IMPACT FACTOR

The 'impact factor' of conversion rates

by Himanish Ganjoo • Last updated on

While Steven Smith's rise in Test cricket has been on a gradual rise, Kohli's has been dramatic during the extended home season. © BCCI

Modern day batsmanship has reached a new crescendo in recent years. With a spate of high scores, Virat Kohli and Steven Smith are racing ahead of their young contemporaries in Tests. Smith, in his magnificent run over the past four years, with 1000 runs in each year since 2013, has drawn comparisons, not for no reasons, to none other than Sir Donald Bradman. On the other hand, Kohli has been in focus for his superior conversion rate from 50s to 100s, which is second only to Bradman (for a minimum of 3000 Test runs).

Conversion rates form an important metric in determining the ability of a batsman to go on and make high scores, which eventually can have a telling impact on the game. A higher rate means a higher probability of a batsman going on to make a ton once he has made a fifty. In technical terms, a conversion rate is a conditional probability: given that the event of crossing a 50 has already happened, what is the chance of crossing a 100 for a particular batsman?

With this general framework, one can go on to define conversion rates for any two scores. For instance, what is the probability of Smith converting a 20+ score into a hundred? In cricketing terms, if one takes 20 to be a "start" for a batsman, with what frequency will a start be converted into a ton?

Similarly, one can define another level: the conversion of a start into a fifty. A fifty-plus score translates to a good innings (barring the context and the scores of the other batsmen in the innings), and one can ask for any batsman, what proportion of starts are converted to good innings. This analysis will throw light on the frequency levels of crossing these parameters, and later about the magnitude of these crossings, in three parts. In the following, we consider 185 batsmen with over 3000 Test career runs. Statistics are updated till after the third Ashes Test in 2017.

Proportions:

So, here are three levels for a batsman's statistics: 20, which is a "start"; 50, which means a "good" innings, and 100 which is the conventional marker for measuring batting impact. In this study, these levels will be referred to as barriers.

The first barrier, that of 20 runs, is a signal of basic batting competence. Let's just simply measure the proportion of innings over 20. If scoring less than 20 is called a failure, a higher percentage of innings more than 20 means a smaller "failure rate". Who are the best batsmen in this regard?

Name Inns Avg % of 20+ H Sutcliffe 84 60.73 78.57 JB Hobbs 102 56.95 72.55 DG Bradman 80 99.94 72.5 WR Hammond 140 58.46 69.29 ED Weekes 81 58.62 69.14 RB Kanhai 137 47.53 67.15 ER Dexter 102 47.89 66.67 KF Barrington 131 58.67 66.41 IR Redpath 120 43.46 65.83 MEK Hussey 137 51.53 65.69

In a rare a metric where Bradman is not heading the chart, one can note that Sutcliffe and Hobbs pip him, though not by much. The list is otherwise filled with the usual suspects: Hammond, Weekes, Barrington, all making expected appearances. The oft-underrated Guyanese 'keeper Rohan Kanhai finds a place in the top ten: 67% of his innings cross the 20-run mark. That figure, in that age, batting at 3 and 4 as a gloveman, is truly remarkable. Ted Dexter crossed 20 in two out of every three innings on average. Six of his hundreds were above the 140-mark, the effect of which can be seen in the following metrics.

Next is the list with the top proportion of 50-plus scores, which is, by conventional cricketing wisdom, a landmark signifying a good innings.

Name Inns Avg % of 50+ DG Bradman 80 99.94 52.5 H Sutcliffe 84 60.73 46.43 JB Hobbs 102 56.95 42.16 ED Weekes 81 58.62 41.98 KF Barrington 131 58.67 41.98 JE Root 116 52.37 40.52 SPD Smith 108 62.32 39.81 Saeed Anwar 91 45.53 39.56 CL Walcott 74 56.69 39.19 KC Sangakkara 233 57.41 38.63

When the barrier is raised to 50, Bradman regains his perch atop the list of batting greats. He might not have had the highest frequency of crossing 20, but he converted his "starts" better than anyone else, boasting of more than half his innings crossing 50. Joe Root and Smith too make early claims to the hall of Test fame, with a fifty-frequency of about 40%.

