World Cup 2018: Who has the toughest route to the final?

The World Cup has a habit of creating strange incentives at the end of the group stage. In 1982, West Germany and Austria famously sleepwalked through the majority of a 1-0 German victory in their final group match, one which pushed them both through at the expense of an Algeria team which had won the previous day. To prevent that from happening again, FIFA began to play the final matches from each group concurrently.

On Thursday, we saw the method's limitations. With Colombia beating Senegal, Japan recognized that they would be able to go through to the knockout round under FIFA's fair play tiebreaker by avoiding yellow and red cards. They and an already-eliminated Poland side played the final 20 minutes of their match with the intensity of two teams trying not to wake up a sleeping child.

For Belgium and England, the die was cast before their match ever began. Both teams were guaranteed to go through and, even on every single FIFA tiebreaker, both sides knew the consequences of winning. A draw would see the winner of the group determined by either the fair play tiebreaker or, barring any gap there, a drawing of lots. The winner of the group would end up on the tough side of the bracket, likely facing a quarterfinal appearance against Brazil and a semifinal against Argentina, France or Portugal.

The loser, on the other hand, might not encounter anybody tougher than Spain on their side of the bracket, and even the Iberian side would have to wait until the semifinal. Both teams rightly saw the benefits in losing and turned over virtually their entire starting XIs. When England went down 1-0 to a goal by Adnan Januzaj, U.K. bookmakers improved their odds of winning the tournament from 8-1 to 6-1. England lost. So they won. I think.

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While some will fret about England losing their momentum heading into the knockout round, there isn't much in the way of recent evidence suggesting a 3-0 group stage is a precursor to World Cup glory. Manager Gareth Southgate was also able to rest many of his primary contributors in advance of the round of 16, where the Three Lions will go up against Colombia. A win, on the other hand, would have placed them against the less-fancied Japan team, which ranks 45 spots below Colombia in 61st in the most recent FIFA rankings.

Should England have been so desperate to end up on the easier side of the bracket just two years after they were eliminated in a similar situation by Iceland? Is the trade-off of a more difficult round-of-16 matchup for an easier path to the final worth it? How difficult is that side of the bracket, anyway? Is Belgium -- or any team from that side of the 16 -- facing a historically difficult path to the final? Let's find out.

Were England better off losing?

We'll never truly know whether England should have benched most of their starters against Belgium. The only way we could be sure Southgate made the wrong move would have been if he had played his first-choice XI and lost while seeing an irreplaceable star like Harry Kane go down with a tournament-ending injury. Thankfully, that didn't happen. To estimate England's chances in either scenario, we can use the win probabilities generated by FiveThirtyEight using the Soccer Power Index to figure out England's chances of advancing on either side of the bracket.

In the round of 16, England are guaranteed to have a tougher matchup than they would if they had won against Belgium. Colombia simply has more top-level talent than Japan; even if you removed the clearly unfit James Rodriguez from the equation, the 22 men remaining in Colombia's national team are worth more than twice as much as Japan's 23-man roster, per Transfermarkt.

FiveThirtyEight, without knowing about Rodriguez's fitness, estimates that England have a 60 percent chance of winning against Colombia on Tuesday. On the other hand, if they had finished top and faced Japan, their chances of winning and advancing would be 72 percent. That's a significant difference, and if England go out in the round of 16, Southgate's going to be slaughtered in the press for rotating his team against Belgium.

Once we get to the quarterfinals, though, we begin to see why England find themselves in better shape. In their current bracket, a victorious Kane & Co. would be favored to beat either of their possible opponents, Switzerland (62 percent chance of winning for England) or Sweden (63 percent). Had they faced Japan and won, though, they would get the winner of Brazil and Mexico, which is likely to be the South American giants, against whom England would have just a 36 percent chance of advancing. FiveThirtyEight assigns them a 67 percent chance of beating Mexico, far closer to their chances against Switzerland and Sweden.

