The most popular formations in FPL seem to be 343 and 352 (general observation). This is hardly any surprise, more focus on attack mean more chance of getting goals and assists and picking up more FPL points. But how much difference it would make over the course of one full season ?
Well, what I came across was quite amusing  more so because I was not looking for it in the first place but performing some other analysis and what I saw just dropped my jaw a little.
So, as the story goes  one fine day I was looking at the Official Dream Team of the season 15/16 trying to figure out  What could the best possible team a manager can pick over a season.
The issue with the picture above is: you can call it the 'best 11' but not really a 'Dream team'. Shouldn't a team be something a manager be able pick or field in practice (even by the most primitive definition of 'A Team') ?
So much for the 'Dream team'  I needed a 'Reality Team' which can actually be used. I set myself out to write an algorithm to figure out that 'Reality Team'. Starting from the Dream team of above  if we make it max 3 player per team, then the first logical thing to do would be to replace the lowest scoring player from the team which has more than 3 players  in this case Koscielny from Arsenal and replace him with the next best defender (which would be Fuchs from Leicester who score 150 points total  only 3 points less than Koscielny).
After some struggle, I finally got where I wanted to be with my algorithm and the result was:
There were altogether 723 registered players in FPL last season  if one takes possible combination of 11 players from there, the result she arrives at is 6.548877005 E+23 [nCr = n! / (r! (n  r)!)]. Whoa.
I performed a series of steps in my algorithm to reduce the number of rows in this dataset (details of which I will skip here). But the very last step was, to reduce the data by dividing it to 7 different possible sets.
The 7 allowed formations.
By getting the Best team of each formation  one could easily find the best of the best. The result was:

The Best Possible FPL teams of season 15/16 for every combination 
[NOTE: The last column 'Points Per Player Per Game' does not represent the all 38 games of the season, and hence for example on 1st row 4.97 * 11(team) * 38 (game weeks) is not same as 1933.
The column 'Points Per player per game' is actual representation of avg. points of each player on the particular formation. For example Ã–zil played only 35 games and Mahrez 37 and the average of those totals are taken in calculation.
]
This was the Eureka moment. Even though I already mentioned, in general we know the most popular formations among all FPL managers are 343 and 352 and not surprisingly they have yielded most points over the course of 38 games marathon. The pattern is on the table above is not only about 343 and 352, it is implying something more profound. To sum them up:
step 1 : Reduce the possible number of defenders.
step 2: If you have already reduced the number of defenders  reduce the number of midfielders.
Those two statements are ALWAYS holding true on the table above. Just pick any two formation anywhere on table and compare. Lets look at the same data on a bubble chart:
Lets not get carried away here, the data is from only one season  one can not stop thinking. However, how would anyone can ignore the fact that there is the difference of One Hundred and Eleven points between the best 343 and best 541 formations. Lets plot those two formations on bubble chart again, player by player this time with Total points on Xaxis and Points per game on Yaxis for each player.
This makes things clearer, 343 formation has 7 players with the avg. points per game 5 or higher and the lowest scoring player has the average of 4.1. On the other hand, 541 has 6 players below 6 points avg. and lowest scoring player had the avg. of only 3.9.
Things get ridiculous, when you realize 9 out 11 players in both combinations are exactly same. So the massive gulf of 111 points are down to 2 players. How that can be ? We only replaced two attackers by two defenders  and not just any defenders but the best in their positions.
The difference being  343 has Kane and Lukaku, 541 has Fuchs and Smalling. Yes, it all boils down to Fuchs and Smalling.
But still, One hundred and Eleven points ?
For Fuchs sake, no one can say this gap Smalling.
Ponders. But the math is simple:
211 (Kane) + 185 (Lukaku)  150 (Fuchs)  135 (Smalling) = 111.
Of course, it is always not possible to go for most attacking formation and strategy wise sometimes a defensive unit makes more sense. There are also other factors to consider, like double or no game week for a team, injuries and suspensions to players or plain strategy.
In some way, the strategy of selecting a team for any one game week is like day trading while where a manager finishes at the end of the season is like a result of long term investing. Every FPL manager should recognize this and have their own strategy for long and short term goals along with their own regression formula of risk and reward calculation. The whole point of this post is not to endorse a certain formation always without the scope of personal wit. The point is always keeping in mind that whenever you choose a more defensive formation  there is extra cost attached to it. Just like the 4 points extra cost one pays for every extra transfer each game week.
Last season between those two formation we analyzed, this cost was 111 points  which is close to 3 points every game week whenever a manger chose to play 541 instead of 434 without any specific plan or strategy. If her strategy yielded more than 3 points by switching to that setup  then it was profit otherwise not.
Now lets try to prove this theory in another way, a team must have 1 to 3 Forwards and 3 to 5 Defenders in any formation. The difference between best performing forward (Vardy, 211 points) with best performing defender (Bellerin, 172 points) was 39, which is about a point every game. Compare Bellerin to Mahrez and the point gap per game grows to 2. Thus any extra defensive player  even if the very best, is costing 1 to 2 points on average per game (i.e. about 1.5 points per game).
The same holds true when we compare the worst performing Forward (Lukaku, 185 points) and Defender (Smalling, 135 points  5th best forward in FPL so would get into dream teams of 541 or 532 formation) from the best formations, as we see the gap of 50 points (avg. per game 1.32). Compare Smalling with the worst performing midfielder (Ayew, 171 points) and we still get a deficit of about 1 point per game.
When it is applied over two players, as in case of 343 vs 541  where two attacking players were swapped for two defensive players, the gap should be about 1.5 * 2 = 3. And that was exactly what we saw with the result of 111 points over 38 games.
The stats can not be clearer than that.
Avoid overthinking  when in doubt go 434.