To finish the set, here is the proportion of 100-plus scores, which just tells us how frequently batsmen score hundreds:

Name Inns Avg % of 100s DG Bradman 80 99.94 36.25 SPD Smith 108 62.32 20.37 CL Walcott 74 56.69 20.27 H Sutcliffe 84 60.73 19.05 V Kohli 106 53.76 18.87 ED Weekes 81 58.62 18.52 KC Sangakkara 233 57.41 16.31 ML Hayden 184 50.74 16.3 GS Sobers 160 57.78 16.25 JH Kallis 280 55.37 16.07

Smith and Kohli too find a spot here. Their careers are short compared to the modern-day greats that make up the rest of the table, but longer than the party of Walcott, Sutcliffe and Weekes, with hundred frequencies that challenge them. One can also notice that Kohli has the second-lowest average of the ten, but makes it to the list, signifying his penchant for big tons mixed with low scores. Joe Root falls out of the table, who is consistent at good scores, but fails to convert.

Concluding this section, is a look at the 20, 50 and 100 frequencies of the top 10 run-getters in Test cricket:

Name Inns Avg 20% 50% 100% SR Tendulkar 329 53.79 58.66 36.17 15.5 RT Ponting 287 51.85 62.72 35.89 14.29 JH Kallis 280 55.37 62.5 36.79 16.07 R Dravid 286 52.31 62.94 34.62 12.59 KC Sangakkara 233 57.41 63.09 38.63 16.31 BC Lara 232 52.89 58.19 35.34 14.66 S Chanderpaul 280 51.37 61.43 34.29 10.71 DPMD Jayawardene 252 49.85 57.54 33.33 13.49 AN Cook 272 45.57 56.99 31.62 11.4 AR Border 265 50.56 61.51 33.96 10.19

Conversions:

Certain players rose and fell through the tables, changing the barriers. The relative rise and fall with a change in these barriers for a certain player is directly indicative of their conversion rate between any two levels. For instance, if Joe Root falls out of the top 10 as one goes from a 50-barrier to a 100-barrier, one would know 50-to-100 conversion rate must be low (as is common knowledge).

So, one is inclined to ask: Who has the best conversion rates from a half-century to a hundred? Who converts his starts the best into fifties? Who is most likely to take his starts to a century? The following table presents the top ten ranked as per conversion rates:

Name 20->50 Name 50->100 Name 20->100 DG Bradman 72.41 DG Bradman 69.05 DG Bradman 50 CL Walcott 67.93 CL Walcott 57.15 CL Walcott 33.33 V Kohli 66.2 V Kohli 51.72 V Kohli 32.79 SPD Smith 65.14 SPD Smith 51.18 SPD Smith 31.88 Ijaz Ahmed 64.86 Ijaz Ahmed 51.17 Ijaz Ahmed 31.57 DL Amiss 64.45 DL Amiss 50.9 DL Amiss 27.5 RN Harvey 63.21 RN Harvey 50.83 RN Harvey 27.28 ED Weekes 63.17 ED Weekes 50.73 ED Weekes 26.79 Younis Khan 62.97 Younis Khan 50.02 Younis Khan 26.77 SR Tendulkar 62.31 SR Tendulkar 50 SR Tendulkar 26.42

Root and Kane Williamson have some of the best rates of making fifties when they cross 20 runs, but on the 50-to-100 conversion chart, they fall to ranks 137 and 57 respectively. When it comes to converting starts to tons, one can observe that Kohli and Smith rise to the very top, be it converting 50s or 20s - a numerical reflection of their dominance in the Test arena. The worst 50-to-100 conversion rates among batsmen with an average greater than 45 are:

Name Conversion (50->100) MiddleMean Misbah-ul-Haq 20.42 70.38 VVS Laxman 23.3 67.25 EH Hendren 24.99 71 ER Dexter 24.99 68.52 RB Simpson 27.03 69.96 B Mitchell 27.59 72.67 JE Root 27.67 70.06 SM Katich 28.57 73.28 FMM Worrell 29.02 68.59 AR Border 30.01 68.87

Misbah-ul-Haq is a surprise entry at the bottom, but as the "MiddleMean" column shows, he makes a mean of 70.38 runs when he stays between 50 and 100.

Saeed Anwar just misses out and joins Joe Root in falling from high positions in the 20-to-50 table to the 50-to-100 conversion rates. Ted Dexter, Frank Worrell and Allan Border are the other celebrated batsmen who make this ignominious table of wooden-spooners.

For a more visual way to look at this data, below is a bar graph that best suits the comparison of proportions of innings and conversion rates. The method is to stack the percentages of the different barriers one behind the other, so that one can look at overlaps between them (which show us conversion rates). More importantly, looking at one horizontal level allows one to compare the proportions for different batsmen.

