As of 5pm Saturday 21 May, Sportsbet betting odds imply:

Labor to form the next government with 70.2% probability.

11 House of Representatives seats are priced as changing hands; see section 3.3 below.

Independents favourites or equal favourites in 4 seats: Clark, Goldstein, Indi, and Warringah.

Current Sportsbet prices are consistent with a 3.2 percentage point TCP swing from the Coalition to Labor; see 3.4 below.

This analysis examines Sportsbet odds in various election betting markets for the 2022 Australian federal election.

We convert odds into *implied probabilities of winning* (IPOW) using a procedure
explained in the Appendix.

In the tables and charts below, we express IPOWs as percentages. Long shots (IPOWS < 10%) are set to zero and the remaining IPOWs re-normalised to sum to 100%.

As of 5pm Saturday 21 May:

Result | Price | IPOW | IPOW (no long shots) |
---|---|---|---|

Labor | 1.38 | 69.5 | 70.2 |

Coalition | 3.25 | 29.5 | 29.8 |

Any Other | 101.00 | 0.9 | 0.0 |

Time series:

We compute expected seat counts by summing the seat-specific probabilities of winning implied by Sportsbet’s odds as at 5pm Saturday 21 May.

Party | Expected Seats |
Expected Seats (no long-shots) |
Seats where favourite |
Current Seats |
∆ seats |
---|---|---|---|---|---|

ALP | 71.1 | 76.0 | 79 | 69 | +10 |

GRN | 4.0 | 1.9 | 1 | 1 | 0 |

IND | 7.8 | 7.3 | 4 | 3 | +1 |

LNP | 60.7 | 63.8 | 65 | 76 | -11 |

OTH | 2.7 | 2.0 | 2 | 2 | 0 |

PHON | 1.5 | 0.0 | 0 | - | - |

UAP | 1.3 | 0.0 | 0 | - | - |

**Notes on table:** the second column of seat counts removes “long-shots”; the third column counts seats where the indicated party has the highest
IPOW (tied leads are split proportionately among equal favourites); “Current Seats” is the count of each party current seats (won in 2019 or notional after redistributions etc); \(\Delta\) is the implied gain or loss in seat totals for each party, based on the current betting market front-runner in each seat.

The following 11 seats do **not** have the candidate of the incumbent party as the unique market favourite:

With long-shot probabilities again set to zero, we examine the relationship between IPOWs and two-candidate preferred results in each seat, using 2019 results or notional results in the event of electoral redistributions since 2019.

Current Sportsbet prices are broadly consistent with the assumption of a 3.2 percentage point TCP swing from the Coalition to Labor.

The blue line is a smoothing spline.

Roll a mouse or pointing device over individual data points for more information.

Australian bookmakers tend to use decimal odds, the return to the punter of a successful unit or one-dollar wager. In general, the more likely the event, the closer the decimals odds approach 1.00 from above; conversely, the less likely the event, decimal odds take on increasingly larger values.

If \(d = (d_1, \ldots, d_J)'\) are decimal odds over \(J\) mutually exclusive and exhaustive outcomes then the implied probability of event \(j \in 1, \ldots, J\) is conventionally recovered as

\[\begin{equation} p_j = \frac{1/d_j}{\sum_{k=1}^J 1/d_k} \tag{4.1} \end{equation}\]

In the context of elections, we refer to \(p_j\) as the *implied probability of
winning* or IPOW for party or candidate \(j\).

This transformation of decimal odds into IPOWs can be rationalised as follows.
Bookmakers set prices not merely as a function of their beliefs about outcomes,
but also to lock in profits. The most telling case comes from observing that for
coin tosses ahead of cricket matches, bookmakers typically offer prices of \(d\) =
1.91 or thereabouts for each of the two outcomes; more surprising is that
gamblers participate in this market at all. This is a case where the *actual*
probabilities held by both bookmakers and punters can be reasonably presumed to
be .5 for each of the two outcomes. A fair price on a unit wager is therefore
2.00, with expected value of 1.00 = .5 \(\times\) 2.00 + .5 \(\times\) 0.

