Long-format batting involves getting your eye in, because one mistake can send a batter back to the hut. Getting your eye in refers to the vulnerable period at the start of an innings when the batter is acclimating to conditions, aiming to settle in and then gather runs. It follows that batting is harder and getting out much easier when one is new to the crease. To see this borne out by the data, we can look at something called the hazard rate, which tells you the chances of a batter getting out on a given score if they have already reached that score unbeaten. (Note that this is not the chance of getting out for a score at the beginning of the innings. Instead, this tells you how likely someone is to be dismissed if they are batting at a given score.)

The figure below shows this hazard rate for Test innings at batting positions one through seven since 2016 through to the end of the first England-New Zealand Test earlier this month, and it tells us a number of things about the nature of batting.

Firstly, the hazard peaks early in the innings, from a score of zero to about four runs. Then it falls steeply and continuously from a score of around 4 to about 30 runs - this is the "settling down" phase. The process of a batter traversing this period is the often quoted "getting a start". Through this phase, the chances of getting out decrease rapidly, and once past a score of 30, the hazard rate effectively plateaus within a small range, which means the chances of dismissal remain more or less the same - the batter is "in". Finally, the curve shows the effect of an approaching hundred, as batters take fewer risks after 90. After 100, the curve shoots up - a possible indicator of batters relaxing after the milestone.

This number can be recast into an "effective average" (first used in this paper) that tells us how well the batter is doing at every stage of their innings. This is not the average runs expected from a given point in the innings. Rather, it quantifies the quality of a batter at a given score. For instance, as the graph below shows, someone batting at a score of 5 runs has an effective average of 30.1, which increases to 37 for a batter at 20 runs. In going from 5 to 20 and settling in, the batter increases their quality from someone with an average of 20 to someone with an average of 37. The range from 40 to 80 runs is the best period for batting: one has an effective average of 40-50 in this phase.

Remarkably, splitting the hazard rate curves by home and away batters shows that the two have almost identical shapes, but the away curve is higher at all stages of the innings. A visiting batter shows the same periods of vulnerability, but they are more vulnerable at all stages of their innings compared to the home batters.

Comparing the hazard curves for batters from 2000 through 2015, and then from 2016 onwards (graph below), we see that it has been significantly harder for batters to settle down in the last five years, as the hazard rates for scores less than 25 is consistently higher compared to those for the 2000-2015 era.

The other noticeable difference is the presence of multiple upticks in the hazard rate throughout the innings in the post-2015 data. Batters in this period have intermittent vulnerable stages and are less settled than those in 2000-2015. This could point to a combination of deeper bowling attacks, higher risk-taking at all points in the innings, and possibly, more frequent lapses of concentration. Note also the sharp drop in the 80-to-100-run period for batters after 2015. A possible inference there is that these days batters are playing it much safer as the century milestone approaches than before.

The difficulty in getting the innings started can be quantified by summing up the hazard until the threshold score of 25. This number is the chance of crossing 25 runs, which we shall call the success rate. Getting dismissed under this score is mostly labelled an unsuccessful innings, across conditions and situations.

To shine a light on the drop in the success rate from the pre-2015 era to recent times, I broke it up by host country, and then by home and away batting. At home, players are primed to bat on familiar pitches, and their numbers set a baseline for batting. For visiting batters, run output depends on a combination of their ability to adapt and the quality of the home bowlers. Read in conjunction, the shifts in success rate for the two subsets of batters can help us disentangle the effects of quality and conditions, and to assess the progress of a team.

Even at home, batters are finding it tougher to get starts, which can be attributed to tougher batting conditions around the world. Considering UAE as a home country for Pakistan, we see that the home success rate has dropped for all countries except New Zealand, who have had a set of quality batters in Tom Latham, Kane Williamson and Ross Taylor perform superbly at home. The deflation of success rate in Sri Lanka might be indicative of the general drop in their batting stocks (more on this later). It is similar for West Indies, although the Dukes ball has surely played a role. England too have seen a significant drop, which results from greener pitches and not being able to find a stable top order in the past few years.

