Is Salah essential? Yes at (say) 10.5M, no at 13M

There’s a question I am trying to get my head wrapped around. At what PPG is Salah worth getting in the team? I thought there is a mathematical solution to this.

Math:
Caveat: You know I do not have Salah in my team. But I have tried to keep the bias out of the equation.

So above are the numbers. How to interpret them?

Part A – If Salah has a similar season to 17-18

On the left
Assume Salah will get 8.4 ppm
The standard 9.5M midfielder (Mane) will get 6.28 ppm as per the gradient of last year.— (NOTE: this is not Mane’s number, but the gradient of all the popularly owned midfielders, and where it coincides with 9.5M).
Also, since Salah will not be a captaincy option, I would assume the captain would be the next highest ppm-getter for the season i.e. Aguero at 7.30.
Now, if you have the control group to compare Salah with as (Mane + Aguero as captain),
You will have 3.5million (no having Salah) giving you 3.22 ppm as your control case.

On the right
While drawing the gradients as we had done below, we have arrived at the ppm gain per 0.5m addition in price. We see that the highest gradient is for the defender, and lowest for the goalkeeper.

Now even for the best case -i.e. we utilize the 3.5m into the best defenders and take advantage of the incremental benefit of the extra money, we would still be about 33 points in arrears. more realistically, if you spread it around (0.5 GK; 1M DF; 1M MID, 1M FW), you are in arrears by ~40 points.

Inference: If Salah captures last season’s form, you have to have him. He is essential. Nothing else you do can top not having him, even at 13M (i.e. unless there is another player who is giving similar returns as Salah)

But if Salah would do a little worse than last season, then? How much worse can he do if you compare him against the most realistic control case (same as what we tried last time

Part B – If Salah does slightly worse than 17-18

On the left
Experiment has given me the number of 280 points. i.e. 7.8 ppm for a 36-game season. This is the tipping point below which having Salah does not remain a realistic option.

If Salah will get 7.8 ppm
The standard 9.5M midfielder (Mane) will again get 6.28 ppm as per the gradient of last year.
The next highest ppm-getter for the season i.e. Aguero will be the captain at 7.30.
Now, if you have the control group to compare Salah with as (Mane + Aguero as captain),
You will have 3.5million (no having Salah) giving you 1.98 ppm as your control case.

On the right
Now even for the worst case -i.e. we utilize the 3.5m into the two worst gradients – 1.5M for GK, and 2M for striker; and take the least advantage of the incremental benefit of the extra money, we just about make 1.98 ppm, par. More realistically, if you spread it around (0.5 GK; 1M DF; 1M MID, 1M FW), Salah will have to get 282 points to just make par.

Inference: Salah will have to get at least 280 (7.8ppm for a 36 gameweek season) points to be a realistic option at the 13M price. Salah’s score can fall only by about 7.5% from his lofty standards of last year for him to not be viable anymore.

PS: even with my horrible captaincy targets (7.0 ppm target), Salah will still need to get 272 (~7.6ppm) to make par.