If a betting market is inefficient, significant profits may be attainable by informed bettors. In this article, the weak form efficiency of Pinnacle’s tennis match winner odds for ATP matches from 2007 to April 2018 will be investigated.
The Efficient Market Hypothesis, first discussed in respect to financial markets, describes an efficient market as one in which prices reflect all available information. If a betting market is efficient, odds will reflect true probabilities, there will be no systematic biases in odds, and, on average, simple betting strategies should be incapable of generating significant long-term profit.
Why may biases in odds exist?
To better understand how and why biases in odds may exist, an important consideration is how bookmakers set and adjust prices. If bookmakers are skilled forecasters they may set accurate prices reflecting true win probabilities (the relationship between odds and probabilities is explained well in the Pinnacle article: ‘What do odds represent?’).
This will generate the bookmaker positive returns in the long run, given they will always add a margin. If bookmakers can predict what bettors will bet on they may set inaccurate prices or adjust their forecasts in such a way to exploit these bettor biases and earn an even greater return. In any case, unless bookmakers are perfect forecasters, biases in odds may exist from time to time.
Testing Pinnacle’s odds for efficiency
To test pricing efficiency in the ATP tennis market I used Pinnacle’s own closing prices, without adjusting for the margin. The reason for not removing the margin is that it is impossible to know how the bookmaker has allocated the margin between the two players’ win prices.
For example, if a bookmaker offers win prices of 1.80 and 2.15 for a match, it is impossible to know if the 2% margin is entirely in the favourite’s price, (fair prices of 1.87 and 2.15), the longshot’s price (1.80, 2.25) or if it has been shared (1.83, 2.2).
The chart below plots Pinnacle’s odds calibration for each implied probability decile. For example, the average implied win probability for the 2915 players with prices 1.11 or shorter (91-100% range) was 94.3%. 2713 of these players won, for a win percentage of 93.4%
As we can see, the win percentage doesn’t exceed expectation in any implied probability range. In an efficient market this is what we would expect, with the difference accounted for by the margin.
Pinnacle’s prices appear to be very well calibrated. A simple regression [Average Expected Implied Probability = Coefficient * ATP Win %] confirms the strength of the linear relationship between expected and actual win percentages, returning a Coefficient of 0.994 and an R squared of 0.999.
In an efficient market the Coefficient should equal 1. The range where the win percentage was closest to expectation was 70-80% implied probability, or when prices were between 1.25 and 1.43. Players in this range won 74.4% of matches, of which they were expected to win 74.7%.
While Pinnacle’s prices are well calibrated statistically, the definitive test of efficiency is whether any simple odds-based betting strategies can generate a positive return for the bettor. The table below shows the returns to the simple strategy of a fixed stake bet on all players in each implied probability range.
Over the past 12 years the most attractive decile for a bettor has been 71-80%, yielding a return of -0.4% from a fixed stake strategy. As there is no implied probability decile where bettors would have generated a positive return we can conclude that the market is both statistically and economically efficient.
Does the ATP tennis betting market have a favourite-longshot bias?
One of the most well-documented inefficiencies in sports betting markets is the favourite-longshot bias, identified across numerous sports including soccer, horse racing and tennis. The favourite-longshot bias is a pricing inefficiency where favourites win more than their implied probabilities predict, and longshots less often.
In the table below, we can see that the difference between expected and actual win percentages is reasonably constant, and thus it’s unlikely that a favourite-longshot bias is present.
Previous analysis has pointed to lower fixed stake returns at higher odds as evidence of the favourite-longshot bias, however under certain assumptions this is expected. Consider a match where a bookmaker accurately determines player A’s probability of winning to be 5%, and thus player B’s probability to be 95%.
Fair prices (no margin) would be 20.00 and 1.053 respectively. If the bookmaker desires a 2% margin and attributes this evenly between the players, the prices offered would be 16.67 and 1.042 (implied probabilities of 6% and 96% respectively). The expected return for a 1 unit bet on each player is:
Expected Return= [Win % * Win Profit] – [Lose % * Bet Unit]
Expected Return Favourite= 0.95*(1*(1.042 – 1)) - 0.05*1
= - 1.042%
Expected Return Longshot= 0.05*(1*(16.67 - 1)) - 0.95*1
= - 16.67%
This example shows that with fixed unit staking and an evenly distributed margin, a bettor is expected to lose more at higher odds. In fact, this is also true for a strategy of placing a bet to win 1 unit. Lower returns at higher odds therefore cannot necessarily be used as evidence of a favourite-longshot bias.
If the margin is distributed evenly between the players, this is expected. If we take the midpoint of each decile and vary the equally distributed margin, the expected returns from a fixed stake strategy are shown in the table below.
We can see that regardless of the margin, expected return increases with the true probability (or as the odds shorten). To determine whether Pinnacle’s tennis prices exhibit a favourite-longshot bias, we must compare returns to this expectation schedule.
Using a margin of 2.5% (an estimate of Pinnacle’s average margin for ATP matches), the returns from a fixed stake strategy are shown in the table below. In a market with no favourite-longshot bias, returns would not differ from expectation at different odds.
Theoretical returns appear to closely adhere to expectation, with significantly larger losses at higher odds. Despite returns in some ranges exceeding expectations, there is no implied probability decile where bettors would have generated a positive return, and thus we can conclude that Pinnacle’s ATP tennis closing prices do not exhibit statistical or economic evidence of a favourite-longshot bias.
Betting on ATP tennis
While Pinnacle’s closing prices for ATP tennis are, on average, highly efficient this does not rule out the potential for an informed bettor to generate a positive return from betting in this market.
Prices can move considerably before the start of a match, and if a bettor can beat the closing price consistently, Pinnacle’s low margin means it is likely they will generate a positive return.
Bet with the best tennis odds online to take advantage of Pinnacle's low margins.