Observe that the fair price of \(d\) = 2.00 is simply the inverse of the probability of \(p\) = .5. This result generalises: fair decimal odds are simply the inverse of the probabilities of the corresponding events, or \(d = 1/p\) and conversely \(p = 1/d\).

But bookmakers prices can not be assumed to be fair. For the coin toss example,
the bookmakers’ prices of *less* than the fair price of 2.00 reflect their
profit margin. With decimals odds of \(d\) = 1.91, the bookmaker will lose 91
cents on each successful dollar wager, but keep $1.00 on each unsuccessful
wager. This asymmetry in payouts with respect to equally likely events is the
key to the adage that “the house always wins”. In this example the bookmaker has
an expected yield of 4.5c cents per dollar waged.

Alternatively, applying the rule that probabilities are the inverses of the corresponding decimal odds, then with prices of 1.91 on both outcomes, the bookmaker’s apparent probabilities are 0.5236 for each outcome. This clearly violates the law of total probability (that the probabilities over the set of possible outcomes sum to one), in this case summing to 1.0471.

The apparent “extra probability” is known as the “over-round” or “vigorish”. Bookmakers prices therefore reflect at least two inputs: (1) probabilities about events; (2) profit margins (Cortis 2015). Let \(p_j\) be the bookmakers’ privately held probability of event \(j\). A profit-motivated bookmaker offers prices of \(d_j = 1/\pi_j\), where \(\pi_j = p_j(1+k_j)\) with \(k_j > 0\) the source of the bookmaker’s profits.

In the literature assessing the predictive value of betting markets, the conversion from decimal odds almost always assumes \(k_j\) is a constant \(k\) over all events \(j\), giving rise to the transformation

\[ \frac{1/d_j}{\sum_j 1/d_j} = \frac{\pi_j}{\sum_j \pi_j} = \frac{p_j(1+k)}{\sum_j p_j(1+k)} = \frac{(1+k)\, p_j}{(1+k)\sum_j p_j} = p_j, \] as per equation (4.1).

Štrumbelj (2014) and Levitt (2004)
survey cases where \(k_j\) might reasonably be expected to *not* be constant over
outcomes \(j\); examples include information and skill asymmetries between
bookmakers and punters and/or bookmakers seeking to counter insider-trading.
Betting markets with large numbers of gamblers and bookmakers should generally
drive these effects towards zero, resulting in small variability in \(k_j\) over
alternatives, validating the mapping from odds to IPOWs in equation
(4.1).

Of course, prior research suggests that seat-by-seat markets are thinly traded, and so we interpret IPOWs in these markets with appropriate caveats. Following my earlier work (Jackman 2015), one of the goals of this analysis in its post-election phase will be to assess the calibration of IPOWs with election outcomes.

Cortis, Dominic. 2015. “Expected Values and Variances in Bookmaker Payouts: A Theoretical Approach Towards Setting Limits on Odds.” *The Journal of Prediction Markets* 9 (1): 1–14.

Jackman, Simon. 2015. “All That Glitters: Betting Markets and the 2013 Australian Federal Election.” In *Abbott’s Gambit : The 2013 Australian Federal Election*, edited by Carol Johnson, Wanna, John, and Lee, Hsu-Ann. Canberra: ANU Press. https://doi.org/10.22459/AG.01.2015.09.

Levitt, Steven D. 2004. “Why Are Gambling Markets Organised so Differently from Financial Markets?” *The Economic Journal* 114 (495): 223–46. https://doi.org/10.1111/j.1468-0297.2004.00207.x.

Štrumbelj, Erik. 2014. “On Determining Probability Forecasts from Betting Odds.” *International Journal of Forecasting* 30 (4): 934–43. https://doi.org/10.1016/j.ijforecast.2014.02.008.