Yes, but bookmakers' odds bear little relation to real-world probability - that's how they make their money.

As I think I pointed out in a post above, for FPL purposes, what you need is the relative magnitudes of the odds (i.e., some means of guidance as to the relative chance of a team (and therefore its defence) getting a clean sheet. So the actual probabilities aren't an issue (in the way they would be if you actually wanted to place a bet). Now, it is true that bookmakers' odds don't obey the mathematical laws of probability, and this is how they make money... the over-round on a book means that the sum of the probabilities based on bookmakers' odds will come to more than 100%. But it is a trivial matter to convert bookmakers' odds to percentage probabilities (that do obey the mathematical probability laws), and this normalisation will preserve the ranking of the original (odds-based) probabilities. So we still have what we need for FPL purposes.

Proviso... you don't define "real world probability"... so I don't know whether, for example, you are taking a frequentist or a subjectivist view (or something else again - this really is a tricky issue). But even if you are taking a subjectivist view and saying that bookmakers' subjective views bear little relation to yours, I still think that the bookmakers provide a better source of clean sheet probability predictions than you do. For one thing, I have never seen your predictions published; for another, bookmakers' odds are usually very similar from bookie to bookie; and for another, their livelihood depends on getting it right and I'm guessing yours doesn't (apologies if I am wrong there). Yes, they make money by distorting probabilities, but the distortion is of the magnitudes and not of the ranks, so we don't have a problem of the kind you suggest.

I'm guessing you knew all that already and your post was just a wind-up, in which case, you got me

Edit

What en extraordinary statemement. Apart from the over-round (profit margin) thye bear every resemblance to real world probabilities of things happening - if they didn't then we could all get rich!

here's something I put together that translates you guys' work into a fixture table - i've probably got a couple of the scores wrong in the calculations but in all fairness inputting 400 scores on a sunday afternoon isn't the easiest thing to maintain concentration on...

a few thoughts that came up whilst doing it:
-fulham haven't conceded in their last 4 home games - what what whaaat?
-with defensive form as it is, even the biggest mismatches only have a 48% chance of keeping a cleanie - west brom and blackpool have a paltry 7.2% chance of keeping Arsenal out in gws 30 and 32 as things stand
-what relevance does a match played on 11th December really have on a match this week?
and finally
-is there any way of weighting the form calculation according to the difficulty of the 5 matches played (of each opponent at the time)? - would also have to be applied historically. could be getting a tad complicated but if the stats are there it'll make a fair difference imo.

NB: this is using an old fixture list! anyone got a new version or is it just the next couple of gameweeks that need editing?

http://www.tempfiles.net/download/201102/145789/CleanSheets.html

In my opinion, it really comes down to this. Can Chelsea be Chelsea without a John Terry or Man Utd hold without a Vidic?

Can we identify a team who have consistantly (over 3 seasons or more) played solid defense, but done so with different KEY players? Maybe this might provide some insight (my current best guess is it has something to do with the formations played & played against). For example, would we see a correlation between "strong" defenses when they are playing teams fielding defensive sets (easier to defend when the attack is minimal), and maybe more importantly, would the lack of clean sheets from these teams have any correlation to teams fielding offensive sets?

It might come to nothing, but it might be interesting to explore it a little.

There you go

FPL 09/10 Full Player/Fixture breakdown

a zipped xls - same layout as the previous one - use Excel's filters to limit rows shown etc.

RomynPG you are a gentleman

gonna put this into practice with a weekly flutter.

GW28's bet looking at the fixtures: Stoke vs. West Brom

According to MyQ's spreadsheet, Stoke have a 45% chance of keeping a clean sheet (comparatively around the 95th percentile if the whole season's matches were to be played on current form)
West brom apparently have an 18% chance of keeping a clean sheet (comparatively around the 15th percentile)
(thus an 8.3% chance of a 0-0, albeit much less accurate if my A Level maths serves me correctly)

Looking at available odds, we have best home clean sheet odds at 2.63 at bet365... a percentage of 38% - giving me a 7% advantage. Worth a pop? Not much advantage to be had...


