Winning the White House (the easy way)

In a bid to create a more easily accessible list of my articles for the Significance website, I'm going to start updating this thing with links to them (maybe with some bonus content if there is anything I couldn't fit in).

It's (US) election day, so here's an article about how to win the Presidency with as small a share of the popular vote as possible. In the process of doing this, I tried a few other things that I didn't think quite made the cut.

After dealing with some trivial(ish) cases, I base my calculations in the article on turnout at the 2008 election. However, I thought I'd see what happens if I assume every member of the electorate voted. Unsurprisingly, not much changes: the minimum popular vote share required increases only a little to 22.3%.

I also looked at the analogous problem for becoming Prime Minister (assuming I had somehow persuaded a major political party to appoint me their leader). The maths is a lot more straightforward for the UK, as we just have one parliamentary seat per constituency (so none of this electoral college business). With 650 seats available, I'd simply have to win the 326 constituencies with the lowest turnout to form a (very) minority government. Admittedly, our politics are rather more complex than the two-party system stateside, but if we continue to assume 50% of the vote is required to win a constituency, then at the last general election a party could have won with just 22.1% of the national vote (the Liberal Democrats, by comparison, received 23%).

Eurovision 2012: split jury/televotes are in!

After several months of inactivity on here (mainly owing to the combined powers of a PhD thesis and steadily worsening eyesight), submission of the former and surgery to remedy the latter means I suddenly find myself with considerable time of my hands. Fortunately, I have found the perfect excuse to get back into the blogging boat (that's a thing, right?): the Eurovision Song Contest.

It may not seem the most topical of subjects, with this year's competition a relatively distant memory (if you don't recall, try and remember when it wasn't raining), but the long-awaited split jury/televote results are finally here, allowing for one last bit of fun. In case you're unfamiliar, the points awarded by countries in the Eurovision Song Contest are determined by an equal weighting of votes from the public (the televote) and a jury of music 'experts' (the jury vote). Introduced in 2009, the idea was to try and water down the alleged 'political' voting that many (particularly on these shores) thought was spoiling the contest, with juries theoretically providing a much more objective assessment of the songs. Whether this works in practice is for another time, but for now we can at least have some fun seeing how various countries performed under each system. This year's highlights include:

• There can be no argument over Sweden's triumph, with Loreen finishing on top in both votes. This makes it three times out of four that the public have chosen the same winner as the juries, the only exception being Azerbaijan's win in 2011 where the jury placed them a lowly second (behind Italy). In terms of who actually wins, then, the jury vote has yet to make a difference.

• That said, Russia pushed Sweden extremely close in the televote, with the grannies' 332 points only just behind Loreen's 343. As many expected, Russia fared far worse with the juries, finishing in a fairly unremarkable 11th place. (How much of this was the 'mother Russia' vote, and how much was down to adorable grandmothers and a spinning pastry oven is, however, difficult to judge.)

• The biggest winner under the televote was Turkey, whose 4th place with the public was a whopping 18 places higher than their position according to the juries. (It seems transforming into a boat gets you votes, and quite rightly too.)

• Other big televote winners were Ireland (10th with the public, 25th with the juries) and Romania (7th with the public, 20th with the juries). Next year then, I would recommend Ireland teach Jedward how to sing and play the bagpipes, and victory could be theirs.

• At the other end of the scale four countries (Italy, Spain, France and Ukraine) all finished 13 places worse in the televote than with the juries. France in particular owe a lot to the jury voters: had it been purely down to the public they would have finished on the (in)famous nul points for the first time in their history. (Perhaps they would have fared better if they could have used their delightfully bizarre official video.)

• As for our very own Engelbert Humperdinck, who finished 25th out of 26 on the night, these results don't offer much comfort. Whilst many (as usual) blamed our poor placing on Eastern European bloc voting, these new data suggest that maybe it just wasn't a very good song. The Hump finished 21st with the public, but with the juries? Dead last.

There may well be more gems lurking, but these were my personal highlights. I'll leave you with what is becoming something of a tradition from these parts, with a map of Europe summarizing how countries in the final compared on the two different votes. It's worth bearing in mind that this is something of a simplification, but it gives (I hope) a reasonable impression of this year's competition. (Click for big.)

Euro 2012: How deadly is the group of death?

Much (well, some) has been made of the Euro 2012 draw last Friday, where thanks in part to co-hosts Poland and Ukraine being the top two seeds a rather nasty looking 'group of death' formed. Group B sees the Netherlands, Germany, Portugal and Denmark pitted against one another, with certainly three of the four capable of winning the tournament. But how deadly are we talking?

It gets interesting if you compare the latest UEFA rankings with the latest FIFA ones which are very similar (about 95% correlation) but not identical. Highlights include Portugal, who are ranked 11th by UEFA, but are the 5th best European team according to FIFA The table below summarises the Euro 2012 groups with each team's UEFA and FIFA ranking (where I've filtered out all the non-UEFA teams). (Click for a full-resolution version.)

