Friday, 30 November 2012

Minimum Alcohol Pricing

The government is proposing a minimum retail price for alcoholic drinks of 45p per unit (a unit is ten cubic centimetres of alcohol), despite having received legal advice from the EU that minimum pricing is not permitted.  The EU suggests increasing excise duty instead.

The BBC has published a graphic showing the minimum price of various drinks under the 45p limit:
It's instructive to compare these prices with the duty + VAT on duty currently charged:

Can of lager Can of cider Bottle of wine Bottle of whisky Bottle of vodka 
Increase required53%456%85%40%40%

The bottom row shows what percentage increase would be required in excise duty to make duty+VAT come to 45p/unit.  What stands out is how low the duty is now on cider.  This is the result of pressure on successive chancellors to protect the cider industry, as depicted in adverts where the apples are hand picked in a scene of rustic simplicity.  In reality, very little apple and a lot of sugar go into the production of cheap cider.

Proponents of minimum pricing argue that the alternative of raising duty would not stop retailers undercutting the intended minimum price by selling at a loss.  I doubt that would be much of a problem, and if it were the government could revive its previous proposal, now abandoned, to prohibit selling at below duty + VAT on duty (I don't know whether the EU would object to that).  However, I don't believe that's the real reason to prefer minimum pricing - the real reason is the almighty fuss that would be raised by the trade if excise duty were radically increased.  With minimum pricing, the extra money paid by consumers goes to the trade, to compensate it for lost sales.

If minimum pricing were introduced, the effect would be to increase smuggling and illegal production, and to compress prices at the bottom end, leaving products to compete on brand recognition rather than price.  Can football fans look forward to the Diamond White Premier League?

What of the health arguments for minimum pricing?  Back in September I raised both eyebrows at a BBC report claiming that "The deaths of 50,000 pensioners could be avoided over the next decade if minimum alcohol pricing is rolled out in England, according to new research. The BBC's Panorama programme commissioned the research from statisticians at Sheffield University."  I've just discovered that the BBC corrected its report three weeks after publication:
Correction 28 September 2012: The main figure in this story has been amended from 50,000 to 11,500 after it emerged that there had been an error in the calculations carried out for Panorama by the School of Health and Related Research at the University of Sheffield.
Well, it's good that they corrected it.  But this won't do.  Sheffield University has got a substantial team doing Alcohol Research, they produced a report for a television programme whose key findings were bound to be widely repeated, but they committed an error so obvious that it could easily be spotted by a random blogger (albeit not by a Panorama reporter).  It's common to make mistakes with numbers, so anyone doing statistical work needs to be checking every step for plausibility.  Evidently the Sheffield team isn't doing that.  I see no reason why one should trust their output not to be littered with less obvious errors.

Tuesday, 27 November 2012

One more thing about two-point attempts

With the scores level late near the end of an NFL game, your side scores a touchdown.  You've worked out that the chance of success with a two-point conversion, for either side, is a little over 50%.  So you should try for two?  No.  It makes a difference only if your opponents are going to score a touchdown of their own.  Then if you've failed with a two-point attempt, they're certain to win by kicking a single point (under the simplifying assumption that these kicks always succeed).  Whereas if you've succeeded, they can still tie the game with their own two-point conversion.  In fact, to make your two-point attempt the right strategy the chance of success has to be more than (2 - sqrt(2)), about 58.6%.

Friday, 23 November 2012

Numerate Coaching in Sports

Moneyball documented the rising importance of numeracy in baseball coaching, starting with Billy Beane at Oakland in the late 1990s: gratifyingly for nerds this has spread to other sports.  There was a hint of this in a Thanksgiving game of American Football this evening (it's a good game for armchair coaches).

Dallas was behind by 22 points early in the fourth quarter.  The scoring system is that you score six points for a 'touchdown', and that qualifies you to attempt to kick a 'point after' - like a conversion in rugby.  As an alternative to the point after you can opt to try to score again from the two yard line: that's worth two points.  More easily than scoring a touchdown, you can get three points for a 'field goal' - the difference of 22 points was a difference of four converted touchdowns against two field goals.  In practice the success rate for two-point attempts is about 48%, whereas points after are a near certainty, assuming a regular kicker in reasonable playing conditions, so the two-point option is selected only at certain scores late in the game.

