After refining my Expected Runs model in my last blog, I will now apply the same methods to investigate wicket taking deliveries. I use the same factors, namely where the ball pitched, the line and length when it gets to the batsman and the speed of the ball. For a particular delivery, the nearest neighbour algorithm finds the 50 most similar deliveries in terms of those attributes. The number of wickets resulting from those deliveries divided by 50 is the Expected Wickets, or xW, of that ball.

We use the same dataset as before – 41,104 balls from 208 T20I matches. The algorithm predicts a total of 2,279 wickets compared to the actual 2,298 wickets. Firstly, we can visualise which kind of balls are most likely to take a wicket. The image below shows the pitch map and beehive plot of the 100 balls with the highest xW figures ranging from 0.20 to 0.28. Red points indicate actual wickets and deliveries to left-handers have been flipped so they can be compared.

We can observe that these 100 balls cluster into 5 distinct bowling areas: yorker length deliveries, balls on middle and leg stump, good length top of off, back of a length outside off and bouncers outside off stump. Interestingly, the few deliveries which pitched beyond the stumps are full tosses highlighting their canny knack in getting wickets.

The performance of a batsman can be measured by comparing how many times they were dismissed to their total xW, or how many times we would expect the average batsman to be dismissed if they faced the exact same deliveries. The graph below shows the xW of every batsman in the dataset against how many times they were actually dismissed. The grey line separates over and under-performing batsmen. The over-performing batsmen are below the line and those tend to be the ones who have batted (and been dismissed) most often. It seems the more established batsmen get out less often than what the metric predicts compared to the many tail-enders who hardly bat in T20 matches.

The table below shows the best performing batsmen calculated by the ratio of wickets to xW, for batsmen dismissed at least 15 times.

Virat Kohli comes out on top with a dismissal to xW ratio of just 45%. This means he is dismissed less than half the number of times the average batsman would if they faced the same type of deliveries he has. This is a true testament to his ability to negotiate any kind of bowling and still score runs at a good rate. The other end of the scale looks like this:

Perhaps unsurprisingly, notorious wicket giver-away Shahid Afridi comes out way on top with a dismissal to xW ratio of 1.70. In other words, he has given away 70% more wickets than the average batsman would have done facing the same balls. Further down the list are some more notable hitters like Darren Sammy and Kieron Pollard. Interestingly, AB de Villiers is under-performing with respect to this metric, which may suggest to need to incorporate game state into the model. It is likely this ratio increases toward the end of the innings as batsmen become more willing to sacrifice their wickets.

It would be pertinent to view the relationship between wickets/xW and runs/xR as these are both metrics which independently rate how good a batsman is.The graph above shows a slight negative trend as you would expect. The more runs you score above expectation, the less likely you are to give your wicket away compared to the average batsman. However an R^{2 }of 0.185 suggests the relationship is not completely significant. This does mean the two metrics can be treated more or less independently and therefore be combined in some way to rate a batsman more reliably.

Out of interest, the leader of the runs/xR metric, Glenn Maxwell, has a wicket/xW ratio of 0.979 meaning he is over-performing ever so slightly.

We can also investigate how bowlers fare with this metric. The table below shows the best performing bowlers (with at least 300 balls) ordered by Expected Strike Rate, or xSR. This is the number of balls bowled divided by xW.

Mitchell Starc is first with 15.8 balls per Expected Wicket. Next come 8 more pace bowlers before the first spinner, Ravindra Jadeja. For reference, the strike rates in all T20I matches for pace bowlers and spinners are 19.0 and 19.9 respectively, so we would expect this split. The bottom 10 bowlers are as below.

Here we see mostly spin bowlers with the only two seam bowlers in 9th and 10th place. Interestingly we see Mohammad Hafeez and Sunil Narine in the list, both of whom the xR/ball metric rated highly. In both lists there are bowlers who take more or fewer wickets than what xW predicts. This is not something xSR takes into account as the xW of a delivery is only a function of the attributes of that delivery and not the eventual outcome. Bowlers who happen to take fewer wickets than expected have most likely bowled to more capable batsman more often and vice-versa.

I hope this article has demonstrated the usefulness and validity of the Expected Wickets metric in rating the performances of batsmen and bowlers. In future blogs I will see how this complements the Expected Runs metric and hope to include more variables to refine the model further.

As ever, if you have any questions/suggestions please feel free to tweet me here.