A pressure index for the team batting second in T20I cricket

In sports, players usually undergo pressure situations in order to meet certain performance standards set by themselves or others. During the course of any competitive sporting event, players are often motivated to take calculated risks in attempts to secure a victory or to showcase their performance capabilities. However, quantifying the pressure experienced by players at any given stage of a game is quite a challenging and imposing task. This study discusses a method to compute the pressure experienced by batters when pursuing a target in a T20I cricket match. Diligent and extensive exploration of psychological pressures motivates us to formulate a differential equation, based on a set of reasonable assumptions, whose solution gives rise to a useful pressure index formula for quantifying the level of pressure experienced by the batters of the team batting second, i.e., the team chasing the target. This index takes into account two key assumptions: first, the rate of change of pressure on the batters at a given stage of the game depends on the pressure at that stage; and, second, the required run rate commensurate with available resources remaining at that stage of the game. The available data are used to fine-tune the parameter of the model. The applicability of the proposed pressure index is illustrated using data for T20I matches played by the major test playing countries during the years 2017, 2018, 2019, and 2021. Additionally, this pressure index can be used not only to predict the probability of winning at any given stage of the second innings, but also to quantify the contribution of each batter, taking into account the pressure situation in which they score runs.