Making sense of odds

Sat 11 October 2014 by Eoin Travers

Love or hate them, you don't get to call yourself a "scientist" nowadays without some training in statistics. Of course, this comes with some advantages: we're forced to at least partially understand something that the vast majority of people struggle with: probability.

However, out in the real world, we don't often see probabilities as nice clear rational number in the range $0 \to 1$, or even as percentages; the probabilities most people, or at least most people down the pub, deal with are bookies odds.

Note: if you're reading this from outside of UK or Ireland, I'm going to be talking the fractional odds we use here, which are probably different from what's used in your country, so this probably won't be of a lot of good to you.

Fractional odds are written in the format

$$ Probability\ (No\ event)\ /\ Probability\ (Event)$$

so what we think of as a 25% chance, or $P = .25$, is represented as $3/1$ (i.e. if you bet €100 and win, they'll give you back your stake, plus €300 winnings). Similarly, a 50% ($P = .5$) chance is $1/1$, so if you bet €100 and win, you'll be given back your stake, and €100 in winnings.

A solution for the lazy

If, like me, you don't think in these bookie's terms, but want to know what the odds means in terms of actual probabilities (what is the chance Donegal will win the All Ireland Championship next year), you might be interested in a little tool I knocked together, cheesily called "Odds-Off".

Odds-Off

To use it, either right click on the button above, and select "Bookmark this link" (or whatever it's called in your browser), or, alternatively, if you have a bookmarks bar in your browser, just drag the button there. Then, go to your bookie’s page (i.e. this one), and click on the bookmark you've just made, and it should translate the fractional odds into percentage probabilities.

So far I've only tried this out on a few websites, so let me know if it doesn't do what it should.

You'll notice that in every case, the percentage probabilities make it obvious that the bookie’s odds add up to more than 100%. A certain amount is always added to what they think the true odds are, in what's called the over round, in order to ensure the bookie always makes a profit.

Nuts, bolts, blood, guts

For the catechises, the script looks like this:

(function(){
  percent_odds=function(txt){
    var odds_re=/\d+\/\d+/;
    var matched=txt.match(odds_re);
    while(matched){
      var as_ints=matched[0].split('/').map(Number);
      var pcnt=as_ints[1]/(as_ints[0]+as_ints[1])*100;
      pcnt=Math.round(pcnt*100)/100;
      txt=txt.replace(matched,pcnt+'%');
      var matched=txt.match(odds_re);
    }
    return(txt);
  };
  var all=document.getElementsByTagName("div");
  for(var i=0;i<all.length;i++){
    all[i].innerHTML=percent_odds(all[i].innerHTML)
  };
})()

and was indemnified into a single line using this handy tool.