Mutual Exclusive Points

[Stu255]

I’m going to introduce a new term (don’t see it used often enough), into the FISO lexicon.

Mutually Exclusive Points

I’m sure by now most of us (FPL nerds) are using xG or IO or some combination of something to assess players in terms of xFPL alongside all the traditional stuff such as actually watching games on TV.

Now there is one scenario in FPL that happens often, where you have players in your team who are on opposing sides in the same game.
There is some maths behind what is sensible to do here, but how does everyone actually handle it?

e.g. if one of your strikers is playing one of your defenders then a goal will bust your CS. Likewise a CS at the back means your striker has blanked.
What does everyone think / believe about that common situation?

(I have follow up material )

[raoul]

Where possible I take a punt and bench one side of the problem. But it is not something I get over excited about tbh.

On another point, despite being known as stat boy by some friends I have barely looked at things like xg and so far have preferred to assume that my eye test approximates it well enough.

I am also a tad sceptical because footballers are humans and subject to sudden unexplained changes of form such that past performance is not a great guarantee for many players.

But that's not your primary point on this thread so I will stop there.

[bspittles]

I've done it a lot this year because I've been behind in my work league, and I treat it a bit like needing a differential. You need every player to score to the max.

If you're out in front it makes sense to play both a defender and striker with the assumption that if one blanks it's because the other has succeeded.

Some defenders are selected for their attacking potential, so I treat that differently.

[Smurphy Paw]

I consider this to be a benching dilemma query (& FH). Players are going to face each other twice a year, it’s the way the league works and unavoidable.

The impact of one on the other is one of the judgement points I’d take into consideration.
To illustrate, I would try to avoid a defensive mined defender up against an attacker. However players such as TAA can justify their inclusion with or without a clean sheet and I’d probably play him. Likewise Doherty, but perhaps not Gomez or Saiss.
Similarly a Salah would probably play whoever they are up against, but I’d bench a middling player and play the defender against a team with a good defensive reputation.
All of which demands an equal or better option who would otherwise be on the bench. If that third player is less likely to contribute and score points I might hedge bets and play both who are up against each other.

TL:DR I’d analyse the numbers and expected points and factor it in as I try to maximise overall score. It’d be part of the consideration

[Stemania]

I virtually always ignore this consideration, as all it does is reduce how much your total score is likely to deviate from the total xPts that week (i.e., reduces total variance). Caveat: if you need a Hail Mary massive score to win a minileague in the last week, probably a bad idea to pick a striker vs a defender for this reason. More generally, I'd just play the 11 that I thought had the best points potential on average regardless of any clashing fixtures.

(I'd apply exactly the same principle to player ownership vs weekly rank volatility too, but then I'd also take into account the implied likelihood of being wrong in my assessment vs others' assessments, so take a little more notice. )

Either way, presumably the attacking player picked poses a decent and constant threat to opposition defenses and presumably the team the defender is from is decent defensively (otherwise, why did I pick them?), so the xPts of both would probably be lower than normal in the first place. Though, if picking a defence successfully, I suppose it's a situation that won't come up as much as it should naturally as people often have defensive rotation players on the bench that have been picked precisely to avoid these tougher fixture against a presumably decent striker. So, in practice, I suppose there is some taking of note and avoidance, but for a different reason. Of course, TAA vs KDB type things are a different kettle of fish a both are likely better than any subs.

[blahblah]

It's Floors vs Ceilings for blah.

[hancockjr]

Stem saved me the bother - what he said.

Had to laugh at a poster once who’d seen Ville pick a defender v attacker and confidently called him out for his “mistake”. Some people don’t know how little they know!

[hancockjr]

Where possible I take a punt and bench one side of the problem. But it is not something I get over excited about tbh.

On another point, despite being known as stat boy by some friends I have barely looked at things like xg and so far have preferred to assume that my eye test approximates it well enough.

Off topic but you can’t watch all players all the time surely, so don’t things like xG put into context what you have watched?

[Hogmeister]

Stem saved me the bother - what he said.

