Simulation-Based Optimisation of Batting Order and Bowling Plans in T20 Cricket

Tinniam V Ganesh

cs.LGApr 15, 2026

Simulation-Based Optimisation of Batting Order and Bowling Plans in T20 Cricket

Authors: Tinniam V Ganesh

Abstract

This paper develops a unified Markov Decision Process (MDP) framework for optimising two recurring in-match decisions in T20 cricket, namely batting order selection and bowling plan assignment, directly in terms of win and defend probability rather than expected runs. A three-phase player profile engine (Powerplay, Middle, Death) with James-Stein shrinkage (a technique that blends a player's individual statistics toward the league average when their phase-specific data is sparse) is estimated from 1,161 IPL ball-by-ball records (2008-2025). Win/defend probabilities are evaluated using vectorised Monte Carlo simulation over N = 50,000 innings trajectories. Batting orders are evaluated by comparing all feasible arrangements of the remaining players and selecting the one that maximises win probability. Bowling plans are optimised through a guided search over possible over assignments, progressively improving the allocation while respecting constraints such as the prohibition on consecutive overs by the same bowler. Applied to two 2026 IPL matches, the optimal batting order improves Mumbai Indians' win probability by 4.1 percentage points (52.4% to 56.5%), and the optimal Gujarat Titans bowling plan improves defend probability by 5.2 percentage points (39.1% to 44.3%). In both cases, the observed sub-optimality is consistent with phase-agnostic deployment: decisions that appear reasonable under aggregate metrics are shown to be costly when phase-specific profiles are applied.

Figures & tables

Phase	Overs (0-indexed)	Characteristic Conditions
Powerplay (PP)	0 – 5	Fielding restrictions; elevated scoring rates
Middle (MI)	6 – 14	Spin-friendly; dot-ball accumulation
Death (DE)	15 – 19	Yorkers; pull shots; explosive hitting

Table 1

Parameter	Value
MI score	148/1
Runs needed ( $r_{0}=d_{0}$ )	73
Legal balls remaining ( $b_{0}$ )	44
Required run rate	9.95 per over
MI batsmen at crease	RD Rickelton (non-striker, fixed)
MI batting pool $\mathcal{P}$	SA Yadav, Tilak Varma, HH Pandya, Naman Dhir

Table 2

Batsman	Hist. balls (MI)	Hist. balls (DE)	Death SR	$p^{W}_{\text{DE}}$	Middle SR	$p^{W}_{\text{MI}}$
RD Rickelton	342	156	156.4	0.079	152.9	0.100
SA Yadav	1,765	460	181.3	0.089	143.8	0.035
Tilak Varma	1,132	388	185.5	0.070	137.3	0.030
HH Pandya	844	512	171.6	0.070	134.0	0.037
Naman Dhir	498	204	203.9	0.070	145.9	0.049

Table 3

Figure 1: Figure 1: MI batsman phase-specific profiles (KKR vs MI, over 12 intervention). The phase asymmetry of Naman Dhir is the key structural feature driving the optimal batting order.

Next-In	Best Win%	Optimal Remaining Order
SA Yadav (actual)	56.5%	Naman Dhir → Tilak Varma → HH Pandya
Naman Dhir	55.7%	SA Yadav → Tilak Varma → HH Pandya
Tilak Varma	55.1%	Naman Dhir → SA Yadav → HH Pandya
HH Pandya	53.3%	Naman Dhir → Tilak Varma → SA Yadav

Table 5

Rank	Position 4	Position 5	Position 6	Win%
1 (opt)	Naman Dhir	Tilak Varma	HH Pandya	56.5%
2	Naman Dhir	HH Pandya	Tilak Varma	56.1%
3	Tilak Varma	Naman Dhir	HH Pandya	55.2%
4	HH Pandya	Naman Dhir	Tilak Varma	52.9%
5 (actual)	Tilak Varma	HH Pandya	Naman Dhir	52.4%
6	HH Pandya	Tilak Varma	Naman Dhir	51.8%

Table 6

Figure 2: Figure 2: Best achievable win probability by next-in choice at Position 3. SA Yadav’s low Middle-over dismissal probability makes him the optimal bridge.