Interestingly we also have a 26% Wigan clean sheet and a Man U 23% clean sheet. What on earth is going on there. If I was twice the man I am, I'd be getting on the 6.5 odds of a wigan clean sheet (13% as opposed to 26%) or even wigan to score at 1.65 (37% as opposed to 77%?! Suggesting wigan's actual odds of scoring are twice as high as the bookies are offering?!) Just not sure about that if i'm honest! Maybe this is where the money is to be made? Betting against the big trends?

Mr Clarinet understood what I was getting at when he pointed out that the sum of the probabilities based on bookmakers' odds will come to more than 100%. Quite a lot more than 100%, actually.

Out of interest, take next week's Chelsea v Man Utd game. There are only three result outcomes, the combined probability of which, in the real world, must add up to 100%. A Chelsea win is typically priced at 5/4, which represents a 4/5 chance of a win, or a win probability of 80%. A Man Utd win is priced at 9/4, or a win probability of 4/9 = 44%. A draw is the same price, 9/4, ie a draw probability of 44%. Add up the three probabilities and you get 168%, not 100%. That's what I meant by it having little relation to real-world probability.

To arrive at the real-world probability of a Chelsea win (assuming the bookie's got it about right), take that 80% and divide it by 1.68 - and you're left with a much more realistic 48%. (The equivalent real-world probability of a Man Utd win, or of a draw, is 26%.) Nothing like the bookie's odds, in other words.

The problem with bookies odds is that they start out with the best intention of reflecting what a bookie considers to be the likely odds (albeit with a healthy over-round built in), thus encouraging punters to bet even money either side of the line. This even money split means the bookie shouldn't make a loss, as what he loses on one side he gains on the other, and with the over-round he makes his profit. However, once the money on one side begins to outweigh the other the bookie is at risk and he will shift the odds, not to reflect the likely outcome, but to protect himself from loss by addressing the imbalance. If you add to this the artificially shortened odds afforded to teams whom punters place money on with total disregard to the fixture (or enlarged odds for the reverse) then you can see why the odds don't always reflect the probabilities; for a bookie its about predicting the bet spread not predicting the result. This is why betting strategies often refer to betting with value by assessing the probabilities according to their system and identifying what you consider to be favourably imbalanced odds.

Anyway, I've fixed a fairly large screw up in the spreadsheet (ie. some season's fixtures were entirely in the wrong order for the calculations) and managed to get some r squared figures for both home and away that I'm much more happy with. I'll post my predictions tomorrow for the next gameweek and we'll see how things stack up.

I'm also trying to work on a weighting system to account for goals conceded/scored against tougher/weaker teams but what I've got so far is just a jumbled mess.

What I can't work out is what problem you are trying to solve. For example...

Problem 1. I don't like the odds that bookmakers offer, so I want to devise my own system of caclulating probabilities in the hope that this may lead to profitable betting opportunities. (In which case, ok, but what is this thread doing on the FPL board?)

Problem 2. I have a decision to make about which defender to play in my FPL team. For example, this weekend, it looks quite a close call as to whether Aston Villa or Newcastle are more likely to keep a clean sheet. I wonder how the clean sheet probabilities are ranked?

Problem 3. Another problem.

My view is that nothing that has been pointed out in this thread so far means that a quick glance at the ranking of the bookmakers' clean sheet odds for the teams in question isn't a reasonable way of informing a decision such as the one outlined in Problem 2 (which is the one I am interested in). Of course, I will still take resposibility for the eventual decision, but I will take into account this little bit of easily obtained data that I think is based on more than, for example, my mate's opinion.

ha, i'm glad I didn't make a move on that bet then

looking forward to your new results.

You could start by simply matching the Goals Against column for Villa at home with the Goals For column for Blackburn away; then comparing that with the Goals Against column for Newcastle at home matched against the Goals For column for Bolton away. Convert that to a goals-per-game prediction and you get:

Game 1 Aston Villa 1.2 (av home goals against) versus Blackburn 1.3 (av away goals for)
Game 2 Newcastle 1.5 (av home goals against) versus Bolton 1.0 (av away goals for)

Of course this doesn't take into account current form, injuries etc, but the best that statistics can do is give us an objective basis on which we can make an informed judgement.

You can see from the above that, averaged out, both Villa and Newcastle look like conceding 1.25 goals, which will only add to Mr Clarinet's dilemma . But that's the case for the majority of games. Even the team with the worst goal-scoring record - Wolves away, at 0.7 goals scored per game - are, against an average home defence, more likely to score than not (since 0.7 is closer to 1 than to 0).

