Was the India-Bangladesh match in the recent ICC World T20 as exciting as everyone says it was?
Is there any way to objectively measure this excitement or interest? The scorecard won’t help because that only gives a snapshot of the game.
And is this measure even important?
Third answer first: there are many reasons why objective determination of whether a game was interesting helps. Firstly, it helps tournament and series organizers choose teams and schedules better. Secondly, it helps broadcasters and advertisers make more optimal decisions. Thirdly, it helps fans looking to watch highlights packages make better choices. And finally, with cricket being an evolving game, it helps administrators of the game make better decisions on how to change the rules in order to make the game more interesting.
Second answer next—and it is a long one.
How to measure excitement/interest?
The margin of victory says nothing because well-fought and interesting cricket matches need not result in close finishes. The game between India and Australia in the recently concluded World T20 was widely regarded by spectators and commentators as being exciting. India won the game with six wickets and five balls to spare, a large margin by 20-over cricket standards.
It is thus clear that we need to go beyond the scorecard. To figure out an objective formula to determine the “interestingness”, let us start by looking at a few games from the recently concluded ICC World T20. Instead of the scorecard, we will look at how the advantage in each game changed hands between the participating teams.
The simplest way to measure the likelihood of each team winning the game at a particular point in time is by looking at the “betting odds”. With sports betting being illegal in India, this information is not available to us. Hence we need an alternative method to determine the likelihood of each team winning a game based on the current game situation.
In 2012, Sky Sports in New Zealand debuted a feature known as the “Winning and Scoring Predictor” (WASP) built by two economists from the University of Canterbury in New Zealand, Scott Brooker and Seamus Hogan. During the first innings of each limited overs game, WASP would predict what the team batting first would score. During the chase, WASP would indicate the probability that the chase would be successful (these numbers were displayed along with the scores at the bottom of the broadcast screen).
The algorithm, a basic version of which has been put in the public domain by Hogan in a blogpost relies on a technique called “dynamic programming” and calculates the odds based on the score by assuming that an “average batting team” is playing an “average bowling team”. Using this algorithm, and making a couple of modifications, we can compute the likelihood of each team winning at any point of time in the game based on the score alone.
The first change is to convert the expected first innings score to the odds of winning. This can be achieved by combining the distribution of possible first innings scores with the odds of a successful chase for each score.
The second change is to do with pitches—since the nature of the pitch can significantly alter the dynamics of a game of cricket. In this case, a Bayesian learning system has been used to dynamically “learn” the nature of each pitch as the game goes along.
This way, a suitably modified WASP can be used to substitute for odds from betting houses in our algorithm to determine whether a game was interesting.
Figures 1,2 and 3 show the way the winning probabilities moved during three notable games from the recently concluded World T20. Figure 1 shows that while England “led” through most of the final against the West Indies, it was undone by the four consecutive sixes hit by Carlos Brathwaite. Figure 2 shows England’s largely straightforward victory over New Zealand in the semi final, while Figure 3 shows the group game between India and Bangladesh, where Bangladesh imploded to lose by one run.
Looking at these graphs, it is clear to the human eye that Figures 1 and 3 represent games that were rather exciting to watch, while Figure 2 shows a mostly one-sided game. The challenge is to construct a formula that can measure how interesting the game is.
Closeness of the contest
One way to identify an interesting game is to see how closely it was contested, and till what point both teams stood a reasonable chance (or 50%). As the figures show, the lines representing the first and the third games cross the 50% mark fairly late in the game. Figure 2, on the other hand, represents a game that was decided early. This suggests the use of the last point when the line crossed the 50% mark as a metric to measure the interestingness of the game.
But what if the game crosses the 50% mark multiple times, like we see in Figure 3? Can the number of times the 50% line is crossed be used as a metric? While this is indeed plausible, the fact is that this requires clever weighting based on when the line is crossed, and this can make the formula complicated. A simpler formula would be preferred.
