World Cup Permutations/Computations: What teams need to advance to Round of 16

The time has come. The time has come to break out your calculators and pencils, maybe a little scratch paper, too, because it's time to do some math. Eight teams are already eliminated, and six teams are through -- but their positioning in the Round of 16 is unknown right now.

Everything will be known by 4 p.m. on Thursday.

Until then, we've already figured out what each team needs to advance, keeping a running tally over the second series of matches. We've checked the math, double-checked, and even triple-checked ... and I had Tom Benedetto check it, too.

Group A

Russia (2-0-0, 6 points, +7 goal difference), Uruguay (2-0-0, 6, +2)
Eliminated: Egypt, Saudi Arabia

Even with both teams through to the knockouts, there is still plenty to play for in this group, seeing as there is still positioning at stake -- and both play each other Monday. Russia can’t be caught on goal difference, and a Russia win or a draw keeps things as they are: Russia would win the group on goal difference with a draw, and by three points with a win. The only way the table changes is if Uruguay wins to take the top spot in the group.

Group B

Spain (1-0-1, 4, +1), Portugal (1-0-1, 4, +1), Iran (1-1-0, 3, 0)
Eliminated: Morocco

With three teams in the mix in Group B, Monday’s second set of matches are expected to be full of drama, and I may have to rig up my spare TV (or stream it on my phone; not like I haven’t done that before) to keep up with both. Spain plays already-eliminated Morocco, while Portugal gets still-alive Iran. The easy math is Spain wins, Portugal or Iran win, and the winners advance.

But with the World Cup that we have on our hands, nothing is simple. Both Spain and Portugal are level across the board, with points, goal difference, and number of goals scored in the group (four apiece) all being equal, and with the next three tiebreakers also washing out, it comes down to discipline, also known as Fair Play points – and better known as cards issued.

Fair Play points break down as follows:

A player’s first yellow card: minus 1 point
An indirect red card (the second yellow for a player): minus 3 points
A direct (straight) red: minus 4 points
A yellow card and a straight red: minus 5 points

Spain is at a -1 in Fair Play points, while Portugal is at -2, so as it stands, Spain is in first, and Portugal second. Should Spain and Portugal produce equal positive results (win or a draw) on Monday in both goals scored and points, i.e. matching 2-0 wins, both will go through, but the positioning will be decided by the number of cards issued to each. If everything is even, the next tiebreaker is the drawing of lots by FIFA. No one wants that. If one gets a 2-0 win and the other a 1-0 win, the 2-0 win is the group winner.

Of course, Iran could shock the world — and after last Wednesday, I’m not counting that out — and beat Portugal, which would see the Melli advance to the knockout stage for the first time ever.

Should both Spain and Portugal lose, the team that gets is the team that lets in the least goals — or is the team that keeps its cool when it comes to fouling.

Group C

France (2-0-0, 6, +2), Denmark (1-0-1, 4, +1), Australia (0-1-1, 1, -1)
Eliminated: Peru

France is through, but there is still a question of which side of the bracket it will be next weekend. A win or a draw against Denmark on Monday will be enough (a win will be plenty) to give France the group. A loss to the Danes will see both sides through, with France in second. A draw will also see both sides through, with France first, Denmark second.

But there is still the wild card in all of this, and that wildcard is Australia.

Australia is still alive, but will need to take care of its own business against Peru on Monday — a draw will not be enough — to remain in the conversation. An Aussie win and a two-or-more-goal France win would tie Australia and Denmark on points (4), but those two results would see the Socceroos through to the knockouts on goal difference.

For example, a 1-0 Aussie win and a 2-0 France win, or vice versa, or 3-1 to France, or 4-2 to France, would trigger that scenario. France would be first on nine points, and Australia would be second.

