Stats Analysis

What Karachi need to do to qualify

Qualification scenarios for the last spot in the top four in PSL 2017

By virtue of a better net run-rate than Lahore Qalandars, Karachi Kings can qualify for the playoffs even if they lose to Islamabad United  •  PCB/PSL

By virtue of a better net run-rate than Lahore Qalandars, Karachi Kings can qualify for the playoffs even if they lose to Islamabad United  •  PCB/PSL

With only one league game left in the PSL, two teams - Karachi Kings and Lahore Qalandars - are battling for the last spot. Peshawar Zalmi, Quetta Gladiators and Islamabad United have qualified for the playoffs.
Lahore have already played their eight games, finishing with six points and a net run-rate of -0.223. Whether they qualify or not depends on the result of the last match of the league stage, between Karachi - also on six points with an NRR of -0.150 - and Islamabad (eight points, NRR -0.113).
Islamabad will move to ten points and top the group if they beat Karachi, while Karachi will qualify if they win. (In that case, these two teams will again play each other in the second playoff on Wednesday.)
However, with Karachi having an NRR of -0.150 to Lahore's -0.223, there is a possibility of Karachi qualifying even if they lose to Islamabad, as long as their NRR stays above -0.223. Here are a few scenarios that indicate how Karachi can qualify even if they lose to Islamabad on Sunday.
If Karachi bat first…
The table below lists the minimum overs Karachi must bowl, if they bat first and lose the game. For instance, if Karachi score 160 and lose, then they must ensure that Islamabad take 18.3 overs or more to chase down the target. If Islamabad chase it down in fewer overs, then Karachi's NRR will drop below that of Lahore, who will qualify instead. (However, the over cut-offs will change slightly if Islamabad level the scores and then win with a boundary. For instance, if Karachi score 160, and Islamabad level the scores and then win with a four (total 164), then Karachi will have to drag the game till at least 18.5 overs.)
Min overs for Islamabad's chase to ensure Karachi qualify
Karachi's score (20 overs) Min overs to chase
 120  18.2
 140  18.3
 160  18.3
 180  18.4
 200  18.4
If Karachi bat second…
Similarly, if Karachi bat second and lose, they need to come close enough to the target to ensure their NRR doesn't drop below -0.223. For instance, if Islamabad make 160, Karachi will need to make at least 147 to keep their NRR above that of Lahore.
Min scores for Karachi chasing to ensure they qualify
Islamabad's score Karachi's min total
 120  106
 140  126
 160  147
 180  167
 200  188
In case of a washout, both teams will qualify as they will get a point each. Islamabad will finish third and Karachi fourth, which means they will play each other again in the second playoff on Wednesday.

S Rajesh is stats editor, and Gaurav Sundararaman is senior stats analyst, at ESPNcricinfo.