* As it happens, Berra gained his nickname “Yogi” because a childhood friend thought he sat like an Indian mystic when waiting to bat. The cartoon Yogi Bear, if you are wondering, didn’t appear until 1958, long after Yogi Berra was a household name, and was no doubt called after him—although the animation studio Hanna-Barbera denied this when challenged legally.

* Curiously, anti-corruption investigators have since exposed a 5 million Euros payment made by FIFA to the Irish Football Association after that match. The Irish now say this was to block legal action contesting the handball decision, while FIFA say it was to help build a new stadium. If you ask me, there was never going be a legal action, nor were stadium costs the issue—this looks like just one more of the dodgy payments with which Sepp Blatter and other FIFA officials sought to maintain the support of their member associations.

* The moral status of manners was the subject of an interaction between unlikely adversaries a couple of decades ago. When the eminent Oxford philosopher Philippa Foot contrasted moral principles with the “silly rules” of etiquette in her influential paper “Morality as a System of Hypothetical Imperatives”, she aroused the attention of the novelist Judith Martin, probably better known as the author of the widely syndicated “Miss Manners” etiquette advice column. In a long and carefully reasoned article in The American Scholar, Martin pointed out that the particular forms of etiquette adopted in different times and places might be arbitrary, but in general they function to uphold the universal and by no means silly requirements of communal harmony and respect for others. In my judgement, Miss Manners had far the better of this argument.

* Incidentally, it is a matter of some dispute in my household whether Müller really was faking, as opposed to reacting instinctively to a genuinely painful blow. I would be pleased to learn that he wasn’t, but I remain unsure. In any case, it doesn’t matter to my substantive point, which is that it would represent a moral falling-off if Müller were faking. (You can judge for yourself: https://www.youtube.com/watch?v=P6nf4hdSwMg.)

* In a partial admission of guilt, the Badminton World Federation changed the rule for the 2016 Olympics, adopting a version of the UEFA system in which a partly random draw determines the knockout matches.

* For an insider’s view of how this all works, I recommend Tim Krabbé’s novel The Rider (London: Bloomsbury, 2002)—a transfixing narrative entirely devoted to a 140-kilometre amateur race through the mountains of Provence.

* If B stands for Beach, M for Movies, S for Sun, and R for Rain, then:ExpUtility(B) = (10 × Pr(S)) + (0 × Pr(R)) = 10 × Pr(S).ExpUtility(M) = (5 × Pr(S)) + (5 × Pr(R)) = 5.So ExpUtility(B) > ExpUtility(M) if and only if Pr(S) > 5/10.

* If L is Left and R Right, and the subscripts show who is going which way, then:ExpUtility(L_Wilshere) = (4 × Pr(L)_Giroud) + (0 × Pr(R_Giroud)) = 4 × Pr(L_Giroud).ExpUtility(R_Wilshere) = (O × Pr(L_Giroud)) + (1 × Pr(R_Giroud)) = Pr(R_Giroud).So ExpUtility(L_Wilshere) > ExpUtility(R_Wilshere) if and only if 4 × Pr(L_Giroud) > P(R_Giroud), that is, if and only if Pr(R_Giroud) < 4/5.

* In fact it is something of a myth that you need identical twins for such studies—which is just as well given how rare they are. Ordinary siblings reared apart will do fine. Since we know that they share 50 percent of their genes, and so possess exactly half the genetic variation of the overall population, the extent to which they remain more similar than the overall population when reared apart tells us quite enough to work out the genetic component of the original population variation.