# T20 cricket winning probability

Given that an opponent Team A has scored X runs (in the first innings), what is the probability that Team B will beat this score? Also, what is the expected score of the chasing Team B? Suppose I have a lot of past match data for both teams but let us just keep it simple and use only data of the form $$(x_i,y_i)$$ where $$x_i$$ was an opponent team's score and $$y_i$$ was Team B's final score in matches when Team B batted second. Alternatively, we could have only opponent score and match result (win/loss/toss) data for Team B. e.g. (212,lost);(163,won) etc

I have noticed that the batting scores are normally distributed. Using this I have built a simple, untruncated model that gives a probability for a particular team scoring X runs in first innings, based on its past first innings scores. However, I am unable to build a good model for giving a probability of beating a particular score. What to do? Should I post my approach? I haven't done so yet so to avoid priming others with a particular approach.

Background: A T20 (Twenty 20) cricket match is a game in which a toss win allows a team to choose whether to bat first or bowl first. The team batting first gets to play 20 overs (sets of 6 balls thrown by an individual bowler in one go), or "first innings", and score runs. Zero is the minimum possible score in a ball and also the game. After 20 over are over or after ten batters are out, the other team gets to bat and beat the score. So, in the data above $$y_i>x_i$$ implies a win, $$y_i=x_i$$ implies a tie and $$y_i implies a loss, for the chasing Team B.

p(win_x)=1/e^(-19.12506+0.09340*x)