In that case, and if we're just looking for clean sheets, couldn't the "goals scored" value (anywhere between 0 and 4, 5, 6, etc) be replaced by a "scored" yes/no 1 or 0 value to reflect just if the team scores at all or not. This would mean Wolves wouldn't have that 0.7 goals scored per game stat to work with, but simply a 57% chance to score any number of goals away from home. Yes, that's still more than 50%, but I think it more closely reflects reality.

That's very very basic number crunching tho, how it works with form and opposition strength all factored in I'll leave to the people who have already built all their spreadsheets.

Thank you BW, but I have given you the wrong impression. I, personally, do not have this dilemma. I offered it as an example of a problem that an FPL player might be interested in resolving using external sources of advice. My point is, I do not know if this is the generic problem that MyQ is working on, and I was trying to elicit a response...

Everyone... this is not a thread about solving a dilemma of mine... I never ask for team advice on this forum (so I do not feel obliged to post an FPL link). I am interested in the generic problem and offered a little example as an illustration, that's all.

Mr Clarinet - don't worry, your credibility is not at stake! I assumed this was a generic example and was just having a laugh about it being your "dilemma" . I'ts an interesting example to choose though, since it's such a close call.



That's a very good point, as using such a system would help counter the odd freak result. And I agree that, intuitively, a 57% chance of Wolves scoring away feels better than 70%. (Although remember that this is against an average home defence. The figures will fall against a better than average defence.)

And what credibility would that be?

The example was not selected accidentally, of course! And I don't have a defender from either team.

Edit: I looked it up, out of interest. Currently Villa are 7/5, Newcastle are 17/10 with PaddyPower.

And lest we lost lose track of what we want from an FPL point of view (and I think has already been stated)...

Who's more likely to get a clean sheet?

If we were using this data to bet, we want to know whether a team will get a clean sheet or not. In FPL, it's more important to know which team is more likely to get a CS so that we can choose between our various defenders on who to play.

From an FPL perspective, if you've got both a Villian & Newcastle defender, play them both. From a betting point of view, you might conclude you should bet both and hope that at least one pays (to cover the other) or bet neither. But you'd be much more interested in the actual chances for this than simply the relative chances amongst teams for FPL.

Edit: And fwiw, Sky gives both the same cs odds, the "Past-5" seems to favor Newcastle & the approach I've been using favors Villa. So now both teams are sure to be scored on at least twice.

Unfortunately, the example I used seems to have proved a distraction. I tried to frame a generic scenario in which there was a choice - possible quite a fine choice - to be made between two players - so using a specific example and saying "play them both" is not helpful to the problem as posed. Indeed, I did not actually pose the problem. What I wanted to know (and still don't) was what problem the analysts driving this thread were trying to solve. Ho hum...

I guess we all take from it what we will.

I personally like the approach because it gives me another way to look at the relative likliness of teams getting clean sheets (and therefore defensive FPL points). And I'm pretty sure that without this post, I would have completely missed the fact that West Brom have scored only a single away goal in their last seven away matches in all competitions (and none in their last five).

Sorry I didn't get around to posting for last GW for those of you taking interest, but here is what the spreadsheet spat out at me for the coming week. Remember the Clean Sheet averages are a 37% chance at home and 25% away.

Data:

Birmingham (40%) ----------v---------- West Brom (25%)
Arsenal (48%) ----------v---------- Sunderland (23%)
Bolton (31%) ----------v---------- Aston Villa (25%)
Fulham (38%) ----------v---------- Blackburn (12%)
Newcastle (31%) ----------v---------- Everton (12%)
West Ham (45%) ----------v---------- Stoke (27%)
Man City (38%) ----------v---------- Wigan (12%)
Liverpool (31%) ----------v---------- Man United (27%)
Wolves (33%) ----------v---------- Tottenham (25%)
Blackpool (16%) ----------v---------- Chelsea (27%)
Everton (38%) ----------v---------- Birmingham (16%)

My recommendations would be:

Goalkeepers & Defenders

Arsenal (The Emirate's fortress has conceded only 1 in the last 5 at home vs Sunderlands middle of the road 5 goals in 5 away games)
West Ham (Cant believe I said that. Stoke have scored only 1 in the last 5 away from home. Consider only if already in your team!)
Birmingham (One game at 40% with a 2nd game against a weakened Everton, which probably boosts the 16% shown)
Everton (Don't stand out statistically but still have 2 games, therefore 2 chances. Injury concerns?)