The lowest, darkest-colour level denotes the percentage of 100s. The second level shows the percentage of scores of 50 or more, and the top bar shows the frequency of crossing 20 runs in an innings.

Here is the chart for a few young batsmen of the current day, with Bradman for comparison:

Graphical representation for conversion rates of 50 to 100 as compared to Sir Don Bradman. ©Cricbuzz

This representation immediately yields interesting results:

Cheteshwar Pujara reaches 20 most frequently out of these (the top-most level), but his percentage of fifties is well below Kane Williamson, Root and Smith.

Virat Kohli's proportion of fifties is around Bradman's proportion of 100s.

Azhar Ali has a slightly better proportion of tons than Root.

Moreover, looking at the area that is in overlap, one can also view the conversion rates of batsmen. For instance, the darkest band for Smith covers half of the second, lighter blue band, whereas for Williamson it covers a noticeably smaller area in overlap. One can note Smith's better conversion rate at a glance, here.

Here is the same graph for the top ten run-getters in Test cricket:

Graphical representation for conversion rates of the top ten run-getters in Tests. ©Cricbuzz

It tells us that Tendulkar had the lowest rate of reaching just 20, but a similar chance of scoring a 50 as Ponting, giving him a better 20-to-50 conversion rate. Sangakkara was the most likely to score a fifty, and Chanderpaul was the least likely to score a ton.

Impact:

With all this talk of probability and conversion, one seeks to count the number of "crossings" of a barrier in a batsman's career, which is all well and good, but what about the "height" of these crossings? After all, simply crossing a hundred is great, but isn't crossing a hundred and making a big score a more impactful achievement?

If one sets century as a barrier for an impactful innings (again, ignoring the context of the innings for simplicity), one should not only measure how often the hundreds are scored, but also how high they go. This can be encapsulated in the impact factor: the product of the probability of crossing a 100 runs with the mean runs scored in all innings when it is crossed. Notice that here the mean is taken, as this number concerns the impact in one particular innings, rather than the concept of the batsman getting out.

The top ten by that metric are:

Name % of 100s Mean Impact DG Bradman 36.25 185.97 67.41 SPD Smith 20.37 146.68 29.88 V Kohli 18.87 150.4 28.38 ED Weekes 18.52 150.4 27.85 KC Sangakkara 16.31 166.95 27.23 CL Walcott 20.27 133.33 27.03 WR Hammond 15.71 167.5 26.31 BC Lara 14.66 173.21 25.39 H Sutcliffe 19.05 130.56 24.87 GS Sobers 16.25 150.69 24.49

Of course, the barrier defining this impact can be set to different values, which gives different rankings (the table of the entire data set can be found at the end of the analysis)

With this defined, one can also try and chart the evolution of the impact factor through a player's career. For the purpose of this analysis, one can look at the impact factor at a barrier of 100 runs, and start at 40 innings, proceeding till the end of a batting career.

The curve on the graph for any batsman spans his career in innings, and shows the impact factor at that point in the career. Here is the graph for the "Fab Four":

Graphical representation of the Impact Factor for the top-four batsmen of the current generation. ©Cricbuzz

This graph unravels the evolution of the impact as careers have unfolded, with the information of form imprinted on the motion of the curve.

Smith rises to a high level steadily early on in his career, and then, despite some fluctuations, is miles ahead of his three contemporaries for the most part. His curve only rises, on average, as his career progresses. Kohli projects dramatic undulations in his impact, the very hefty slope downward from innings 60 to 70 being his abysmal England tour dragging him down the most. However, from then on, he has only risen on average, and on the back of massacring a hapless Lankan side, has now managed to touch Smith's curve.

Williamson's impact rises consistently from a low value early on, and then stabilises around the 80-innings mark. A middling Indian tour and no tons against Pakistan at home make his graph dip, which picks up again after two centuries against South Africa.

Root's is the most worrying curve: starting out better than the others, but going flat, and then falling in recent times, below all the others eventually.

A similar graphical representation will also throw light on arguably the most talked about batsmen from the previous generation. It is clear how Tendulkar was mostly dominant in terms of ton-scoring almost all throughout his career. His peak might not have been higher than that of Ponting, but he was very good for very long, and therein lied his greatness, both skillwise - well documented through stats too.

Graphical representation of the Impact Factor for the top-four batsmen of the previous generation. ©Cricbuzz

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Himanish Ganjoo is a graduate student in physics from Delhi, who indulges in kebabs, Ghalib and Delhi history when not working on cosmology.

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