What is a Safe Score to Post in ODIs?
By: Amol Desai
Tags: Cricket, Data Science, Analytics, Sports Analytics

What is a Safe Score to Post in ODIs?

Exploring what makes up a safe first innings score & building a model to quantitatively guide the assessment mid-game

Back in the 90s, 250 used to be considered a par first innings ODI score. In the late 90s and a large part of the 2000s, this became a 280. 300 was still considered to be a sure-shot victory. I vividly remember India chasing down 315 against Pakistan at Dhaka in the Independence Cup in the late 1990s, the highest chase at the time, and it was considered to be heroic. It was heroic.

Recently, we have seen some seemingly crazy totals being set, and chased down in the World Cup 2019 warm ups and some pre-world cup games.

Fig. 1: Successfully Chased Down Total Over the Years. (90th percentile indicates that the top 10% of chases were between this line and the max line)

Yes, that huge spike at 434 in 2006 is the incredible Herschelle Gibbs led heist by South Africa against the Aussies.

We are in an age where no total seems unassailable. At the same time, we have also seen a bunch of matches in the recently concluded CWC2019, where even a 240 produced a close contest. “Seems” isn’t enough though. Let’s see if we can quantify this, figure out what a safe first innings total is, and explore some of the factors that affect it.

Starting Simple & Stupid

Let’s start by being very naive and figure out, given a target, what the likelihood of it being chased down is. Since every single target possible hasn’t been achieved multiple times for us to calculate a statistical aggregation, we can bucket the targets into bins.

Fig. 2: Chasing Outcomes Based on Binned Targets Regardless of Context

While there still aren’t too many matches at very low and very high scores, maybe it is acceptable for us to not have a good estimate in these ranges; since, for these scores, the question of whether a target is chase-able may not arise. But then, when it does arise, these are the ranges where answering the question accurately, would be most critical.

However, the score alone couldn’t possibly be the only consideration. A 300 against an Australia on a flat wicket surely can’t provide the same level of assurance as a 180 against a Canada on a green top. When we start slicing the above by more and more factors (e.g. the chasing team), we don’t have a lot of matches to give signal to our model. Consider this: India & Australia are arguably two of the most active (play a lot of games) teams on the circuit. But, before World Cup 2019 and since 2011, both have played just 2 games at Lord’s. Australia last played at Lord’s in 2015.

Context Matters

Before we talk about the sparsity of scenarios further, let’s think about factors apart from the target itself that could be interesting? The conditions at the ground are the first thing that come to mind. Since I don’t have data available on pitch conditions, we will look at chased totals by ground.

A lot of the visuals in this piece use box-plots to represent distributions. Here is a good primer of box-plots. The gist is that the solid rectangle represents the meat of the data distribution and the lines or whiskers represent the extent of the extreme values.

Fig. 3: Chasing Results on Grounds w/ Most Matches Played Since 2011

We see here, that identifying the ground that a game is being played at, determines the confidence with which we can say whether a chase will be successful or not. Think about the overlap in distributions for winning and losing as an indication of uncertainty. Given the lack of an overlap in the distributions for victories and defeats while chasing, for grounds like Bulawayo & Colombo, we can be much more confident about setting a target if we were the team batting first. On the other hand, if we were playing at the Oval, we would be far less confident about setting a target in the 300 range since the overlap between the two distributions is significant, suggesting that the game could go either way if the target is in that range.

Another factor that should determine a successful chase is the chasing team itself.

Fig. 4: Chasing Results by Chasing Team

Again, overlapping distributions in victory and defeat suggest uncertainty of success, given a target in the overlapping range. As a team setting a target, one would be much more confident in setting Pakistan or West Indies a target, than they would against Australia, South Africa or Bangladesh, since there is a clear separation between the meats of the distributions for Pakistan & West Indies. Note, that the ideal safe score would also be different between these teams, because the distributions are centered at different scores and the separation between the distributions happens at a different score.

A Short Digression on The Goodness of Chasing Teams

When we talk about teams that chase well, it isn’t just the total that they chase down, but also how consistently they do it. Since 2011, Australia, England & India have been the best chasers, but Australia have won less consistently when chasing huge totals as evident in the larger overlap in their winning and losing distributions while chasing. Fig. 5 shows this more intuitively. Here, on the X-axis, we are looking at the 80th percentile score chased down for each team, implying that for all the targets chased down, 20% were above this score. The Y-axis shows the proportion of successes when posed a target above the 80th percentile score i.e. how consistently teams chase down these large targets.