And this was one of them.  Dallas scored a touchdown, and tried (successfully) for two points.  This is clearly the correct strategy.  The only real chance of getting anything out of the game from 22 points down was to outscore their opponents by three touchdowns to none over the remainder of the game, and to get at least one two-point conversion.  It was right to make the attempt at the first opportunity because if it succeeded they could revert to points after following the next two (presumed) touchdowns*, whereas if it failed they could attempt to compensate with two more two-point attempts.

There's a more common application of this sort of strategy for a team behind by 14 points late enough in the game that its only chance is to score two touchdowns to none.  The correct strategy** is to attempt two points after the first touchdown, because if you fail you can attempt to compensate by scoring two points after the next, whereas if you succeed you can win the game with a point after the next touchdown.

However, having reduced the deficit to 14 points, Dallas did score another touchdown, and kicked a point after instead of trying for another two.  So perhaps I've overestimated the coach's intelligence.  Or perhaps he understood what he ought to do, but lacked the courage to do it.

Unsurprisingly enough, none of this affected the result.  Dallas lost.

*This consideration is sufficient to demonstrate the correctness of the strategy, but as the rest of the post suggests, it's not the whole story

**Assuming that points after are certain, this latter strategy is correct if the two-point success rate is more than (3-sqrt(5))/2, about 38.2%.

Thursday, 15 November 2012

Thoughts on the US Election

Barack Obama has been duly re-elected president, winning the Electoral College by 332 to 206, and the popular vote by 50.6% to 47.8% (with the rest going to minor candidates).

The result was closely in line with the projections of the poll aggregators, so no one had any right to be surprised by it.  And yet much of the Republican Party seems to have been genuinely shocked.  A host of Republican pundits predicted a Romney victory - "I am now predicting a 330-vote electoral landslide" (by which definition the actual result was an Obama landslide").  Romney's campaign agreed that he was ahead.  Now, media pundits don't necessarily say what they think - they are writing to please their readers as much as to inform them.  And even pessimistic politicians need to present a reasonably confident demeanour during elections, so as to maintain enthusiasm among party workers and donors.  But Romney's campaign tactics in the final weeks - his cautious approach to the last two debates, and his decision to campaign in Pennsylvannia on the day of the election - seem to suggest that his campaign really thought he was going to win.

So how can they have been so wrong?  To win the election, Romney would have had to overcome not the 2.7% margin in the popular vote, but the 4.7% margin in Colorado, along with lower hurdles in Virginia, Ohio and Florida.  You deserve to be wrong if you make a projection based on reports of enthusiasm at Romney rallies and how many yard signs you've seen, but most of the Republican analysts were looking at raw polling numbers much the same as everyone else's.  What they did with them was different - they thought turn-out would be much higher among Romney supporters than Obama's.  One non-partisan polling organization - Gallup - agreed with them, so they've got some excuse.  But if your interpretation of what's happening is well away from the consensus, and if the consensus turns out to be right, you have to wonder whether you've overestimated your own competence.

The demographic breakdown of votes cast is interesting - Romney did as well among white voters as did GHW Bush against Dukakis.  But whites are no longer a large enough proportion of the electorate for that to be sufficient.  Since the demographics shifts are going to continue, the Republicans need a new strategy.  It's always a pleasure to offer advice to a defeated foe, so here's mine:

1) Ditch Bush.  You can't stop the electorate blaming Bush rather than Obama for the USA's economic difficulties, but you can stop them expecting more of the same from the next Republican they elect.

Republicans are convinced that Obama is woefully incompetent.  I really can't understand why they think so, but if they want people to take them seriously on the subject they need first to face up publicly to the fact, obvious to much of the electorate, that GW Bush was a disastrously bad president.  He failed to prevent the 9/11 attacks, then he invaded Afghanistan to follow up his demand that the Taliban must "hand over the terrorists" but failed to catch the most important terrorist, Osama Bin Laden, whom he'd said he wanted "dead or alive".  He invaded Iraq because it hadn't complied with demands to rid itself of "weapons of mass destruction" and the weapons turned out not to exist.  He had no sort of exit strategy for either war, with the result that the war in Iraq lasted officially for nearly nine years, and the war in Afghanistan is in its twelfth year.  And he destroyed the USA's reputation for respecting human rights by adopting the torture of suspects as a routine practice.  Meanwhile on the economic front he exploded the budget deficit by cutting taxes and expanding Medicare benefits, then steered the USA and the world into the worst financial crisis for eighty years.  And he indulged in government by crony, most visibly in the case of FEMA and its feeble response to Hurricane Katrina.  Against this litany of disaster, Republican charges against Obama are vanishingly small beer.

