The Math

“Since you’ve finally stumbled here, and I’d like to believe it’s not by accident, let me show you the math behind our inferred table referenced in my piece pertaining to T20 selections. If you’ve followed the link via Twitter then please read the post above it to fully contextualize what you’re about to read in the subsequent literature. If you’ve come directly off my other T20 article on forecasting selections, read the below to understand the logic behind our Model Significant table.”
Explained Terminology
— — — — — — — — — — — — — — — — — — — — — -
RPI = Runs per innings
SR = Strike rate
MR = Mean runs per Innings for international Games
MS = Overall Strike Rate for international games
X = Intersection Point of domestic RPI for pre and post debut
Y = Intersection point of domestic SR for pre and post debut
Delta R (ΔR) — Percentage change of RPI between X & MR
Delta S (ΔS) — Percentage change of SR between Y & MS
— — — — — — — — — — — — — — — — — — — — — — — -
Cutting right to the chase, the method I used to procure the necessary datasets were divided into three categories (batting metrics only):
(1) International RPI and SR numbers for each match
(2) Pre Debut RPI & SR Numbers (All Non-International Games)
(3) Post Debut RPI & SR Numbers (All Non-International Games)
Once the datasets were collect, I plotted them as an XY Scatter plot with RPI (Runs per Innings) on the X-Axis while SR (Strike Rate) on the Y-Axis. Filling a single graphical plot with all three variables gave trend lines for each individual player along with their R squared values (I omitted the R squared values for ease of inference though)
For each individual, a completed scatter plot with all the necessary trend lines established gave us either a convergent or divergent trend on domestics (Pre & Post debut). However, to mark a commonality among both observed metrics for List A T20s, I took the XY intersection of Pre & Post debut and then compared that to the mean RPI and actual SR of the athlete’s international numbers.
The process allowed me to generate a Delta R (ΔR) and Delta S (ΔS) which acted as a percentage change to the player’s batting numbers in domestics vis-à-vis his international exploits. The Intersection of Pre and Post Debut were resolved using a simple linear equation method while the percentage change on Delta R & S were calculated as below:

I replicated this process on 9 different players to generate data points for Delta R and Delta S so that I could obtain different percentage changes on different players when comparing their X & Y to the Mean RPI and SR of their international numbers. The selected players used to generate these metrics were governed through a certain set of rules. These rules allowed me to filter out anomalies and focus on players who had a large sample size before debut and also provided reasonable data points post international debut as well. Based on these factors we ended up with the following table:

Players like Shehzad and Umar Akmal did not make the cut because their pre-debut game sample size was incredibly low (for Shehzad it was 3 games) while for Umar Akmal it was just 10 T20s. The same was the case with Sarfaraz who even though featured in a lot of T20s prior to his International T20 debut in 2010, in most of the games he had a ‘Did Not Bat’ which reduced his overall innings to 10. For players like Hafeez & Shoaib Malik their pre and post debut had severe anomalies since internationally, they debuted way before the T20s were even a part of at the global scale and the game played back then, was supremely different to how it is played today.
If you closely look at the above tabulation then we are even omitting Asif Ali since his numbers do not show any convergence between his pre and post debut trend lines on the positive X-axis. A lack of convergence on the positive X-axis scale implies two properties for the batsmen in question:
(a) An international debut has had no effect on the player’s domestic game (Very Small percentage change in Gradient of pre and post debut)
(b) The player has a diverging trend showing that an international debut has had a phenomenal effect.
In the case of Asif Ali, the (a) part of our hypothesis seems true which is why his numbers were not included in the data set as well. Conversely enough, if there is indeed a convergence of XY on the positive X-axis it would infer either of the two properties:
(i) If after debut gradient is greater than before debut; the player is progressing
(ii) If after debut gradient is less than before debut; the player is regressing
As a sample, look at Iftikhar’s numbers in the below graphical representation & try to isolate the properties that I have just defined above. Iftikhar’s numbers clearly show that his International debut in 2015, even though very brief (1 game), had a significant impact on him, so much so, that he completely revamped his T20 exploits domestically.

The jump in domestic numbers due to featuring in an International T20 basically provides a launching platform for a career comeback. This is the reason why Pakistan keeps on recycling tried and tested individuals because selectors can’t seem to wrap their heads around on who to debut in T20s, based on domestic-only numbers. Our inferred model which uses the above-metricized results not only provides benchmarks but also generates a Model Significant table with potential names and their variance from the stated Benchmarks.
To calculate those benchmarks I took the aggregate mean of Delta R and Delta S (figure 1 tabulation) which came to about -38.71 and -4.94 respectively. Since we know that Delta R & S are basically representations of RPI and SR, I then reverse-engineered (by using RPI 20 and SR 161.17 as the minimum international thresholds) to generate a domestic only RPI of 32.63 and a SR of 169.54.
I understand the need to explain the minimum international threshold but if you’ve not checked out my Twitter thread (link here) please go through it. In that handful of tweets I have explained why in international cricket, an over 20+ score with a 160+ SR is basically the most impactful performance a batsman can give. The inference was determined using all scorecards recorded of the Top 10 T20 teams in the last three years.
That said and based on our calculations, the benchmark for a domestic-only batsman was set to 32.63 for the RPI and 169.54 for the SR. This means that the closer the non-debuted batsman is to this magical number the more likely he will succeed in international cricket. I finally generated another tabulation with 23 names of all the non-debuted under 30 players that have featured as the top 50 batsmen in our domestic T20 comps in the last 4 years — This tabulation basically is the Model Significant Table which can be used to prioritized T20 debuts if Pakistan might need someone in a pitch prior to the World T20.

You can now go back to reading the piece which you were directed from. Based on the above calculations and metricized results I am inferring the stated POV in my earlier piece. If you want to look at the raw numbers on how I generated those benchmarks then please visit (here) — It’s an excel file with all the data for figure 1 tabulation.
Appendix
Babar Azam

Imad Wasim

Haris Sohail

Fakhar Zaman

Asif Ali

Mohammad Rizwan

Shadab Khan

Sharjeel Khan

Iftikhar Ahmed