Fig. 5: Chasing Capacity & Consistency of Teams Since 2011

Collapses Are Costly

In addition to the venue itself, another indicator of the pitch and conditions is also how the team batting first got to their total. Let’s look at the number of wickets that teams lose in the first innings and how that affects the success of a chase. (In a later piece, I intend to take a more nuanced look at how the first innings progressed, to get an indication of whether the pitch was slowing down or becoming flatter and drier towards the end.) Intuitively, we would expect that teams that lose a lot of wickets, have their premier batsmen spending less time at the crease, and so are unable to get to really high scores. This is illustrated by the data. The lower the set target, the more wickets the team batting first is likely to have lost.

Fig. 6: Wickets Lost Per Target Bin By Chasing Result

However, we see that the correlation to wickets lost in the first innings goes even further. Especially for higher totals, even within a given score range, when the chasing team wins, the team batting first usually loses more wickets than they do when the chasing team is unsuccessful. Note that this isn’t directly causal; it doesn’t imply that you have to conserve wickets if you get to higher totals in order to win. This may indicate that the pitches on which these higher scores are achieved are playing true throughout the day and the team batting first was unable to set a higher total due to a collapse, thus not having a safe score on the board.

Time to Touch Base & Re-Orient

At this point, we have a few different factors that we believe affect the probability of a first innings score being safe enough to secure victory. We have:

The score posted itself The ground on which the match is being played, giving us a signal on ground size, outfield, and pitch quality The number of wickets lost by the team batting first in posting the total, indicating how the conditions are on that particular day The team chasing

These are all things that we would know at the innings break. If we now build a model that uses all of these factors, we should get a good indication on whether the team batting first has achieved a safe score. We could also use the same model during the first innings itself to determine what a safe score to post would be.

Handling The Sparsity Elephant

Let’s briefly go back to the sparsity issue that we touched upon earlier. Since we don’t have all possible scenarios played out for us enough times to base our judgement on, we will stick to a few key signals and refrain from pretending that we know a lot when we don’t. For example, we know about how well a particular team chases and how successful chasing teams are at a particular venue. But we don’t have a lot of signal on how well a given team chases at a given venue. One way to address this would be to identify similarities between teams and venues and cross-pollinate information across teams and/or venues weighted by similarity. However, we won’t go there in this piece.

To address the sparsity issue in the choice of a model, I decided to use a Bayesian approach. This allows us to use partial information that we may have in a given situation. For example, if a certain team hasn’t set a given total before or played on the ground in question before, we can still make a reasonable prediction using the model by using information on how the team has done in general and how the other teams have done on the ground. We do this by assuming that the factors that we are considering are independent of each other. So, if we consider the target and the ground we will assume that the target isn’t dependent on the chasing team or the ground and that it could have been the target regardless of which team was doing the chasing. From Fig. 3, we see that this isn’t such a bad assumption. While some grounds do see more high scoring or low scoring games than others, overall, targets have spanned a wide range on most grounds.

Additionally, it allows us to incorporate any prior beliefs that we may have regarding the situation at hand e.g. if we have reason to believe that the chasing team has an unequal chance of success. We will see how this can be useful in the section on pressure games later in this piece.

Win the Toss, Bat First?

While there are several opinions in pop discussions on whether batting first or chasing is a good idea in ODIs, the data (463 wins, 446 losses, 12 ties, 11 no results since 2011) suggests that almost exactly half of all games are won by the chasing team. So, given no additional information, both teams have an equal chance of winning. This tells us that the toss is important given the context of the match, not in isolation; which is a good thing for the game. This 50:50 win-loss ratio is what we will use as a prior assumption for our model.

So, How Well Does This Work?

We will let the model learn from matches played between Jan 2011 and the beginning of World Cup 2019. We will then see how well the model does on the matches in the World Cup.

While it is harder to visualize how the model works across factors, here is how it works for just the target score dimension.

Fig. 7: Model Predictions Overlaid on Actual Data

Fig. 7 shows how adding the contextual signals on conditions and chasing team help to differentiate likelihood of a successful chase for the same target.

Now, let us look at how the model works for matches from CWC2019 that were not used in building the model. This is akin to having had the model built at the beginning of CWC2019 and evaluating each match at the innings break.

Fig. 8: Predicted Probability Distributions By Actual Match Result

Overall, we see very good results where the bulk of the predicted probabilities of the target being chased down are in line with the actual outcome of the match. Note, that the focus here is not on doing a black/white prediction on the outcome of the match, but instead, on assessing the safety net provided by the posted total.

We do see that the lower tail of the distribution where the chasing team pulled off a victory goes down below 0.2 (20% probability). This suggests that there were matches for which our model would have given a false sense of security as far as the safety net provided by the target was concerned. There were four matches where the predicted probability was below 40% and yet, the team batting second won.