The possibility of a comeback
Another measure of an exciting game of cricket is the possibility of comebacks, which Figure 1 is a great example of. The game was with England most of the way, and when the West Indies pulled it back in the last over, it made for spectacular viewing. This suggests that we use the extent to which the game was tilted in favour of the team that eventually lost as a measure of excitement. In other words, we can calculate the average probability (across balls) that the ultimate winner would win the game. The lower this average, the more the surprise in that the ultimate winner won, and the more exciting the game.
The problem with this metric, however, is that a comeback need not necessarily be successful for the game to be interesting. In the India-Bangladesh game, for example, our model shows that India was ahead for most of the game, but Bangladesh came back very strongly, only to ultimately lose in what is accepted as an exciting finish. The comeback metric will not rate this game as exciting, though, since India “led” for most of the game. We need something else.
The changing probabilities of winning
A better approach is to not look at the absolute position of the probabilities of winning, but the changes in these probabilities. After all, the more the game flows back and forth between the two teams, the more exciting it is to watch. Games where the advantage to one team steadily increases are less exciting to watch.
This suggests the use of the total vertical distance “travelled” by the line as a measure of excitement. We simply total the magnitude of the vertical distance between the probabilities suggested by consecutive balls to get our measure of excitement. Exciting games with more back-and-forth movement of probabilities will see this line wriggle a lot more.
The problem with this measure is that a game with a few big swings is likely to be far more interesting than one with lots of small swings (most of which can be accounted for due to sheer volatility in the model). In other words, it is desirable to give larger weight to big swings. A good mathematical technique of doing so is to weight each swing by its own magnitude. In other words, we use the sum of squares of vertical movements in the line as a measure of how interesting the game is. (This kind of weighting large numbers by themselves is a common method in mathematics. The formula for the widely used Standard Deviation comes out of one such weighting).
There are several advantages to this measure. Firstly, there is a clear relationship between large back-and-forth movements and interestingness. Secondly, it doesn’t matter whether a comeback resulted a victory or not.
Thirdly, odds of a cricket match don’t shift too much during the initial stages of the game, unless there is a sustained performance by one of the teams. So the algorithm is less sensitive to extreme early performances (some of which might be due to pitch conditions). And most importantly, the measure is objective and easy to calculate.
All we need is the odds of each team winning after each ball; we just take the movement of these odds between consecutive balls, square it and sum it up to get our score!
This method is not perfect, of course. Games that are firmly in the balance without moving either way are likely to score low on this measure despite being exciting. Also, this measure rewards equally comebacks at different times of the game— maybe we need to give additional weight to late comebacks. The formula is not mathematically sound, and has no “physical meaning”—maybe one that focuses on information content might do better?
Nevertheless, it is a perfectly serviceable formula.
Let’s use it to answer the first question.
Which match was more interesting?
This formula rates the India-Bangladesh game (Figure 3) as the most interesting game of the tournament with a score of 0.98. The West Indies’ group victory over South Africa in Nagpur comes second with 0.80 (Figure 4: this is possibly anomalous and due to the inaccurate odds the algorithm used). The finals (Figure 1) are only the fifth most interesting game of the tournament with 0.59, with the West Indies’ victory over India in the semi-finals (0.69) and Oman’s victory over Ireland in the preliminary stages (0.67) rating higher.
The England-New Zealand semi final was the second least interesting game of the tournament, with a score of 0.15. Only New Zealand’s victory over Bangladesh in Kolkata (0.14; Figure 5) scored lower.
And the data does bear out that the ICC World T20 was far more interesting than this season’s IPL thus far (data until 16, April). The World T20 had an average excitement rating of 0.35, against IPL’s 0.27 thus far. It will be interesting to see if the IPL gets more interesting with time.
Finally, how has the IPL’s interestingness moved with time? Figure 6 shows the average excitement level of each IPL thus far, and it is easy to see that the first two seasons have been the most exciting. The least interesting tournament was in 2011 which featured 10 teams. The excitement level saw a significant jump in the next year which saw one less team!