Yeah, same here

[Stu255]

I agree with what people say above, I’ve always ignored it. Laughed at people who didn’t like their players facing off. It seemed greedy and naive with regard to statistics.

But now I’ve seen the math.


Basically, when two players play each other a part of their xFPL is mutually exclusive. You cannot have an attacking goal and a defensive CS. The effect approximates to... losing half the non appearance xFPL of both players.
It’s a bit more complicated in reality but in a 50:50 odds game with both def and att players on equal xFPL then that’s the mathematical result of the mutually exclusive scenario.

No model I have seen recognises this.

If you have 1 pair of MEP’s it probably reduces your team xFPL by 3-4pts that week (assuming 5-6xFPL per player).

Some weeks you might have 2 pairs of MEP’s. Which doubles the effect to 6-8pts.

Over 38GW’s this is very significant.

Could easily cost you >100pts per season if you just ignore it. As I always have.

I imagine those who underachieve xFPL by a statistically significant margin probably just had a lot of MEP’s.

Would encourage anyone to explore the maths for themselves.

[blahblah]

But they don't play against each other in 38 GW's?

[Stu255]

But they don't play against each other in 38 GW's?

Not the same pair obvs.

But count up all your MEP pairs over the season.

[blahblah]

But they don't play against each other in 38 GW's?

Not the same pair obvs.

But count up all your MEP pairs over the season.

My Def tends to come from very few Clubs and GK is irrelevant as Save Points.

It would be interesting to know which sort of "pairs" you are thinking of.

[Stu255]

But they don't play against each other in 38 GW's?

Not the same pair obvs.

But count up all your MEP pairs over the season.

My Def tends to come from very few Clubs and GK is irrelevant as Save Points.

It would be interesting to know which sort of "pairs" you are thinking of.

Any time players in your team play against each other there are Mutually Exclusive Points in play.

The value of the MEP’s varies for each specific scenario but when all is equal it is basically 50% of the non appearance points.

MEP’s are double counted by every xFPL model out there. So you need to correct these models by subtracting the MEP’s out again.

If you ignore MEP’s, over a whole season they can accumulate a significant impact on your score.

I am only realising this now.

[Stemania]

The math is that

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B),

regardless of whether the events A and B are independent or not. Makes no difference to expected points.

[blahblah]

AS above it is Floors and Ceolings for me ie the risk of the (risky) ceilings being lower than the (reliable)floor.

I often play both in this situations, and sometimes take a punt on the attacker\defender - but it it depends on Club and Player.

I am not dissing your idea as I like debate of "stuff", but I have a "stance" and I am interested in an alternative....

[blahblah]

The math is that

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B),

regardless of whether the events A and B are independent or not. Makes no difference to expected points.

But it isn't?

ExpectedValue(A+B) = ExpectedValue(A-B) + ExpectedValue(B-A)

???

[blahblah]

Although Actuals are better than Expected, but opens up the hindsight debate, which I do not accept lol.

[Stemania]

Nope, its

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B).

No expected points models take conflicting fixtures into account because.....it's not a thing. Don't want to sound all Brexity, but MEPs are irrelivant in maximising our potential.

[blahblah]

Nope, its

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B).

No expected points models take conflicting fixtures into account because.....it's not a thing. Don't want to sound all Brexity, but MEPs are irrelivant in maximising our potential.

But if A is and Attacker and playong Defender B...... ?

[Stu255]

The math is that

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B),

regardless of whether the events A and B are independent or not. Makes no difference to expected points.

It’s different for mutually exclusive events.

eg

unrelated events... flipping 2 coins.
defender needs tails on coin 1, attacker need heads on coin 2. In this scenario both will win in 25% of runs.

The above is what you describe.

mutually exclusive events... flipping 1 coins.
defender needs tails, attacker need heads. In this scenario both will win in 0% of runs.

^^ you need to subtract the MEP’s from the expected returns. If you don’t they are double counted.


BPS are also mutually exclusive.

[Pirlo's Beard]

What do Members of the European Parliament have to do with FPL? Should I have picked Luke 'Ming' Flanagan on my wildcard? How do his stats compare with Susana Solís Pérez?