Bangladesh pulled off an emphatic win against the West Indies riding on the brilliance of Shakib Al Hassan & Litton Das on the smallish county ground at Taunton. The 321 total posted by the West Indies, was deemed 40–50 short by Jason Holder, but note that Taunton hasn’t hosted an international ODI in a long time and so we don’t have a lot of signal on the ground, West Indies lost 8 wickets getting to the 321 themselves (which in this case was due to poor batting, but could have been due to a changing wicket), and Bangladesh’s highest successful chase since 2011 had been a 318; all of which don’t exactly align with the manner in which Bangladesh executed the chase.

Two of the other matches in these 4, were in Birmingham which hasn’t seen too many high scoring games, with a highest successful chase of 277 since 2011.

The predicted probability for the India vs Sri Lanka game at Leeds may be a bit of a surprise in the context of the tournament, but Leeds has seen 3 victories and 4 losses by chasing teams since 2011 including a loss for India when chasing 294 against England in 2014 in the only game they have played at the ground. Besides, a 65% probability should, by no means, have lured any team into a sense of safety.

The Big Three Pressure Games

Finally, let’s look at the knockout games that decided the tournament. These are particularly interesting because the targets for each of these games were similar and so their assessment truly gives us an indication of how other factors play into the elasticity of that safety net for the team batting first. Our model predicted a probability of India chasing down the 239 in the first semi-final at 80%. England had it easier at 94% against Australia at Edgbaston and somewhat harder in the final at 67%. These outcomes are not surprising and they show how good New Zealand were against India at Old Trafford. It also puts England’s dominance at Edgbaston in perspective, despite them chasing a similar target. But, it truly helps us understand how close that final was set up to be even before England had played a single ball in the second innings. This was definitely not the popular perspective during the innings break at the fan zone in Trafalgar square where I happened to catch the game.

Let’s add some more color to this by considering that these being high pressure games, the chasing team were always going to be under additional pressure. If we factor this in by changing our prior assumption of a 50:50 chance of victory for each team to a 60:40 in favor of the team batting first, our model’s output for the probability of a successful chase changes to 66%, 94% & 47% for SF1, SF2, and the Final, respectively. This makes New Zealand’s semi-final win look a bit less like an upset than it was popularly perceived to be (maybe because India are always unbeatable when it comes to being popular favourites), and speaks to how Ravi Jadeja & Dhoni lit up that chase under pressure to get India so close, after a top order collapse that must have left that probability number reeling. This new set of outputs also makes the tied final a likely event! Both of these, would have been extremely valuable & insightful pieces of information to have at the innings break for each of those matches.

As it turns out, this 60:40 assumption isn’t unreasonable. In fact, it may be a bit conservative. Only 14 of the 43 matches with results before the knockouts at CWC2019 were won by the chasing team. So, the prior, in hindsight, should have been 67.5:32.5. Using this would give us predicted probabilities of 52%, 94%, 31% for the two Semi-Finals and the Final respectively. Note, how England were such overwhelming favourites at Edgbaston for the second Semi-Final, that the prior assumptions hardly change the guidance for that game.

The Final

Kane Williamson has spoken of having thought that a 240 would be a good total when he was batting with Ross Taylor in the Semi-Final against India. And that turned out to be just enough after India were 24/4 in the first 10. But you can’t expect that kind of a top order collapse every time you go out to bowl, and sure enough, England struggled early in the final, but didn’t lose too many wickets and got a few boundaries in as well. Our model shows that New Zealand were actually better off at the innings break against England than they were against India. The question is: what would have been a winning total to set for New Zealand in the finals without being over-optimistic about their bowling line-up?

Fig. 9: Safe Score Under Different Scenarios For the CWC2019 Final

The answer lies in the Fig. 9. Here, we use our model to look at the probability of England chasing different targets down for different scenarios of wickets lost in the first innings. Remember, we are using wickets lost as an indicator of the conditions, and of whether the team batting first were able to have their top batters utilize those conditions to achieve a target to their full potential.

Note, how the lines in Fig. 9 are slightly wider at lower scores than they are at higher ones. This makes sense because the wickets lost is only an indicator of whether a higher score could have been achieved. However, intuitively, the lines should be much closer or convergent at very higher totals. Since we are using wickets lost and scores achieved as independent factors, the model doesn’t pick this up. The catch is, that using them together would have sparse data that our model would have to interpolate from. Replacing wickets lost with an innings progression metric and adding actual information on conditions are likely to help this.

The further up you go on the Y-axis, the less safe your total is. I would think that New Zealand would have felt comfortable being at about 2:1 odds of winning or at a probability of about 0.33 (33%) for England to chase the total down. This would put them at about a 260. Sounds about right in hindsight, doesn’t it?