    There is precedence for this:

    Not sure the Germans have any love for Klinsmann, and as Joe says, there is an infinitessimal chance that Germany could be eliminated, but even that isn’t necessarily an incentive for them to give their all–a “bargain” for a draw eliminates all risk for Gemany at zero cost.

    Is this a real issue? Almost certainly not. But it’s hard to believe that the world’s most popular, prestigious event would allow a circumstance in which something like this could even be speculated about.

    • SoDak Tony says:

      Richard beat me to it by a minute, but yeah. I like his suggestions for changing the rule for advancing.

  11. DjangoZ says:

    It’s great to read you writing about soccer. I hope it happens more often.

  12. MisterMJ says:

    These kind of things happen every now and then but at the 2009 Confederations Cup, the US were in a crazy group where advancement into the KO stages required tie-breakers. Brazil had rolled in group play, beating the US, Italy, and Egypt but there was a three-way tie for second:

    US: 1 win, 2 losses (lost to Italy 3-1, Brazil 3-0, but beat Egypt 3-0)
    Italy: 1 win, 2 losses (lost to Egypt 1-0, Brazil 3-0, but beat US 3-1)
    Egypt: 1 win, 2 losses (lost to Brazil 4-3, US 3-0, but beat Italy 1-0)

    In terms of goal-differential, the US and Italy both were -2 and Egypt -3. But the US scored more goals (4) than Italy (3) and advanced … even though Italy had won the H2H. Fairly famously, the US would go on to beat Spain in the semifinals 2-0 and would go up 2-0 at half-time in the rematch vs. Brazil, only to give up three late goals to lose in the finals. I believe Spain and Brazil were the top two countries in the FIFA rankings at that time.

  13. ozsportsdude says:

    Actually Joe FIFA have drawn Lots once before, at Italia 90 Holland and Ireland had identical records (England topped the group) however this was back in the days where 2 best performing 3rd place teams from a group got to go through so it did not cost either team progress to the knockout stage, however it did meant Holland who lost the drawing of Lots so were classified 3rd faced eventual champion Germany and Ireland got the comparatively easier game v Romania in the Rd 16

  14. David says:

    I had been thinking about this same idea all day yesterday and generated a graphic that is publicly shared in Google Drive that summarizes 81 possible outcomes of Thursday’s matches:

  15. MikeN says:

    I think drawing lots is the 7th tiebreaker, not the 5th.

  16. MikeN says:

    Shaquille O’Neal missed the playoffs his rookie season because of a deep tiebreaker, with six points scored over the season being the difference between the Magic who beat the Knicks plenty that year and the Pacers.

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