Scenario	Win% (MI)
Worst possible batting order	50.0%
Actual batting order	52.4%
Optimal batting order	56.5%
Gain from optimal order	+4.1 pp

Table 8

Parameter	Value
PBKS score	83/2
Runs needed ( $r_{0}=d_{0}$ )	80
Legal balls remaining ( $b_{0}$ )	60 (overs 10–19 after Rashid completes over 9)
PBKS wickets in hand	8
Required run rate	8.00 per over

Table 9

Bowler	Overs bowled	Quota left	Hist. balls (MI)	Hist. balls (DE)	Middle ER	$p^{W}_{\text{MI}}$	Death ER	$p^{W}_{\text{DE}}$
Ashok Sharma	1	3	0	0	7.49†	0.043†	9.37†	0.083†
K Rabada	2	2	466	599	7.35	0.053	9.36	0.104
Mohammed Siraj	2	2	451	673	7.35	0.048	9.55	0.067
Rashid Khan	3*	1	2,223	564	6.58	0.047	8.40	0.075
Washington Sundar	2	2	654	81	7.07	0.033	9.61	0.068
M Prasidh Krishna	0	4	398	505	7.47	0.047	9.79	0.086

Table 10

Figure 3: Figure 5: GT bowler landscape at the over 10 intervention point. The optimal Death-over bowler (Rashid Khan) is in the top-left; the most expensive deployed bowler (M Prasidh Krishna) is toward the bottom-right.

Figure 4: Figure 6: Best achievable defend probability by over 10 opener choice. Siraj’s two-over quota makes him the highest-value opener despite not being unused in the actual plan.

Over	Bowler	Phase	Economy
10	Ashok Sharma	MI	7.49
11	Rashid Khan	MI	6.58
12	M Prasidh Krishna	MI	7.47
13	Washington Sundar	MI	7.07
14	M Prasidh Krishna	MI	7.47
15	K Rabada	DE	9.36

Table 13

Over	Bowler	Phase	Economy	Changed?
10	Mohammed Siraj	MI	7.35	←
11	Washington Sundar	MI	7.07	←
12	K Rabada	MI	7.35	←
13	Mohammed Siraj	MI	7.35	←
14	Washington Sundar	MI	7.07	←
15	Ashok Sharma	DE	9.37	←

Table 14

Rank	Ov10	Ov11	Ov12	Ov13	Ov14	Ov15	Ov16	Ov17	Ov18	Ov19	Defend%
1 (opt)	Siraj	Sundar	Rabada	Siraj	Sundar	Ashok	Rashid	Ashok	Rabada	Ashok	44.3%
2	Sundar	Krishna	Sundar	Siraj	Rabada	Ashok	Rashid	Ashok	Rabada	Ashok	44.0%
3	Sundar	Siraj	Sundar	Rabada	Siraj	Ashok	Rashid	Ashok	Rabada	Ashok	43.9%
4	Siraj	Sundar	Siraj	Krishna	Rashid	Ashok	Rabada	Ashok	Rabada	Ashok	43.5%
Actual	Ashok	Rashid	Krishna	Sundar	Krishna	Rabada	Krishna	Ashok	Krishna	Sundar	39.1%

Table 15

Figure 5: Figure 7: Top 10 GT bowling plans heatmap. The vertical divider separates Middle overs (left) from Death overs (right); Rashid Khan appears in Death over 16 in all top plans.

Figure 6: Figure 8: Actual vs optimal GT bowling plan (overs 10–19). The total gain of +5.2 pp is distributed across multiple substitutions, with Siraj’s inclusion and Rashid’s repositioning contributing the most.

Bowler misused	Phase deployed	Death ER	Better option	Better Death ER	Cost (RPO)
MP Krishna	Death (2 overs)	9.79	Rashid Khan	8.40	−1.39
Siraj	Not used	—	—	—	−0.49 per over

Table 18

Symbol	Definition
$(r,b,w)$	Match state: runs remaining, balls remaining, wickets
$R_{\max}$	Maximum runs in the state space
$B=120$	Total balls in T20 innings
$\mathcal{P}$	Pool of available batsmen
$\sigma$	Batting order — permutation of $\mathcal{P}$
$\pi=(\pi_{1},\ldots,\pi_{m})$	Bowling plan — ordered over assignments

Table 19

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Ryota Takamido, Hiroki Nakamoto

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Soumyadeep Roy

St. Xavier’s College (Autonomous), Kolkata, India

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Abstract

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