Politicians in the UK have learnt to disown their former leaders - Labour in particular have moved sharply away from Tony Blair, who shared in some of Bush's folly.  It's really not that hard.

2) Ditch vote-losing rhetoric that's not part of your core message.  The primary system forces presidential candidates to appeal first to their own parties, which makes it harder to occupy the centre ground when it comes to the general election, so Republican leaders need to get started now on persuading their members that Hispanic immigrants are as much a part of the American Dream as anyone else, and that women are entitled to the same sexual autonomy as men.  The examples of Todd Akin and Richard Mourdock should make it easy to persuade the Neanderthals to keep their prejudices to themselves.

My understanding is that the Republicans' core believe belief is in low taxes and small government, and that it's a popular notion in the USA.  So concentrate on that.

3) Get out more.  Republicans have their own version of reality, not just when it comes to opinion polls.  Fox News is helpful to them if it attracts converts, but damaging if it hides the truth about what's happening in the USA from the Primary electorate.  A political party should have its own values, but not its own facts.

Meanwhile, what should Obama be doing?  All the talk is of a "fiscal cliff" - at the end of the year the "Bush Tax Cuts" will expire, and there will be an automatic cut of about 0.25% in federal spending.  The raw effect will be roughly to halve the budget deficit (fiscal multiplier effects will make the actual deficit reduction smaller, as they have when European governments have attempted to reduce their deficits).  But in reality, it's not a cliff, it's a slope - the effects will be gradual.  And they'll cause more pain to Republicans than to the president - why should he care if taxes go back to Clinton-era levels?  And most of the Democrats' favourite programmes are protected from the spending cuts.  And unlike most of Congress, Obama doesn't have to worry about re-election any more.

I think this is what Obama planned all along.  The Republicans have engaged in unprecedented levels of obstruction in Congress, so once the Democrats lost their super-majority in the Senate, Obama found it very difficult to get any legislation passed.  He has responded by extending the use of executive powers, and by exploiting the Republican's weakness - their lack of contact with reality which caused them to believe that they would win the recent presidential election. So he made short-term compromises, attracting much criticism from his own side, in order to get a budget deal which suits him this side of the election - the Republicans assumed they would have the presidency and a Senate majority by now, so they thought it didn't much matter what they agreed to.

Having won his gamble on re-election, all Obama has to do now is sit on his hands.  Income taxes will go up, and he can then offer Republicans proposals he actually likes to reduce them again.  Here are some suggestions from me:
- a carbon tax, in return for revenue-neutral reductions in income taxes.  The tax would be levied on all fossil fuels at a level corresponding to an independent scientific estimate of the global economic cost of carbon dioxide emissions.
- phasing out agricultural subsidies, in return for revenue-neutral reductions in income taxes.  Obama has always supported agricultural subsidies, but then he's always cared about re-election.  He's free now to do what's right.
- legalizing marijuana, and taxing it, in return for revenue-neutral reductions in income taxes.

I can't say I'm confident that Obama will propose any of these things.  But I'd love it if he did.

Tuesday, 6 November 2012

Vote Obama

Today is the day of the US presidential election.  The main candidates are the President, Barack Obama, who sits somewhat to the right of David Cameron in the political spectrum, and the Republican challenger, Mitt Romney, who is off in the ultra-violet.  (You might prefer to call it infra-red if you favour the US political colour scheme.)

Intrade is currently selling Obama 'shares', which pay $10 if Obama wins, for $6.99 (it was $6.68 when I looked last night), i.e. they give him a 70% chance of winning.  Whereas you can back Romney on Betfair at 4.6 (£1 pays £4.60 if Romney wins), i.e. they give him a 21.7% chance of winning.  Since these chances add up to less than 100%, if you've got accounts on both exchanges you can lock in a profit by taking both bets in an appropriate ratio, provided you bet large enough to cover the fixed fees, and the exchange you win on doesn't default.  (Which suggests that arbitrageurs are none too confident in the soundness of one of the exchanges.)