Attacking Players

Fulham (Facing the leakiest away defence in the Premiership, having conceded 14 in the last 5)
Chelsea (Facing the leakiest home defence, conceding 10 in last 5 at home)
Newcastle (Scored 12 in 5 at home, facing a weakened Everton team who have conceded 9 in 5 away when stronger)
Man City (13 in 5 scored, 8 in 5 conceded)
Everton (2 games, home game stands out statistically, Newcastle also have worse than average odds of CS. Odds likely to be impacted by injuries?)
Birmingham (2 games against teams with an average chance of a CS, one home & one away)

Did you fix all the wrong bits then? Do you have a new copy for us?

Haha, I hope I have! Take a look at the spreadsheet and see what you think: http://www.mediafire.com/file/osj0cekpry98i7s/CleanSheets.zip

To be honest, when I saw the West Ham prediction I started to panic.

100% for your highlighted predictions thus far! you could just be onto something here (although you chose your greenies wisely - the 3rd ranking birmingham cleanie was a bit of a washout!)

Here's the tips for clean sheets this GW. Remember that it doesn't factor in injuries etc.

Data:

Tottenham (31%) ----------v---------- West Ham (18%)
Aston Villa (38%) ----------v---------- Wolves (18%)
Blackburn (35%) ----------v---------- Blackpool (18%)
Man United (48%) ----------v---------- Bolton (10%)
Stoke (40%) ----------v---------- Newcastle (35%)
West Brom (9%) ----------v---------- Arsenal (21%)
Wigan (26%) ----------v---------- Birmingham (27%)
Everton (35%) ----------v---------- Fulham (18%)
Sunderland (23%) ----------v---------- Liverpool (25%)
Chelsea (35%) ----------v---------- Man City (27%)

My recommendations would be:

Goalkeepers & Defenders

Man United (conceded only 3 in the last 5 at home, Bolton scored only 3 in 5 away)
Stoke (conceded 5 in 5 home, Newcastle scored 4 in 5 away)

Attacking Players

Man United (Scored 14 in the last 5 home games. Bolton conceded 8 in the last 5 away)
Arsenal (Scored 12 in last 5 away games. West Brom conceded 10 in last 5 at home)

OK, so far so good with the green predictions scoring 4 for 4. Lets hope it keeps going.

Data:

West Ham (26%) ----------v---------- Man United (21%)
Birmingham (35%) ----------v---------- Bolton (29%)
Everton (28%) ----------v---------- Aston Villa (12%)
Newcastle (31%) ----------v---------- Wolves (14%)
Stoke (28%) ----------v---------- Chelsea (23%)
West Brom (19%) ----------v---------- Liverpool (23%)
Wigan (16%) ----------v---------- Tottenham (23%)
Arsenal (45%) ----------v---------- Blackburn (6%)
Fulham (40%) ----------v---------- Blackpool (6%)
Man City (40%) ----------v---------- Sunderland (23%)

My recommendations would be:

Goalkeepers & Defenders

Arsenal (conceded only 1 in 5 at home, Blackburn scored 6 in 5 away)
Fulham (conceded only 2 in 5 at home, Blackpool scored 7 in 5 away)
Man City (conceded only 4 in 5 at home, Sunderlandl scored 5 in 5 away)

Attacking Players

Arsenal (Scored 8 in last 5 home games. Blackburn conceded 16 in last 5 away)
Fulham (Scored 9 in the last 5 home games. Blackpool conceded 15 in the last 5 away)

What are the recommendations this week? I can only view XLS files so can't use the spreadsheet.

Again, I'm just bringing another fantastic topic to the front page to give everyone something interesting to read. Not everybody uses the search function, and quite a few of these are very hard to find.

Only just seen this.

If a team is 9/4, the associated probablity is 1/( (9/4) +1) = 4/13, not 4/9. You add the 1 as you get your stake back.

i.e the proibabilties above are:

Che win = 45%
Man U win = 30%
Draw = 30%

Total = 105%, the over-round I referred to, but if you want probabilities just deivide the above by 1.05.