Regress and progress

Mar 8th, 2009 | By | Category: Ireland

One evening, driving through an area dominated by paramilitaries, with lurid murals on gable ends and kerbstones painted red, white and blue, there was encouragement on the radio.  The man on the radio said the place would not always be as bad as this, that it would improve.

Of course, the man said nothing specific, he did not say that this estate would change, that people would become law abiding, that standards of living would improve.  No, he wasn’t specific, but what he did talk about was something called ‘regression to mean’, the tendency of things to move back towards the long term average.  Had the studio discussion been applied to practical situations, regression to mean in that estate would presumably have meant a shift towards long-term averages in human behaviour, which would mean less gangsterism and greater affluence.

We live our lives believing in regression to mean; if it did not happen we would be asking questions about interference and fairness.  Spin a coin and it’s as likely to come up heads as tails.  There might be sequences of one or the other, but a chart showing the sequences, with tails in one direction an heads in the other, would show most of the sequences clustered around the middle, those are the rules of chance.  Were we to encounter a sequence like that of Rosencrantz and Guildernstern, we might have serious questions about the world, physics, or the honesty of the other person:

Guildenstern takes another coin, spins it, catches it, turns it over on to his other hand, looks at it, and throws it to Rosencrantz who puts it in his bag.
Guildenstern tales a third coin, spins it, catches it in his right hand, turns it over on to his left wrist, lobs it in the air, catches  it  with his left hand, raises his left leg, throws the coin up under it, catches it and turns it over on  to the top of his head, where  it sits. Rosencrantz comes, looks  at it, puts it in his bag.)
Rosencrantz: I’m afraid –
Guildenstern: So am I.
Rosencrantz: I’m afraid it isn’t your day.
Guildenstern: I’m afraid it is.
(Small pause.)
Rosencrantz: Eighty-nine.
Guildenstern: It must be indicative of something, besides the redistribution of wealth. (He  muses.) List  of  possible explanations. One:  I’m willing  it. Inside where nothing shows,  I’m the essence of a man spinning double-headed coins, and betting against himself in private  atonement for an unremembered past. (He spins a coin at Rosencrantz.)
Rosencrantz: Heads.
Guildenstern:  Two: time has stopped  dead, and a single experience of one coin being spun once has been repeated ninety times… (He flips a coin, looks at it, tosses it to Rosencrantz) On the whole,  doubtful. Three: divine intervention, that is  to say,  a good turn from above  concerning  him, cf.  children  of Israel, or retribution from  above  concerning me, cf.  Lot’s wife.  Four: a spectacular  vindication of  the  principle  that each individual  coin spun individually  (he spins one)  is as likely to come down  heads  as tails and therefore should cause no surprise that each individual  time it  does. (It does. He tosses it to Rosencrantz)

If, in the long run, the average number of heads is going to match the average number of tails, if in the long run the highs descend to the average and the lows rise, then regression to mean should be embraced. It means the economy will rise from the trough into which it has sunk back towards a long-term average.

Confidence that things will improve is no consolation to the hundreds of thousands trapped in the pain of the current downturn.  A fair and just society cannot be content simply to regress; we must ask questions on how to progress; how to ensure that the coin comes up enough times on the right side to compensate for the many times on which it has come up on the wrong; people’s well-being cannot be left simply to the rules of chance.

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  1. In your previous post but one you were quoting from Candide and Rosencrantz and Guildenstern popped into my head then. I was going to leave a comment to that effect. Maybe it’s the slight surreality of them both which caused me to make that connection but I’ve been thinking about R and G for the last couple of days. I suppose probability dictates that my thoughts at time will correspond to your posts.

  2. The line I quoted, spoken by the Player, in the Candide post is from ‘R & G are Dead’. The play has been on my mind the last few days as I went to see Beckett’s ‘Endgame’ on Friday (bleak) which prompted thoughts about Godot.

  3. There are a lot of misconceptions out there about ‘reversion to mean’ (RTM). Economists and stock market watchers tend to use it to mean that the further you are from the mean the more likely it is that the next move will take you back towards the mean. It’s like playing coin-tossing with a coin with memory, not a fair coin! In fact there is precious little evidence that real markets behave like this. Instead they tend to behave like a random walk – each move is more like the toss of a perfectly fair coin!

    If you play the coin-tossing game with a fair coin (each toss 50/50 heads or tails) the mathematics of probability tells you that the longer you play the further you expect to be at any one time from the expected result of equal heads and tails!

    For a good analysis see

    The implication, I suspect, is that we cannot expect improvement except in the longest of long terms – and as Keynes remarked, in the long term we are all dead! Perhaps we need to accept that, and find a way of building the kingdom of heaven despite it!

  4. Hi Joc,

    ‘Reversion’ sounds so much more benign than ‘regression’!

    Even Vincent Browne is raging at the church for simply waiting for the markets to solve the problems:

    I continue to be intrigued by those who profess to be Christians, yet are not embarrassed by the question of whether Jesus would think such vast disparities in wealth and income were fair. And if Jesus did not think they were fair, why then don’t Christians support doing something radical about it?

  5. I just remember Listening to Rosencrantz and Guildestern are dead on the radio years ago so maybe that passage stuck in my head somewhere.

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