Based on FIFA rankings, group B is indeed the deadliest, with an average country ranking of 4.5 (and, interestingly, every team a higher rank than any in group A). According to UEFA, however, it's not group B but group C - home to the Republic of Ireland - which is the hardest, although there is very little to choose between the two.

What were the chances of Manchester City drawing Manchester United in the FA Cup third round?

1 in 63.

How do you solve a problem like Sebastian?

A while ago over on Significance I looked at what happened if you compared different Formula One scoring systems with that year's drivers' championship. Yesterday, Sebastian Vettel came within 1 point of snatching the title with a whopping five races to go. In 14 races he's won nine times, come second twice and fourth once, amassing a ridiculous 309 points out of a possible 350.

As it stands, Vettel is 124 points clear of his nearest rival Jenson Button, who would have to win every single remaining race and hope that Vettel scores nothing if he is to win the drivers' championship. In short, the season is as good as over, but is the scoring system to blame? A couple of years ago the FIA tweaked the scoring system to try and encourage second-placed drivers to 'race to win'. Previously you got eight points for second and ten for first, which (it was perceived) didn't offer enough incentive to try and push on for first place. Now you get 25 points for winning and 18 for second, a greater incentive that - in theory - will encourage more aggressive racing.

So what happens if we run this season's results (so far) under the older system? If you're happy to assume that the scoring system doesn't significantly affect how a driver races (quite a big assumption, I admit, but this is Just For Fun) you can enjoy this table:
As my previous dabbles with comparing scoring systems suggest, it doesn't make much difference. Admittedly, Vettel would have already won the championship by now, but only just (a 51 point lead with 50 points available), and no-one in their right mind thinks he won't win this year anyway.

If you ask me, we need something more radical than a tweaked scoring system to make things exciting. My proposal: do away with qualifying and have the cars line up in reverse finishing order from the previous race. It's simple, it would certainly increase overtaking, and no-one likes qualifying anyway.

Addendum: have a bonus table, including the results under the old(er) system of ten points for first, six for second. Perhaps unsurprisingly, Vettel is even further ahead on this one.

Under the weather

I recently got over a cold. Like most people (I hope), I don't like colds, and they often seem to be going on forever. If only there was an easy way to tell when I was over the hump, and the worst was behind me. Sure, I could pay attention to whether I 'feel' better, but that's not very scientific. What's scientific is graphs. And what could be more scientific than a graph plotting the number of tissues I use over the course of a cold?

So, for science, I kept count of the number of tissues I used during my cold. It's not glamorous work, but such sacrifices have always been necessary in the pursuit of human knowledge. The main features seem to be a very sharp increase early on (I had a couple of days of mostly a sore throat before the sniffles set in), a peak at around the 5 day mark, and then a more gradual decline as I got it out of my system. I hope many of you will appreciate the choice of colour here, the "communication theory" module I took as part of my statistics MSc is surely not wasted.

Cereal Killer

I don't know about the rest of you, but I spend far too much of my time in supermarkets reading the backs of cereal packets. I really like breakfast cereal, and seem to think that as a consequence it is a worthwhile use of my time to obsess over exactly how bad for me it is. Unfortunately, there are quite a few different parameters at play when it comes to assessing how nutritious (or otherwise) a particular cereal is, and so I thought I'd devise a simple metric to help me decide quite how guilty I should feel about my bowl of sugar. To keep it straightforward, I decided to focus on the three factors I think are most important: calories, sugar and fibre.

Now, in my rather simplistic school of nutrition, calories and sugar are Bad, and fibre is Good. What's more, calories and sugar are equally as Bad as fibre is Good, and so to calculate how Good overall a cereal is I simply take its fibre content per 100g (as a % of one's guideline daily amount (GDA)), and subtract from this the equivalent number of calories and amount of sugar. It's pretty crude (most notably for not taking into account what type of sugar we're talking about), but who has the time to worry about such things? I ultimately standardise these numbers so the best cereal scores 100 and the worst scores 0, with numbers in between reflecting how far along this scale a particular product is.

Crunching (y'know, like Crunchy Nut) the numbers on some of the major cereals (mostly Kellogg's, but with a couple of Weetabix ones thrown in for good measure), I can exclusively reveal the first ever Statscream Cereal Assessment Ranking:

1. All Bran (100.0)
2. Bran Flakes (56)
3. Weetabix (55)
4. Raisin Wheats (45)
5. Frosted Wheats (41)
6. Fruit 'n' Fibre (34)
7. Corn Flakes (28)
8. Just Right (21)
9. Rice Krispies (20)
10. Special K (19)
11. Honey Loops (19)
12. Krave (11)
13. Crunchy Nut (2)
14. Coco Pops (1)
15. Frosties (0)

It's perhaps little surprise at either end of the scale, although All Bran's utter dominance is perhaps a little disheartening. Of the also-rans I reckon Frosted Wheats offer the best tastiness-to-healthiness ratio, although clearly this is something that needs to be taken into account in a future model. There are also plenty of cereals that could be included, but time is finite after all. If you'd like to know how your particular (non-Nestlé) cereal fares, let me know and I'll run the numbers (if, somehow, you don't quite have the motivation to do it yourself).