GooglyPlusPlus2022 optimizes batting/bowling lineup

Posted on February 6, 2022 by Tinniam V Ganesh in R bloggers | 0 Comments

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GooglyPlusPlus2022 is the new avatar of last year’s GooglyPlusPlus2021. Roughly, about 5 years back I had written a post on Using linear programming to optimize T20 batting and bowling line up. This post has been on the back of my mind for a long time and I decided to pay this post a revisit. This requires computing performance of individual batsmen vs bowlers and vice-versa for performing the optimization. So in this latest incarnation, there are 4 new functions

batsmanVsBowlerPerf – Performance of batsmen against chosen bowlers
bowlerVsBatsmanPerf – Performance of bowlers versus specific batsmen
battingOptimization – Optimizing batting line up based on strike rates ad remaining overs
bowlingOptimization – Optimizing bowling line up based on economy rates and remaining overs

These 4 functions have been incorporated in all the supported 9 T20 formats namely a. IPL b. Intl. T20(men) c. Intl. T20 (women) d. BBL e. NTB f. PSL g. WBB h. CPL i. SSM

Check out GooglyPlusPlus2022!!

You can clone/fork the code for GooglyPlusPlus2022 from Github from gpp2022-1

With this latest update you can do a myriad of analyses of batsmen, bowlers, teams, matches. This is just-in-time for the IPL Mega-auction!! Do check out these other posts of GooglyPlusPlus for other detailed analysis

A) Batsman Vs Bowlers – This option computes the performance of individual batsman against individual bowlers

a) IPL Batsmen vs Bowlers

Included below are the performances of Dhoni, Raina and Kohli against Malinga, Ashwin and Bumrah. Note: The last 2 text box input are not required for this.

b) Intl. T20 (men) Batsmen vs Bowlers

Note: You can type the name and choose from the drop down list

B) Bowler vs Batsmen – You can check the performance of specific bowlers against specific batsmen

a) Intl. T20 (women) India vs Australia

b) PSL Bowlers vs Batsmen

C) Strategy for optimizing batting and bowling line up

From the above 2 tabs, it is obvious, that different bowlers have different ER and wicket rate against different batsmen. In other words, the effectiveness of the bowlers varies by batsmen. Conversely, batsmen are more comfortable with certain bowlers versus others and this shows up in different strike rates.

Hence during the death overs, when trying to restrict batsmen to a certain score or on the flip side when the batting side needs to score a target within certain overs, we need to take advantage of the relative effectiveness of bowlers vs batsmen for optimising bowling and aggressiveness of batsmen versus bowlers to quickly reach the target.

This is the approach that is used for bowling and batting optimisation. For optimising bowling, we need to formulate a minimisation problem based on ER rates and for optimising batting, a maximisation strategy is chosen based on SR. ‘Integer programming’ is used to compute during the last set of overs

This latest version includes optimization using “integer programming” based on R package lpSolve.

Here are the 2 formulations

Assume there are 3 bowlers – $bwlr_{1},bwlr_{2},bwlr_{3}$
and there are 3 batsmen – $bman_{1},bman_{2},bman_{3}$

I) LP Formulation for bowling order

Let the economy rate $er_{ij}$ be the Economy Rate of the jth bowler to the ith batsman. Also if remaining overs for the bowlers are $o_{1},o_{2},o_{3}$
and the total number of overs left to be bowled are
$o_{1}+o_{2}+o_{3} = N$

Let the economy rate $er_{ij}$ be the Economy Rate of the jth bowler to the ith batsman.
Objective function : Minimize –
$er_{11}*o_{11} + er_{12}*o_{12} +..+er_{1n}*o_{1n}+ er_{21}*o_{21} + er_{22}*o_{22}+.. + er_{22}*o_{2n}+ er_{m1}*o_{m1}+..+ er_{mn}*o_{mn}$
i.e.
$\sum_{i=1}^{i=m}\sum_{j=1}^{i=n}er_{ij}*o_{ij}$
Constraints
Where $o_{j}$ is the number of overs remaining for the jth bowler against ‘k’ batsmen
$o_{j1} + o_{j2} + .. o_{jk} < o_{j}$
and if the total number of overs remaining to be bowled is N then
$o_{1} + o_{2} +...+ o_{k} = N$ or
$\sum_{j=1}^{j=k} o_{j} =N$
The overs that any bowler can bowl is $o_{j} >=0$ =0″ class=”latex” />

II) LP Formulation for batting lineup

Let the strike rate $sr_{ij}$ be the Strike Rate of the ith batsman to the jth bowler
Objective function : Maximize –
$sr_{11}*o_{11} + sr_{12}*o_{12} +..+ sr_{1n}*o_{1n}+ sr_{21}*o_{21} + sr_{22}*o_{22}+.. sr_{2n}*o_{2n}+ sr_{m1}*o_{m1}+..+ sr_{mn}*o_{mn}$
i.e.
$\sum_{i=1}^{i=4}\sum_{j=1}^{i=3}sr_{ij}*o_{ij}$
Constraints
Where $o_{j}$ is the number of overs remaining for the jth bowler against ‘k’ batsmen
$o_{j1} + o_{j2} + .. o_{jk} < o_{j}$
and the total number of overs remaining to be bowled is N then
$o_{1} + o_{2} +...+ o_{k} = N$ or
$\sum_{j=1}^{j=k} o_{j} =N$
The overs that any bowler can bowl is
$o_{j} >=0$ =0″ class=”latex” />