Working out potential value of keepers

I asked in one of the GK threads last night how much people think keepers will get to, and although nobody offered any thoughts I decided to do some maths this morning. This is heavily based on many assumptions, but does give a bit of a ballpark figure.
The assumptions are:
 Equal number of DEF/MID/ATT in the outfield players
 I've disregarded substitutes (although this would water down the outfield even more, given subs sometimes do win PB, and GKs are rarely substituted).
 I've assumed the average games for each category below (B  2, S  7, G  14)
 I've assumed each player plays 30 full games a season, 10 in each game category.
 Only first team players win PB (huge assumption and wrong, but needed to keep it simple)
So for each game you have 20 outfield players, and 2 keepers. Thus, on average, these are the players in with a chance of PB:
 Bronze: Average 2 games, so you have a 1 in 13 chance of winning 2p PB in the outfield and a 1 in 4 chance of winning 1p PB for a GK.
 Silver: Average 7 games, so you have a 1 in 47 chance of winning 5p PB in the outfield and a 1 in 14 chance of winning 2p PB for a GK.
 Gold: Average 14 games, so you have a 1 in 93 chance of winning 10p PB in the outfield and a 1 in 28 chance of winning 3p PB for a GK.
So if you assume each player plays 10 games in each category, on average you should expect:
 Bronze: Outfield players to win 1.54p / GKs to win 2.5p
 Silver: Outfield players to win 1.06p / GKs to win 1.43p
 Gold: Outfield players to win 1.08p / GKs to win 1.07p
(The maths is 10 games per category divided by the chance of winning the game, multiplied by the prize  so for Bronze outfield, it's (10/13)*2 = 1.54p. I am not a mathematician so if this methodology is wrong do feel free to correct :) )
Thus the theoretical average total for an outfield player is 3.67p over 30 games, and a GK is 5p over 30 games. That is a 36% difference in favour of GKs.
Now, GKs are unlikely to ever be in with a chance of star player (I think it happened once?), so let's say for arguments sake that nullifies the 36% difference. Thus it seems GKs should definitely be valued around the same price as their equivalent outfield counterparts.
GKs rarely get media attention, and tend to be older, so in comparison I'll look at outfield players who have very little media this year, and are over 25. The top of these are:
 De Bruyne / £4.91
 Depay / £4.59
 Gnabry / £4.51
 Hazard / £3.54
 Kroos / £3.49
The average is £4.20.
So I genuinely think the top keepers that establish themselves as regular GK dividend winners possibly have a ceiling of £4, and could easily breach £3 over time.
TL;DR despite the insane % rises in keepers yesterday, there is still a lot of value in them. Also I'm not taking into account TOTM for the purposes of this post, so the best GKs should be pushed quite far out front eventually.
For transparency, I've bought Donnarumma, Rajkovic, Allisson, Sepe, Gomis, ter Stegen, Rulli, Gulacsi since the rise to capitalise on this if this turns out to be correct.
But please feel free to blast this post apart, as I said it's based on a lot of assumptions and some back of the envelope maths.
(Bold = Edits since I first posted. )

@kristiang85 said in Working out potential value of keepers:
Bronze: Outfield players to win 1.53p / GKs to win 2.5p
Silver: Outfield players to win 1.06p / GKs to win 1.43p
Gold: Outfield players to win 1.08p / GKs to win 1.07pCan you double check these figures? I get them to be substantially lower

@FrankMolePepys said in Working out potential value of keepers:
@kristiang85 said in Working out potential value of keepers:
Bronze: Outfield players to win 1.53p / GKs to win 2.5p
Silver: Outfield players to win 1.06p / GKs to win 1.43p
Gold: Outfield players to win 1.08p / GKs to win 1.07pCan you double check these figures? I get them to be substantially lower
I just realised I put 1p for every day for some reason, which confuses matters! Changed it now. But I've redone it and it still comes out as the same results.

@kristiang85 said in Working out potential value of keepers:
De Bruyne / £4.91
Depay / £4.59
Gnabry / £4.51
Hazard / £3.54
Kroos / £3.49The average is £4.20.
Whilst all the maths is really useful. It still boils down to who we compare the goalkeepers to. If we compare them to Kroos, KBD etc as above then the ceiling £4ish, but we could just as easily compare them to say Munir El Haddadi £1.11 and Andre Silve £1. Both of whom have won good divs. The ceiling price for keepers is substantially lower if we use these comparisons.

@FrankMolePepys said in Working out potential value of keepers:
@kristiang85 said in Working out potential value of keepers:
De Bruyne / £4.91
Depay / £4.59
Gnabry / £4.51
Hazard / £3.54
Kroos / £3.49The average is £4.20.
Whilst all the maths is really useful. It still boils down to who we compare the goalkeepers to. If we compare them to Kroos, KBD etc as above then the ceiling £4ish, but we could just as easily compare them to say Munir El Haddadi £1.11 and Andre Silve £1. Both of whom have won good divs. The ceiling price for keepers is substantially lower if we use these comparisons.
Yes, but the higher value outfield players are that price because they are constantly within div winning range, whereas the likes of El Haddadi are much more inconsistent  when he does well he tends to get a great return, but can be anonymous a lot too, in terms of PB score.
If there's a keeper who tends to always have a good chance of winning the divs whenever he plays, he will rocket in value. Not to mention the TOTM factor as well.