Nate Silver, who got the last presidential election almost exactly right, is giving Obama a 92% chance of winning, based on his analysis of all the good quality state and national polls (recent reports that the candidates are neck and neck have been based on the national polls, which have been tighter, perhaps because sampling controls need to be determined state by state).  That suggests that it's the Intrade market which is off.

Conor Friedersdorf attracted a good deal of attention six weeks ago with his article Why I Refuse to Vote for Barack Obama.  His argument was that the only way to get presidents one agrees with is not to vote for candidates one disagrees with, and his principal disagreement was over Obama's drone warfare in Pakistan.

I agree about the drone warfare.  The general counter-argument is that the primaries are for picking a candidate you like; the presidential election is for choosing a president from the candidates on offer.  Specifically, here are two reasons to vote against Romney, and therefore for Obama:

1) Romney supports torture.  I hoped this stain on the honour of the USA had gone with GW Bush, but Romney wants to bring it back.  He prefers to call it by the Gestapo name,VerschĂ€rfte Vernehmung, translated into English, but whatever you call it the US executed Japanese soldiers for it at the end of the second world war.  This is a line the US must not again cross.

2) It's possible to persuade oneself, based on Romney's more moderate statements of the last few weeks, that he'd be not much worse than Obama - that he won't start a war in Iran, or try to fix the deficit by cutting taxes and increasing military spending.  But that's a dangerous game, because he speaks in code, and it's a code you may not pick up on.

Here's a quote from his website, on the subject of Marriage:
Marriage is more than a personally rewarding social custom. It is also critical for the well-being of a civilization. That is why it is so important to preserve traditional marriage – the joining together of one man and one woman.
This might not be an important issue for you. But look at the argument, which can fairly be paraphrased as "Marriage is critical for the well-being of civilization: that is why we should stop some people getting married".  Which doesn't make any sort of sense.  Romney has got reasons to oppose same-sex marriage, but he's not telling us what they are, because the people he's talking to already know and he's better off not spelling it out for the rest of us.  (On the other hand, if he wanted to campaign for restrictions on divorce his argument would work quite well, I think that's a clue to what he really thinks.)

I haven't got a vote in this election. If you have, and you like Romney's policies, then thank you for reading.  Otherwise, please vote for Obama.

Thursday, 1 November 2012

Evidence-Based Executions

Few people start with a careful study of statistical data before forming a view about the desirability of the death penalty for murder.  Proponents are looking for a fitting punishment, opponents are against killing people, or unwilling to risk executing the innocent, or (me) think that the operation of the death penalty is damaging to the body politic.  However, I suppose that many opponents would, however reluctantly, change their minds if it could be shown that the death penalty saves many people from being murdered - I'd be unwilling to put my own sense of what is fitting ahead of the lives of innocents.  Similarly, I hope that many proponents would be willing to give up on retributive justice if it could be shown that it results in more people being murdered, perhaps by legitimizing killing in the minds of potential murderers.  So statistical data do matter.

In the USA, capital punishment was suspended between 1972 and 1976, as a result of Supreme Court decisions against and for it, and subsequently restored piecemeal.  Currently, 32 States have an active death penalty statute, applied with various degrees of enthusiasm.  This would seem to provide much data for statistical investigation of the effect of the death penalty on the murder rate, but results have been disappointingly inconsistent.  This paper explores the modelling issues involved: I reproduce its chart showing the lives that would be saved or lost per additional execution, averaged across states, according to twenty different choices of model.

One approach is to study the competing models and decide which one likes best on its merits.  But few have got the time and knowledge of statistics to do that.  Even for those who have, the result will be a personal opinion of little use for persuading others - a more common approach for public discussion is to select the study which gives results which suit one's case.

I have a proposal.  The USA should abolish the death penalty for everyone whose date of birth is on an even day of the month.  (Date of birth as officially recorded as of the date of they commit murder.)  If the deterrent effect of the death penalty is important, we should soon see a disparity in murder rate between the odds and the evens.  There might be other effects - from legitimizing arbitrary killing, or, in the other direction, from having fewer executions to remind potential killers of the punishment they risk - but we would at least find out how big the deterrent effect is.

Perhaps the Supreme Court would disallow this under the Equal Protection Clause of the Fourteenth Amendment:
No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
But it would take them a few years to get round to it, so we'd get some data anyway.