Let’s learn how different betting timeframes can possibly impact a sports bettor’s risk perception. Consider that world number one Novak Djokovic is up against some lower ranked, let’s say world number 65 player Paul Henri Mathieu in a second-round match in Australian open. What do you think would be the respective odds for this specific game? Let’s say the odds of Djokovic winning the match are 1.72 and the odds of Paul are 2.40? Do these odds seem realistic to you?

In case these odds seem slightly off the mark to you, it could be because that you won’t normally give Novak a relatively low 58% chance of winning a match against a world number 65 player, and the lower ranked player (Paul) a slightly generous 42% chance. Regardless, these are actual odds, but not for the outcome of the match. Rather, they are applicable to the chances of winning each point, accurate to the extent of all the times that this pair had played up till the Australian open’s first round in the year 2013, when Djokovic had registered a comfortable 6 – 2, 6 – 4 and 7 – 5 victory over Paul.

Let’s have a further breakdown of these figures. That game comprised of a total 163 points out of which Novak had won 95 and Paul had won 68. We can comfortably arrive at the per point probability from these figures - 68/163 for Paul and 95/163 for Novak Djokovic. However, if you look at the real odds for the complete match, they were pretty different than that, and were as follows:

Djokovic – 1.01

It should be noted that both the odd sets are precise, but were decided viewing the game from completely different perspectives, or in other words different frames. They were decided looking at single points or a narrower frame Vs the entire match or a broader frame.

Often people find it hard to reconcile different probabilities related to two different perspectives, despite the fact they’ve been both set for the exactly same event. This can lead to some important consequences, especially with regard to live tennis betting.

Live or in play tennis betting takes a deeper look into the game at a point per point level, and at that scale, Paul definitely enjoys a 42% success rate. Such a rate of success and odds may often lead sports bettors to overestimate Paul’s chances of winning the game, more so if these bettors get caught up with the emotion of the audience as well as the commentators.

People often find it hard to reconcile different probabilities coming from different perspectives.

If you extrapolate the 42% per point winning percentage over all the 163 points, it will translate into an overall chance of 41% of winning the match, as is evident from the broader odds (which suggest that if both these players had played 41 times, Paul would win only once).

The framing bias phenomenon has been well documented by a large number of decision-making theorists. It’s viewed commonly in situations where in someone is averse to placing isolated bets, as subjective reasoning perceives to be a risky affair, despite the positive expected value. One of the famous examples in this regard is:

Tails you win £ 200, heads you lose £ 100

A large majority of people reject this offer displaying the commonly seen risk aversion quality and focusing on the possible loss in the scenario of a single toss, despite the fact that their actual chances of making money or the expected value is an impressive £ 50:

If we look at the academic reasoning behind this, it’s that people often feel that the loss of £ 1 is considerably larger than the gain of the exactly same amount. When we apply this factor of two to the losses, the expected value of the single gamble comes out to 0, and is therefore rejected:

However, if we expand our framing to more than a one off, we’ll gain a better understanding of the likelihood of us winning or losing. Now, let’s compare this marginally bigger frame of couple of coin tosses as follows:

25% lose £ 200; 50% win £ 100; 25% win £ 400. Expected value comes out to £ 100

Same as above, however, with losses doubled owing to loss aversion:

25% lose £ 400; 50% win £ 100; 25% win £ 400. Expected value is £ 50

Despite the heightened fear of suffering loss, the expected value of couple of coin tosses stays more positive when looked at in a wider frame. If you had simply employed a narrow frame for analysing the outcomes of two coin tosses, you would have missed the opportunity to benefit.

The loss averse approach in this bet normally remains consistent when you consider multiple coin tosses, however, with the cumulative losing odds diminishing with aggregate gambles, the loss aversion also diminishes correspondingly.

If you ask a similar question based on more number of coin tosses, and hence a broader frame, people are found to be more comfortable indulging in such a gamble.

When the figure is taken up to 100 coin tosses, such a bet (without doubling) has expected value of £ 5000, and merely 1 in 2300 chance of incurring any money loss; there is a 1 in 62,000 chance of suffering a £ 1000 money loss. However, if you reject the isolated bet the first time, hence resulting in a narrower frame, you end up missing out.

Success probability at different time frames

1 second / 50.02%

1 minute / 50.17%

1 hour / 51.3%

1 day / 54%

1 month / 67%

3 months / 77%

1 year / 93%

The framing issues are commonly observed in environments where in there’s a high frequency of data change, for instance in financial indexes. The higher is the frequency at which you check the markets, leading to narrowing down of the frame, the more is the likelihood of you seeing noise instead of signals.

This has been very neatly summarised by Nassim Nicholas Taleb in his work ‘Fooled by Randomness’ in which he impressively illustrates that a portfolio of stocks featuring 10% volatility and 15% return has surprisingly different success chances with narrowing down of frames. The success chance would be a mere 50.02% if you check this portfolio after every second, still if you look at the broader frame, for instance spanning over one year, it becomes 93%.

The lesson we learn here from narrow framing is that it’s very important to view gambles in their aggregate form, hence avoiding the possibility of missing out on favourable outcomes that our risk averse nature may otherwise reject intuitively.