A Game Of Two Halves: Setting Halftime/Fulltime Betting Odds
How can we determine the odds for halftime/fulltime results? Today on the blog Mark Taylor explains how to set odds for this popular betting market.
In the previous post in this series, I looked at how you can combine a numerical and an intuitive approach to evaluate the relative qualities of sides in the Premiership and go on to use that process to derive useful betting information, such as match odds. The keystone was the expected long term supremacy between opponents, corrected for venue and expressed in tenths of a goal.
Today we will now use this number to create our own market for other types of bet. The Halftime-Fulltime (HT/FT) result market is an old and established one. Fondly remembered as the only way to bet on the outcome of a single match in the days when five-folds were a minimum requirement, it involves predicting the match outcome at half time and again at full time. So that is nine possible combinations for a single match, ranging from the usual “jolly” of the favourite leading at the half and also at the final whistle, to the rarer, but more rewarding selection, where one side leads at the half, but their opponent ultimately wins the contest.
In short, this is a nine runner race, where the typical over-round per runner is around 1.5% for individual firms, but can be whittled down to just under 1% at best prices.
Correlation With Fulltime 1X2 Odds
As with all secondary football betting markets, the odds for the double result are heavily correlated to win/loss/draw match odds which we derived in the last post. We are essentially calculating the odds for each individual score line to occur in the first half, pooling those scores together to get a score differential at half time, repeating the exercise for the second period and then joining the two sets of results together to form the nine possible outcomes.
To achieve this we need to know how the goal expectation for each side, and hence the supremacy is shared between the first and second halves. Historically, it is clear that the second half has more scoring events than the first. Team’s become slightly more willing to take risks, tired legs are replaced by fresher ones and also, added time extends the length of the second half. Over the last six completed Premiership seasons, 57% of the goals scored come after the interval, although the variation between teams can range from lows of around 40% to highs of 70%. Below I’ve plotted the spread and the frequency at which teams have split their scoring between the two halves since 2007-08.
As the plot demonstrates, it is not uncommon for a few sides each year to produce first half/second half goal splits that are significantly different from the league average of 57% of goals being second half goals. It is sorely tempting to rationalize reasons for these outliers to have real, repeatable causes and if this was the case the odds for the HT/FT result would vary accordingly between these outlying teams. However, there is ample evidence that the apparent tendency for some teams to score significantly more or less of their goals after the interval is merely the expected random variation around the mean in relatively small sample sizes.
If factors that lead to skewed totals were repeatable and persistent, we should expect extreme outlying teams to at least retain some of these traits from one season to the next. But as with many apparently strong patterns, there is no season on season correlation. The ten sides which scored proportionally most heavily in the second half in the completed seasons since 2007/08 scored, on average, almost 70% of their total goals in the second 45 minutes. Well in excess of the league average 57%. Yet in the following year, as a group, they scored second half goals at the league average 57%.
It was the same with sides that scored well below par after the break. The ten lowest second half scorers averaged 46% of their total goals after the break in their lowest seasons, but reverted to 57% on average, as a group in the following years.
The rate at which a side concede their goals behaves in the same manner. A side may allow proportionally more or less goals than the league average during the second half of matches over a limited time span, but it is not a repeatable talent. The attraction of the league average value is ultimately irresistible and of the EPL’s ever present sides over the last seven seasons, no team could persistently, year on year, score or concede goals at proportional rates that were constantly above or below the league average.
This term, Aston Villa has scored 77% of their goals in the second half and it is easy to create a narrative based around their relatively young squad, allowing them to carry that fitness into the second half and be rewarded by proportionally more goals. But transient, situational factors, such as red cards and small sample size is almost certainly the cause and any systematic approach based on Villa’s current, but unsustainable, strong second half scoring record, will almost certainly fail.
Therefore, if we want to use the estimate of the quality gap between opponents we developed in the previous post to frame secondary markets, such as the HT/FT result, we should split that estimate across the halves based much more around league trends than around apparent team traits.
Determining The Odds For HT/FT Markets
A Poisson based approach can provide the building blocks for the nine double results. A side that leads 2-0 at half time, for example, has the luxury of “losing” the second half 1-0, 2-1 or even 3-2 and still landing the “lead at half time/lead at full time” result. They obviously also produce that double result if they also “win” both halves, leading to the the combination of score lines from each half that comprise just one possible HT/FT result quickly spiralling in number.
To simplify the procedure, I’ve provided a ready reckoner table below with probabilities quoted from the viewpoint of the favoured side in the game.
Key. TW denotes the favoured team is leading or has won, so TW/TW refers to the team leading at half time and also at full time. D denotes the game was level at the half and/or at the end. TL means the favoured team was losing at the half or lost at full time.
Continuing the horse racing analogy, the half time/full time bet turns a three runner, home win, away win or draw race, often featuring an odds-on favourite, into a nine runner contest, with all the attendant pricing biases that sometimes exist in larger fields. Typically, HT/FT true odds can range from short priced odds on chances to near 501.00 (500/1) shots, should the strong favourite lead at half time, but then falter and lose by full time.
True odds of 501.00 odds will rarely be quoted at anywhere near those prices to ensure that short term bad luck doesn’t strike the books. So to maintain the margins after chopping the prices of longshots, shorter priced outcomes may sometimes be quoted so that they more closely approach their true odds. This manoeuvring of the prices, combined with competition and differing initial opinions among bookmakers can sometimes lead to a variety of value options appearing in the various separate bets that comprise the HT/FT odds.
As an example, on match day 13, Liverpool travelled to Hull for the Sunday afternoon game. Liverpool were placed 2nd prior to the match, by virtue of scoring more goals than 3rd placed Chelsea and Hull were 13th, a point behind a trio of sides and a point ahead of two others. If we took those positions at face value, from the previous post, Liverpool could be considered as 9 tenths of a goal superior to Hull at the KC stadium.
Reading the various probabilities horizontally from a supremacy of 0.9 of a goal from the table above, a HT/FT result where Liverpool led at the half and also at the end, has a true probability of 0.357 or 2.80 in decimal odds (from 1/0.357), compared to a best available price of 2.45. A stalemate at both half-time and full-time was equally unappealing, having a true probability of 0.143 or 7.00 in decimal odds, compared to a best price of 6.50. However, of the nine possible outcomes, a draw at the half and a Liverpool loss at 90 minutes (true odds, 13.20, available best odds 15.0) and a dual Liverpool loss (10.30 compared to 12), were both value bets. So under this particular scenario, the value and the actual result lay with the outsiders.
A cherry picked example and dependent on your valuation of both Liverpool and Hull matching their current league positions, but an indication of how opinion can be converted to supremacy using methods discussed in the previous post and then extended to cover some of the more diverse markets that are available.
Read more of Mark's work on his The Power Of Goals blog
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