Many bookmakers invite punters to bet on the outcome of the next election. Bookmakers set and constantly adjust their odds so that the expected payout is less than the money that has been collected in bets, regardless of the outcome. As a consequence, these odds aggregate the wisdom of crowds. The odds reflect the collective assessment of the punting community on the probability of each party winning the next election.
From odds to election winning probabilities
Converting decimal odds to probability is straightforward. You divide 1 by the decimal odds, then multiply by 100 to get a percentage.
So odds of 2.50 give you 1 ÷ 2.50 = 0.40, or 40% probability.
The catch is that bookmakers build a margin into their prices, called the overround. If you add up the implied probabilities for every outcome in a market, the total comes to more than 100%. That extra slice is the bookmaker's edge.
To strip it out, you sum the raw implied probabilities across all outcomes, then divide each one by that total. This rescales everything so the probabilities add up to exactly 100%, giving you the bookmaker's "true" estimate of each outcome. In terms of Australian election outcomes, I use the following formula (where C is the Coalition's odds, L is Labor's odds and O is the odds for any other outcome).
\[Coalition_{probability}=\frac{\frac{1}{C}}{\frac{1}{C}+\frac{1}{L}+\frac{1}{O}}\]
More generally, in a market with n possible outcomes, where k is one of them, the probability of the k outcome is
\[P_k=\frac{\frac{1}{k}}{\sum\limits_{j=1}^{n}\frac{1}{j}}\]
Rather than build an over-round into their odds, betting exchanges charge a winner's commission (typically 5 per cent of the winnings) before making a payout. To compare exchange prices with bookmaker prices on a like-for-like basis, I strip the commission out of the exchange odds so that summing the inverse odds yields a margin comparable to a bookmaker's overround. I do this with the following formula.
\[adjusted = ((original - 1) * (1 - commission)) + 1\]
The longshot bias problem
There is a well documented wrinkle in betting markets that complicates the clean conversion from odds to probabilities. Punters tend to overvalue longshots and undervalue favourites. This is the favourite-longshot bias, and it has been measured across racing, sport and political markets for decades.
The mechanism is simple enough. Some punters are drawn to the large payout a longshot promises, so they back unlikely outcomes more than cold probability would justify. This pushes the longshot's price shorter than it should be, which inflates its implied probability. The favourite attracts less enthusiasm relative to its true chance, so its implied probability sits a little too low. Bookmakers, knowing this, are free to shade longshot prices even shorter. So the fault is mostly with the punters, with bookmakers happy to lean into it.
The bias is a curve rather than a constant. Across the middle of the probability range it is close to negligible, and on average across a full market the small errors on favourites and longshots roughly net out. The distortion concentrates at the extremes. For a reasonably balanced two-horse contest like Labor against the Coalition, where both sit well away from the tails, the effect on the headline numbers is minor.
It grows sharply as a contest becomes lopsided, and two structural quirks of bookmaker pricing make this worse. There is a floor and a ceiling. A heavy favourite priced near the floor at \$1.01 already implies a 99 per cent probability, with almost no room left to move, so the price understates its true chance for a structural reason as much as a behavioural one. At the other end, bookmakers rarely price an outcome above about \$101, so a genuine no-hoper is capped at a price far shorter than its true odds. Its implied probability is held up by the ceiling, not pushed up by punter enthusiasm, and the price cannot distinguish a one-in-a-hundred chance from a one-in-a-thousand one.
The two effects work in the same direction. The floor understates the favourite, the ceiling overstates the longshot, and because I rescale every outcome to sum to 100 per cent, the inflation held up at the ceiling is pulled straight out of the favourite already pinned at the floor. In a lopsided market the two errors compound rather than cancel. For Australian elections this often shows up most in the "any other outcome" leg, which is exactly where a capped longshot price lives.
Unless otherwise specified, I have not applied any correction for this. The reader should simply keep in mind that the rank outsider is probably overpriced as a probability, and the favourite underpriced, very mildly in a close contest but materially once the favourite shortens toward the floor.
Betting markets are not infallible
Betting markets have proved to be an okay predictor of election outcomes. But they are not infallible. In the 2015 UK election both the polls and the bookmakers got it wrong; both predicted a hung Parliament. The outcome was a Conservative majority of 12 seats.
The 2019 Australian election was a sharper miss. Labor was the short-priced favourite for the entire campaign, firming only as low as \$1.15, an implied probability of about 87 per cent, with roughly 70 per cent of betting money held for a Labor win. Scott Morrison's Coalition then won a majority. Sportsbet was so confident of a Labor victory that it paid out more than a million dollars two days before the vote, then had to pay out again on the actual result.
The 2019 result is a reminder that a short price is not a certainty, and it also shows the demand-side pricing I mentioned earlier in action. The money piled onto Labor, the bookies shaded the price to match where the money sat, and the price ended up reflecting punter sentiment more than the true probability. Note that this was the reverse of the usual longshot tilt. Here the crowd overbacked the favourite rather than the outsider, a different failure but the same lesson: prices follow the money, and the money can be wrong.
My data collection practice
I am collecting daily odds in the lead up to the 2028 Australian Federal Election. I will expand the odds I collect over time.