If they make it to the quarterfinals of their current bracket, England have a 62.5 percent shot of moving on. If they were on the other side, though, their chances of advancing to the semifinals would only come in at 41.3 percent.

After that point, England's odds in the semifinals would be relatively similar regardless of which bracket they're in. In this version of reality, their most likely opponent is Spain, who FiveThirtyEight sees as favorites against England (38 percent win expectancy for England) despite a middling performance in the group stages. Southgate's team would otherwise be favored against Croatia, Denmark or their Russian hosts. They would have a 47.6 percent shot of making it from the semifinals to the final in Moscow.

Having made it past Brazil in the alternate reality, England would be essentially a coin flip against each of their four possible semifinal opponents, ranging from France (47 percent chance of winning for England) to Uruguay (56 percent), with Argentina (50 percent) and Portugal (52 percent) in between. England would have a 50.7 percent chance of advancing out of this final four to the final at the Luzhniki on July 15.

And then, in the World Cup final, England would be an underdog on both sides of the bracket, although not by much. In this reality, the likelihood of England facing Brazil in the final leaves them with a 45.2 percent shot of coming away with their first title since 1966. If they were on the other side of the bracket and facing the likes of Spain or Belgium in the final, their chances of winning a one-off final would improve to 49.0 percent.

In three of the four knockout rounds, England's odds would have been better by winning against Belgium and heading into the more difficult side of the bracket. By using conditional probability, though, we can see that the chances of playing Brazil in the quarterfinals on that side of the bracket make it more advantageous for England to have lost.

In all, while Southgate's team has a greater shot of crashing out after four matches in the round of 16, England increased their chances of winning the tournament by about 9.5 percent (0.7 percentage points) through losing to Belgium on Thursday. Their cumulative schedule isn't easier -- Belgium actually has a slightly easier slate if we include the final -- but avoiding Brazil for as long as possible is the best possible path for England to exceed expectations in Russia.

Who has the toughest path through the knockout stage to glory?

We can calculate the difficulty of each team's path toward the World Cup by using a combination of those advancement probabilities from FiveThirtyEight and the World Football ELO ratings, which uses the ELO system most commonly seen with regard to chess to rate each country's effectiveness. The system has data on international matches going back through 1930 and, crucially, its website displays ELO ratings for each country heading into each World Cup. More on that later.

Each team has already played three countries, so they've already been subject to some dramatically different degrees of difficulty. Through the group stage, Switzerland's opposition has faced an average ELO of 1888, which is the toughest among the 16 qualifiers and roughly equivalent to, well, playing Switzerland three times in a row. (Note that these numbers are all pre-tournament figures.)

Uruguay, meanwhile, have gone up against opposition with an average ELO of just 1638, which would be slightly worse than the pre-tournament ELO of Egypt (1646).

Using those probabilities, we can estimate each team's path to (and through) the final and the difficulty of the schedule they might face along the way. As an example, England have the 12th-most-difficult slate of the 16 remaining teams. Here's how we would calculate their overall strength of schedule, including the group stage and the knockout rounds.

When you run through these probabilities for each team and each possible World Cup opponent, you can find how difficult their respective paths might be.

The easiest remaining schedule belongs to Spain, who went top of Group B in the final minutes after scoring to equalize their match against Morocco, while seeing Iran tie things up with a penalty against Portugal. These numbers don't include home-field advantage, which should help Russia some, but Spain are still comfortable favorites against the hosts.

That doesn't change anywhere else, actually; FiveThirtyEight suggests Spain have a win expectancy of 60 percent or more against everyone else on their current side of the bracket. Fernando Hierro's team haven't looked terribly impressive in Russia, but the friendly schedule is one of the reasons they are among the tournament favorites with bookmakers. Brazil also benefit from avoiding themselves throughout the tournament, as they'll have the second-easiest slate the rest of the way.

The toughest knockout-round slates, unsurprisingly, all belong to teams on the tougher side of the bracket. France (fifth) and Argentina (fourth) entered the tournament within one ELO point of one another, and while France have been the far more impressive of the two in Russia, the Argentines might eventually be able to figure themselves out.