[Stemania]

Stu, you are unfortunately conflating likelihood of extreme outcome with average outcome. Say it is 4 points for a goal or a clean sheet. Then

2 independent coins
(Lose, lose) 1/4
(Win, lose) 2/4
(Win, win) 1/4

Expected points = 0×1/4 + 4×2/4 + 8×1/4 = 4.

1 coin defining both outcomes
(Lose, lose) 0/2
(Win, lose) 2/2
(Win, win) 0/2

Expected points = 0×0/2 + 4×2/2 + 8×0/2 = 4.

Both expected points are the same. Variance is reduced in dependent case.

[Stu255]

Stu, you are unfortunately conflating likelihood of extreme outcome with average outcome. Say it is 4 points for a goal or a clean sheet. Then

2 independent coins
(Lose, lose) 1/4
(Win, lose) 2/4
(Win, win) 1/4

Expected points = 0×1/4 + 4×2/4 + 8×1/4 = 4.

1 coin defining both outcomes
(Lose, lose) 0/2
(Win, lose) 2/2
(Win, win) 0/2

Expected points = 0×0/2 + 4×2/2 + 8×0/4 = 4.

Both expected points are the same. Variance is reduced in dependent case.

Yes, but in FPL blanks are NOT mutually exclusive.

When 2x players face each other you can still realise 2 blanks, but you cannot realise a CS and a goal.

Only the upside scenarios are mutually exclusive.

You should discount xFPL when 2 players face each other. If you do not, you are double counting.

[Stemania]

I thought your gripe was that you didn't want

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B)

to hold for mutually exclusive events (e.g., coin example). It holds for all events; above shows specifically why the coin-based counterexample you described is not a counterexample.

[Stu255]

I thought your gripe was that you didn't want

ExpectedValue(A+B) = ExpectedValue(A) + ExpectedValue(B)

to hold for mutually exclusive events (e.g., coin example). It holds for all events; above shows specifically why the coin-based counterexample you described is not a counterexample.

I’m just trying to show that there is an assumed scenario to which some probability is attached, but in reality it is impossible.

There is no AND only OR.

[Stemania]

"When 2x players face each other you can still realise 2 blanks, but you cannot realise a CS and a goal.

Only the upside scenarios are mutually exclusive."

"AND only OR"

It's not a thing. These are all irrelevant to expected points (even if its not intuitive).

[murf]

Theory = if A scores big, B scores bad and vice versa.

So you only pick one.

If you get it right...
Your picked player scores well - RESULT
Your dropped player scores badly - RESULT

If you get it wrong...
Your picked player scores badly - F***
Your dropped player scores well - F***

So, double the reward but double the swearing if you get it wrong.

What is known as 'shit or bust'

A sensible tactic if playing for Manager Of The Week but 99% of the time just ignore it and evaluate each player's prospects independently.

[Stu255]

"When 2x players face each other you can still realise 2 blanks, but you cannot realise a CS and a goal.

Only the upside scenarios are mutually exclusive."

"AND only OR"

It's not a thing. These are all irrelevant to expected points (even if its not intuitive).

Man Utd V Spurs

Probability of Kane goal = 25%
Probability of AWB clean sheet = 40%

Probability of Kane goal and AWB clean sheet in reality = 0%

Probability of Kane goal and AWB clean sheet in every xFPL model = 10%

^^ in this scenario you need to discount the team xFPL. Team xFPL is not a simple sum of player xFPL when it involves mutually exclusive events.

[hancockjr]

Why would an xFPL model put a probability on that? The individual probabilities are correct, and that is what matters. If xFPL models are wrong then so be it, but that wasn’t the question.

I’d concede there may be a small loss of potential bonus points, but that’s it, and it’s far too small to worry about.

If there is some maths that looks like it works out and it’s not just a basic error I suspect that it’s that it doesn’t take into account that if the defender doesn’t get a clean sheet the attackers Expected Points increases, as there must have been at least one goal.