Four points is not enough

The World Cup just started. As you may know, there are 32 teams, in eight groups of four. Each team in a group plays three games, one against each of the other teams in the group. The top two teams in each group advance to the “knockout round” of 16; teams get three points for a win, one point for a draw, and no points for a loss, so the most points a team can have is 9, the least is 0. (It’s not possible to get 8 points, but every other number is possible.)

So how many points is enough to advance?

With a quick Google I found this article from the Hindustan Times in 2018, saying that traditionally people think four points is enough, but in practice, 17 out of 33 teams with four points were in the top two in their group between 1994 and 2014. (By my count it’s 18 out of 35, which doesn’t materially impact the conclusion.). “Three points for a win” was introduced in the 1994 World Cup, so this is as far back as it’s meaningful to go.

Similarly, in the run-up to the current tournament, Fox Sports Australia writes: “Four points is really that magical mark that they need to aim at. You can miss the top two of your group with four points – 10 teams have done it across the last four World Cups – but the overwhelming majority of teams that reach that figure make it out.”

But if you stop to think about it for a moment, a win, a loss, and a draw (which is the only way to get four points) is a middling result, and you need to be in the top half to advance… this is best illustrated by 1994 group E, where all four teams got four points, and of course only two advanced.

And in Slate a couple days ago, Eric Betts wrote: “One win, one draw and one disheartening loss might be enough to get to the knockout rounds, but not necessarily. Two teams with four points advanced in 2018 and one—Iran—was sent home.” (There’s a slight error here – Argentina and Japan advanced with four points, Iran and Senegal didn’t.)

But if we go through and tabulate all 54 groups in the 1994 through 2018 World Cups (six groups in 1994, eight in each of 1998-2018) we really see that four points is not enough. Here’s a table of the teams by their rank in group and their number of points.

There’s an interesting anomaly here. Teams have not made the top two with six points – in 1994 both group D and group F had the point totals 6-6-6-0, with one team that was beaten by each of the other three, while the other three had a “cycle” of wins. (The third-place team in each of those groups advanced to the knockout round – in 1994 there were only six groups, as opposed to the current eight, so the top four third-place teams also advanced to the knockout round.). But no team has ever failed to advance with 5. (This is possible – a group where team A loses to B, C, and D, and all three games among B, C, D are ties, would have point totals 5-5-5-0.)

So you need five points to win (unless something weird happens.). Four is not enough.

When do the polls close for most people?

I tried to Google this and couldn’t – how many people live in places where the polls close tonight at time X, for each possible value of X? You can easily find a map of closing times, for example at 270towin.com:

But how many people do each of those colors represent?

The Green Papers has a nice table of poll closing times. The wrinkle is that in a state with multiple time zones, there are two possibilities:
  • polls close at the same clock time across the state. For example, in Florida, polls close at 7:00 PM everywhere in the state… as we learned in 2000 when it was called for Democrats before polls in the Panhandle (the westernmost part of the state, the only part on Central time, and a heavily Republican area) had closed. This is the method in Alaska, Florida, Idaho, Kansas, Kentucky, Michigan, North Dakota, South Dakota, and Texas.
  • polls close at the same real time across the state. This is what Nebraska does (8 Central / 7 Mountain) and Tennessee (8 Eastern / 7 Central).
We need to make some assumptions about what proportion of each split state is in each time zone. Fortunately, someone named “segacs” made a Sporcle quiz in 2015 which counted the population in each time zone worldwide, and broke down the results in a Google spreadsheet. We can just extrapolate those results forward – Tennessee was 34% Eastern time and 66% Central according to 2015 Census data, so we’ll just carry that forward to 2020. If everybody’s been leaving Knoxville and Chattanooga to move to Nashville and Memphis, we won’t know.

As it turns out, in most places the polls close at 7 or 8 local time, and those represent about equal numbers of people. The exceptions are:

  • Kentucky and Indiana (6 pm local)
  • North Carolina, Ohio, West Virginia, and Arkansas: 7:30 pm local
  • New York and North Dakota: 9 pm local. (Is there anything else New York and North Dakota have in common?)

The overall distribution is in the chart below.

And in Eastern-time terms, the distribution is:

Both of these charts and the underlying data are at this Google spreadsheet.

This should be familiar to people who make a habit of watching the election returns roll in… you get the first substantial votes at 7, a big chunk at 8, and they trickle in over the rest of the night. (In presidential years the 11:00 chunk isn’t as interesting as you’d expect from its volume – the only polls closing at 11 are California, Oregon, Washington, and small portions of North Dakota and Idaho, and if any of those states are competitive the election as a whole is not.)

Too small to show on the chart is the polls that close at 1 AM. Those are the polls that close at 8 PM (Hawaii-)Aleutian time (UTC-10, five hours behind Eastern time), in that part of the Aleutian Islands of Alaska west of 169° 30′ W longitude. In terms of populated places it looks like this is a really long-winded way of saying Adak. Adak has 326 people. The biggest settlement in the Aleutians, Unalaska, is only at 166° 32′ W and is therefore in UTC-9, “Alaska time”. Brian Brettschneider, Alaska-based climatologist, called out Adak in 2016:

https://platform.twitter.com/widgets.js

and at least a cursory look at a list of Alaska polling places suggests there are two in the Aleutians, “Aleutians No. 1” in Adak and “Aleutians No. 2” in Unalaska. It seems quite reasonable that there is only one polling place, the one in Adak, that closes at 1 AM Eastern. This oddity has been mentioned before, in 2012 and 2016, in both cases by local sources. In 2016 five people voted after 8 PM Alaska / 7 PM Aleutian (midnight Eastern).

Not that anything will be called in Alaska when the polls close… Alaska uses ranked-choice voting, so it’ll take a while to count the votes anyway.

Does Game 3 have some special magic?

Saw a “statistic” during game 3 of the World Series yesterday – teams that have won Game 3 have gone on to win 68 times out of 98 (69%).

First of all, 98 is a strange denominator there… that would be “since 1923”, but the first World Series was played in 1903! But 1922 was the last time there was a tied game in a World Series, so is this presumably 1923 through 2021 (99 years) with the exception of 1994?

You can find this statistic in, for example, this CBS Sports item or this tweet from @MLB: https://platform.twitter.com/widgets.js

Okay, turns out I misheard it – it’s the winner of all Game Threes in best-of-seven MLB postseason series when the first two games were split 1-1.

So is this surprising? Not really… the winner of such a Game Three has to win at least two out of the next four to win the series. If games are coin flips, that happens 11/16 of time (69%). Game Three doesn’t have some special magic… it’s just the a 2-1 lead is substantial.

This post should be going out at the first pitch of Game 4. Go Phillies!