Rating players with xR

In my last post, I described a metric called Expected Runs or xR for short.  This gave us the average number of runs you would expect a batsman to score from a delivery that possesses particular attributes such as its line and length etc.  My first attempt at an xR model just considered the position of the ball as it reaches stump level using data from over 200 T20I matches.

In this post, I look at how batsmen perform under this metric over several T20I matches.  The plot below shows the total runs scored for 507 batsmen in my database against their total xR.  Batsmen above the line score more runs than what xR suggests so are over-performing according to this metric.  blog.pngWe can calculate over-performance by dividing xR by runs.  The table below shows the top 20 batsmen, with at least 300 runs (of which there are 55), ordered by runs per xR.


Glenn Maxwell comes out way on top, scoring over 200 runs more than the average batsman would if they faced the same deliveries as he had.  Further down the list we see some notable hitters such as Aaron Finch and Shahid Afridi.  Interestingly, Luke Wright comes in higher than the likes of Chris Gayle, AB de Villiers and David Warner.

At the other end of the scale we get the table below:


Mohammad Hafeez scores nearly 100 runs fewer than expected.  This suggests he is not putting away the bad balls enough of the time, which is not ideal for an opener batting in the Powerplay overs.  It’s a wonder why Pakistan persisted with him for so long considering he has a career average of just 22.73 and a strike rate of 115.

The xR beehive plots from my last post, show that xR for a particular patch is rarely above 1.5.  Given that a boundary can produce a runs/xR multiple of up to 6 for that particular ball, I wanted to see if frequent boundary hitters generally had a higher runs/xR figure.  Taking batsmen to have scored at least 20 boundaries, we can see whether there is a trend between the number of boundaries hit and the runs/xR multiple.blog.pngThe plot above shows that the correlation is not very strong with an R² value of 0.068.  This is encouraging as it implies xR measures something more than just pure power hitting.  It can be used to identify the batsman who have the ability to hit good balls into gaps for ones and twos as well as those batsman who are not good enough to consistently put away bad balls to the boundary.

xR can also be applied to bowlers.  Bowlers with a low xR/ball figure are bowling in areas that are on average low-scoring.  Note that this is independent of what the batsman eventually does.  The table below shows the bowlers to have bowled at least 300 balls (of which there are 34) ordered by their xR/ball multiple.


Perhaps unsurprisingly, Sunil Narine comes out on top with 1.202 xR/ball.  The average run rate per ball across the entire dataset is 1.245.  This is a difference of 5 runs across a 20 over innings, so certainly not insignificant.  It is interesting to note that Narine’s xR conceded is significantly higher than his actual conceded runs.  This suggests that many batsmen are under-performing when facing him even when accounting for the fact that he bowls a lot of good balls.  Batsmen cannot seem to consistently hit him for ones and twos, never mind boundaries  – a testament to his incredibly tight bowling.

Darren Sammy and Sohail Tanvir are the only two bowlers in the top 10 to concede more runs than expected.  This may be due to a combination of mainly facing above-average batsman and some bad luck.

At the other end of the scale we observe that every bowler in the bottom 10 is a seam bowler bar Imran Tahir – an indication of the need to have separate xR models for spinners and seam bowlers.  Kyle Abbott has the highest xR/ball corresponding to 9 runs more than the average T20I innings.  Two fast bowlers, Mitchell Starc and Lasith Malinga, concede significantly fewer than expected.  Although they bowl in relatively high-scoring areas, their pace may be a factor in keeping runs to a minimum.  Again, this is something that can be built into the xR model.


The full list for both batsmen and bowlers can be found here.

xR has certainly shown its potential in accurately rating players beyond traditional metrics.  xR can also be used to rate individual innings as well as determine who ‘deserved’ to win a match by calculating the total xR for each team.  In future posts, I will look to incorporate more factors to further refine the model, including what balls are most likely to get a wicket.


Author: Cricket Savant


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