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FiveThirtyEight

Brazil defeated Croatia 3-1 in the opening match of the World Cup on Thursday — while looking about as bad as it could while winning by that scoreline. Its go-ahead goal came on a penalty kick following a dubious call by referee Yuichi Nishimura. Its third goal perhaps ought to have been stopped by Croatian goalkeeper Stipe Pletikosa. And the one it conceded was an own goal by Marcelo.

FiveThirtyEight’s World Cup forecasts have been updated to reflect the results of the match, as they will be at the conclusion of each game. The projections don’t account for style points — it’s the scoreline that matters — so Brazil won’t be harmed by winning ugly.

A bit more about how these updates work in a moment, but one soccer-related thought first. Some of Brazil’s edge — it had an 88 percent chance of beating Croatia in our pre-match predictions — was because of home-field advantage. Some of that advantage, as Tobias Moskowitz and Jon Wertheim have found, comes because home teams are more likely to benefit from refereeing decisions. Soccer has an especially large home-field advantage, in part because the officiating plays such a large role in the sport, especially in calling penalties and issuing red cards. Would Nishimura have made that (mistaken) penalty call had the game been played in Dubrovnik, rather than Sao Paulo? We’ll never know for sure, but the odds say it’s less likely.

Back to our forecasts: Technically speaking, there are two programs that our colleagues at ESPN Stats & Info run to generate our World Cup forecasts. One program is a match simulator that plays out the results of the rest of the tournament 10,000 times. The other is the Soccer Power Index algorithm itself, which informs the match simulator’s estimate of how strong each team is.

We’ll be running the match simulator at the end of each game (there will usually be a lag of 20 to 30 minutes before we get the new results on the site). However, the Soccer Power Index (SPI) program, which is computationally intensive, runs only once per day, overnight after all games have concluded.

I’ll explain why this distinction matters by asking you to imagine that Brazil had drawn 1-1 with Croatia, rather than pulling out the win. This would hurt Brazil in two ways: First, it would increase the odds that it would fail to advance from its group. (Granted, Brazil’s odds would still be very high.) That change would be reflected immediately in our forecasts based on the match simulator.

But a draw would also have lowered SPI’s estimate of Brazil’s strength. (SPI rates recent matches heavily, and it regards Brazil very highly, so a draw might have had a fair amount of impact.) That change, however, would not be reflected until our overnight update.

There are also some other, more subtle things that can go on with SPI in the overnight updates. It’s learning more about which players a team has in its starting lineup, which reflects the player-rating component of the model. It also learns more about the relative strength of the continents. A draw for Brazil, for instance, would have (very slightly) lowered SPI’s estimate of the chances for Argentina, Colombia, and so forth, as the match would represent one data point showing that South America was not quite as strong as assumed.

As far as the actual scoreline goes — Brazil 3, Croatia 1 — it won’t do much to improve SPI’s view on Brazil, either, since SPI had Brazil winning against Croatia by slightly more than two goals on average.

Based on the results of the match simulator, however, Brazil’s odds of advancing from Group A have risen to 99.8 percent from 99.3 percent before the match. It’s usually not worth sweating the decimal places since there can sometimes be noise introduced by the match simulator — 10,000 simulations is a lot, but not enough to entirely remove the margin of error. In this case, however, the match simulator is just pointing out the obvious: It was going to be really hard for Brazil to fail to advance, and it will be even harder now that it’s picked up three points.

How much were Croatia’s advancement odds hurt? They weren’t, actually — instead, they rose slightly to 37.5 percent from 36.6 percent. Some of this probably reflects the statistical noise that I referred to earlier. However, there is one way in which the match helped Croatia: Losing to Brazil by only two goals is not such a bad result. Mexico and Cameroon, the other two teams in Group A, could lose to Brazil by larger margins. In fact, SPI has Mexico as a 2.6-goal underdog, and Cameroon as a 3.2-goal underdog. That could make a difference if the second advancement position from Group A comes down to a tiebreaker based on goal differential, as it might. And FIFA’s next tiebreaker is based on goals scored, so losing 3-1 is better than losing 2-0. I doubt the Croats will be happy with the result of Thursday’s game, however.

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