An Aussie win and a France win on matching 1-0 scores puts the Aussies through on goals scored; both Australia and Denmark are currently at two goals apiece in the group. If we have a shootout that sees Australia win by one and France win by one, whichever scores more is through; a 5-4 Australia win and a 5-4 France win sends the Aussies through, while a 1-0 Aussie win and a 3-2 France win sends the Danes through. A 1-0 Aussie win and a 2-1 France win puts both Australia and Denmark at three goals scored each, and with the 1-1 draw Wednesday, the tiebreakers skip to Fair Play points.

A Peru win by any margin or a draw would eliminate Australia.

Group D

Croatia (2-0-0, 6, +5), Nigeria (1-1-0, 3, 0), Iceland (0-1-1, 1, -2), Argentina (0-1-1, 1, -3)

Croatia is already through with six points. Nigeria has the advantage right now, and a win against Argentina will see it through to the knockout stages. A draw against the Albicelestes can do it, too, with two scenarios: Croatia wins or gets a draw in the other match to eliminate Iceland; Iceland can win and a Nigeria-Argentina draw can still allow Nigeria to advance, provided Iceland doesn't win by three goals to erase the goal difference. A Nigeria draw and an Iceland win of two goals will trigger the head-to-head tiebreaker, which goes to Nigeria.

Iceland has the edge in goal difference on Argentina: if Iceland beats Croatia and Argentina beats Nigeria, Iceland goes through if Argentina doesn't score two or more goals than Iceland does.

Argentina goes through with a win over Nigeria, a Croatia win, or a Croatia-Iceland draw; it can also go through if it and Iceland both win, provided Argentina wins by two more goals than Iceland wins.

Group E

Brazil (1-0-1, 4, +2), Switzerland (1-0-1, 4, +1), Serbia (1-1-0, 3, 0)
Eliminated: Costa Rica

With Brazil and Switzerland in the lead, the easy computation for them is simple: win their games Wednesday, and both go through to the knockout stages. But since Brazil takes on Serbia, that match will be tense as Serbia wants to advance, too. Simply put: the winner of Brazil-Serbia is through; a draw is enough for Brazil, though. A draw is not enough for Serbia, unless Costa Rica beats Switzerland by two goals. If that happens, Brazil would be through on five points, and Serbia would be through on four points and goal difference.

Now … should Brazil and Switzerland both win, but Brazil wins 1-0 and Switzerland wins 2-0: they would both go through on 7 points, but they would also be tied on goal difference. Switzerland would go through in first as it would have scored more goals in the group. That Neymar goal Friday was uber important, as twin 1-0 wins by those two squads would see Brazil go through as top.

Group F

Mexico (2-0-0, 6, +2), Sweden (1-1-0, 3, 0), Germany (1-1-0, 3, 0), South Korea (0-2-0, 0, -2)

Mexico will be safely through with a win or a draw against Sweden in Wednesday’s final group stage games. A Sweden win, provided Germany loses, will send both Sweden and Mexico through, regardless of the goal difference. If Germany beats South Korea, it will need a Mexico win or a draw; if Germany wins and if Sweden wins by two goals, Germany and Sweden are through. South Korea is still alive, but barely: it needs to beat Germany and needs Mexico to beat Sweden, with the goal difference in the matches totaling three in favor of South Korea.

Group G

England (2-0-0, 6, +6), Belgium (2-0-0, 6, +6),
Eliminated: Tunisia, Panama

Very simple: Whoever wins between Belgium and England takes the top spot. Right now, they are separated via Fair Play, with England at -2 and Belgium -3.

Group H

Japan (1-0-1, 4, +1), Senegal (1-0-1, 4, +1), Colombia (1-1-0, 3, +2)
Eliminated: Poland

Japan and Senegal are obviously in the driver’s seat, and with the Lions of Teranga taking on Colombia, all eyes will be on that one. Senegal just need a draw to advance, but Colombia will play for the win. A draw would help Colombia as long as Poland hold Japan. A Japan win will see the Samurai Blue through; a draw can do it, too, as long as Senegal beats Colombia.