Excluding home batters, we can look at how different countries have become harder to tour, which results from a combination of change in conditions and the changing quality of home bowlers and their ability to best utilise their own pitches. As the arrow plot above shows, the success rate for touring batters in Sri Lanka has increased. Read in conjunction with the decrease in success rate for Sri Lankan batters at home, we can conclude that both batting and bowling quality have gone down for Sri Lanka 2016 onwards.

In England, success rates for away batters have fallen by about six percentage points, which is the same as the difference for home batters over the two periods. This points to conditions generally shifting towards being conducive to bowlers.

In India, away batters now find it much tougher to cross 25 runs. Since the success rate for the home batters has not changed much, in contrast, we can conclude that this effect arises from tougher conditions, but more importantly, highly penetrative Indian bowling. In fact, India is the toughest place to get a start if you are a touring batter.

The large drop in the success rate of visitor batters to New Zealand exhibits how their bowling has deepened. With both their disciplines showing significant improvement in the years after 2015, their place in the World Test Championship final during a golden era for Test cricket is no surprise.

The most dramatic drop in the success rate for away batters is in Bangladesh, which is a testament to the progress of that team's bowling. The success rate of their own batters has decreased at home, but not more than that of the batters who tour them. We can infer that they have settled on a template of spin-friendly pitches where their spinners can win them Test matches by outbowling the opposition.

If you are a visiting batter looking to start an innings, what kind of home bowling threatens you the most in different conditions? The following table shows the runs per wicket for visiting batters since 2016 in the early part of their innings, before they cross 25 runs. Bangladesh and Sri Lanka stand out as places easy to begin an innings facing quick bowling, whereas starting is comparatively easy against spin in South Africa and the West Indies. India and the UAE are the only two places where facing both spin and pace is difficult for batters new at the crease. Pakistan have traditionally had good spinners and quick bowlers, but the numbers for India signify the rise of a threatening pace unit, and that their fast bowlers and spinners are about equally lethal, even at home.

Not only is starting an innings tougher these days, but the hazard rate for the post-2015 era also bumps up at multiple points after getting set, as we saw earlier. The aggregate numbers seem to hint that in today's era, a batter can never really be settled, even at a score of 40. Anecdotal examples of the kinds of conditions that support these numbers abound. For example, in the summer of 2018, the Dukes ball swung through the day in England, ensuring batters were never coasting even after getting starts.

We saw that the hazard function effectively stabilises within a narrow range when a batter is in the 50-70-run period. After the crossing of the half-century milestone and far from an impending hundred, this phase is the most "settled" for batting. The runs per wicket in different conditions in this phase show us how well settled a player truly is.

The runs-per-wicket figure in this phase is generally higher for home batters, who are experienced at batting long spells in well-known conditions. For visiting batters, Bangladesh, Sri Lanka, and the UAE are the best places to bat when settled. England, New Zealand, and South Africa present a contrast - even when settled, you average in the low 20s and early 30s. In India, the threat of two world-beating spinners looms even after the 50-run mark. Among home batters, India make you pay the heaviest if you let them get set, while England and the Caribbean are still comparatively tough to bat in, even for set home batters.

Except for the UAE and Sri Lanka, the runs-per-wicket figures have fallen everywhere. Not only is it much harder to get in as an away batter, it is also harder to stay in and score runs. In the 2000s, the maxim was to battle tough conditions, survive difficult periods and cash in later. Now bowlers are not only fitter and bowl longer spells more effectively, bowling attacks are more rounded and better manned, offering little to no let-ups: the cashing-in window is drastically smaller. This is further confirmed by looking at how the averages of the third and fourth bowlers in home teams have fallen in all countries except Sri Lanka. Some of this effect results from the difficult conditions, but the increased quality of bowlers has surely had a role to play.

It is accepted that Test match batting has become noticeably harder in the past few years in comparison to the beginning of the 21st century. Couple the deepening of bowling attacks to teams maximising the effect of home conditions and the shortening of Test tours, which gives touring sides less opportunity to practice in alien conditions, and you have a perfect cocktail of reasons why batting averages have plunged in the last five to six years compared to the high-scoring first 15 years of the 21st century.