The winner between these two will have to face the winner of Uruguay-Portugal before a likely semifinal matchup with either Brazil or Belgium. If Spain advance to the final, a country like Argentina might have to win the World Cup by beating teams ranked first, third, fourth, and sixth in the world over four consecutive matches.

While they were saved from an ignominious collapse out of the group stage by a heroic display from South Korea, Mexico's disastrous 3-0 defeat at the hands of Sweden pushed El Tri to the tougher side of the bracket and a round-of-16 match against Brazil. FiveThirtyEight estimates Mexico to have just a 17 percent chance of knocking off the five-time world champions Monday. If they had held on to win their group, and faced Switzerland instead, Juan Carlos Osorio's team would have had a 57 percent shot of progressing into the quarterfinals. Now they face the third-toughest path through the knockout stage.

Slightly tougher is Uruguay, who became the first team since 2010 to make it through the group stage without allowing a single goal. With Egypt's Mo Salah sitting out the opener, the most dangerous attacker Uruguay faced during the group stage was probably Russia fill-in Denis Cheryshev, but their stout defence might have to keep out Cristiano Ronaldo, Lionel Messi and Neymar in consecutive matches to advance to the final. The two-time champions would be underdogs against every team on their side of the bracket, short of Mexico and Japan.

Speaking of Japan, they're the team with the toughest slog through the knockout stage, in part because they're the lowest-ranked side on the tough side of the bracket. (Russia, safely ensconced on the friendly side, are the worst team remaining in the tournament by pre-World Cup ELO.) They are an underdog against every team left per FiveThirtyEight's numbers, although the one bright spot for Japan is that their best remaining matchup is against Mexico, whom they would face in the quarterfinals if El Tri upset Brazil.

Who is likely to face the toughest overall schedule throughout the tournament if they win the whole thing, and would it be the toughest set of opponents in World Cup history?

The answer to that, sadly for Landon Donovan, is Mexico. When we combine the group-stage and round-of-16 ELO with the projected opponent ELO for each of the three subsequent rounds, Mexico will need to run through the most difficult set of opponents to win this World Cup. The combined projected ELO of their opposition would add up to 13,509 points, or an average of 1,930 points per match. That's like having to play Colombia (ELO of 1928) or Belgium (1939) seven times in a row.

While we have ELO figures going back through the 1930s, it's only really fair to start comparing present-day World Cup teams to their older brethren in 1974, which was the first year countries needed to play seven games en route to claiming the famous trophy. As you might suspect from the reduced tournament field size, many of the most difficult paths toward the World Cup came at the beginning of this era. If Mexico were to make it to the final, they would project to have the fourth-toughest schedule of the seven-game era.

While the 1978 Argentina team got to play the World Cup at home, they faced an incredibly difficult slate of opponents. By pre-tournament ELO, their group contained teams ranked eighth (Italy), 12th (Hungary) and 14th (France) in the world at the time. Their second group included third-ranked Brazil and ninth-ranked Poland, although they also got a let-off with 25th-ranked Peru. The final match came against the Netherlands, who narrowly trailed West Germany as the best team in the world.

More recently, while Germany left this tournament in shame, consider what they did in 2014. On their way to the World Cup, they beat the world's best team, Brazil, 7-1 on home ground. You might have heard about that one already. In addition, though, Germany beat Argentina (fourth), Portugal (sixth), France (11th) and the United States (13th), with those five wins coming by a combined score of 14-1.

While Mexico's expected path to a would-be World Cup would only be the fourth-most-difficult run of the past 44 years, we can certainly construct a scenario in which they face a record slate. If Mexico win each of their games but the tournament otherwise stays chalk, with each of the favorites winning their respective games, El Tri would face a breathtakingly difficult group of opponents.

All Hirving Lozano & Co. would have to do to set a new record is beat the four best teams in the world, including three in a matter of two weeks. The good news, I suppose, is that they won't come any tougher than the Brazil side Mexico faces Monday in Samara.