Long ramble about chance, probability, randomness, etc. Not for everyone! Or anyone perhaps….
A big point of discussion this year has been the role of luck in Fulham’s season. We won’t rehash individual events here - that’s been done too often - but I would like to explore the role of randomness in football a little more. Forgive this tangent; it’s something I’m interested in, and here is as good a place as any to start.
We’d all agree that there is a good degree of uncertainty in each football match. If there wasn’t bettors would make money consistently and we, the public, would have a fair idea of what will happen every time we go to the stadium.
Alright, sometimes we do have a good idea. At the extremes we know that we’ll lose to Manchester United more often than not, etc. But in a home game against Birmingham, how can we be in any way certain?
If this were a game between two evenly matched teams we’d expect the home team to win about half the time, and a draw and an away win would be splitting the remainder. I’ve got this data from Joseph Buchdahl’s excellent book on sports betting, and it seems reasonable. Put another way, if Fulham were to play Birmingham at home four times we’d reasonably expect to see two home wins, one draw, and one away win. Fair enough?
So what determines which of those we will see on any one afternoon?
Is it tactics? If it was, wouldn’t those tactics work every time they were used? Why not? Different circumstances? Different personnel opposing those tactics? Maybe.
There would be other issues. Prior form would probably affect confidence, which might shift the probabilities a little. Players having off days can happen. Other things probably.
But ultimately, isn’t it largely chance that determines which of the four games we see? The bounce of the ball, the referee making a strange decision, anything else. If Fulham and Birmingham played four times, wouldn’t you expect to see four very different games? I would. That suggests to me that there is a lot of randomness at play.
I’m going to go along with this assumption: in a game between two evenly matched sides there is a half chance of a home win, a 25% chance of a draw, and a 25% chance of an away win, and that whichever of those it is to be, we cannot reasonably predict this, and therefore we cannot say that there is a reliable logic behind this outcome.
For the purposes of what we’re about to do, which of the four outcomes (2 x home win, 1 x draw, 1 x away win) we see is purely driven by chance. Let’s see where that could lead.
Let’s say that, loosely speaking, there are seven teams of about Fulham’s quality in the league this year. These are Bolton, Birmingham, Sunderland, Newcastle, Reading, Wigan and Middlesbrough. I’ve taken the 50:25:25 assumption for Fulham’s home games against these teams and worked out what that might mean for results.
| Pts | Total % |
| 21 | 1% |
| 19 | 3% |
| 18 | 3% |
| 17 | 4% |
| 16 | 8% |
| 15 | 4% |
| 15 | 3% |
| 14 | 10% |
| 13 | 10% |
| 13 | 2% |
| 12 | 3% |
| 12 | 7% |
| 11 | 10% |
| 11 | 1% |
| 10 | 7% |
| 10 | 3% |
| 9 | 2% |
| 9 | 5% |
| 9 | 0% |
| 8 | 5% |
| 8 | 1% |
| 7 | 3% |
| 7 | 1% |
| 7 | 0% |
| 6 | 1% |
| 6 | 2% |
| 6 | 0% |
| 5 | 1% |
| 5 | 0% |
| 4 | 1% |
| 4 | 0% |
| 3 | 0% |
| 3 | 0% |
| 2 | 0% |
| 1 | 0% |
| 0 | 0% |
[probabilities corrected, thanks to Joseph Buchdahl - rounding by me, 0 not always 0, could be 0.2 or something].
This has toned down the wilder assertions based on my own numbers, but you can see how a team with its results derived at random like this could just as easily get 8 points as 16.
Where am I going with this? Well, if we take the 50/25/25 assumption to be reasonable, and I have no particular reason not to, in any given season the results of games between eight teams of comparable quality *could* be almost entirely random. Of course the teams may not be of equal quality, but I doubt there is that much between them. One team could win all seven of these encounters through the laws of probability. They would be safe. It is not out of the question that one team could lose all of these home games. They would be down. Again, all this is through chance.
My contention, and over the years I hope to do a better job of explaining it, is that football is a very random game and that much of what we ascribe to managerial/team ability is just chance.
I agree with you to an extent about luck being a big factor in football. Obviously ability too has a big bearing - so, Man Utd probably have about the same luck as anyone else - it’s just that they play a lot better and create more chances so whether they have a good day ‘luck-wise’ or not they’ll still probably win. It’s struggling teams like us who need luck on our side, especially in the early part of the season can have a big bearing on confidence (and I would say confidence is a bigger factor in influencing results than luck).
However, I don’t think luck HAS to be the defining factor. Had Sanchez started off with lots of good luck, things might have been different, but the fact remains that he didn’t, and he didn’t deal with it well at all. A good manager should probably be able to ride the bad periods, account for bad breaks, and come out ok at the end of it. In retrospect, we needed the luck to go our way because Sanchez wasn’t adept enough to keep things going if they didn’t. The worse manager you have, the more luck starts to come into play. Coleman had quite a lot of luck during his time here I thought.
I dunno, perhaps it’s useful to think of it this way - luck DOES play a part in football - but - the worse the manager/tactics, the more you’re relying more on luck for in order to do well. And conversely, if you have a really good manager, he can set a team up that needs a lot of bad luck in order to do badly (although it’s still possible). Ultimately, things like the bounce of the ball are in the hands of the gods. But managers do have the opportunity to give themselves a better chance.
(PS. Not sure about your probabilities. For example, for your first one (7-0-0) if you want a 50% chance thing to happen seven out of seven times, then that’s 0.5 to the power of seven, which is 0.625%. It’s the same chance as flipping a coin and getting seven heads in a row - in other words, pretty unlikely.)
JamieR
12 Mar 08 at 11:40 am
J —–I agree with you to an extent about luck being a big factor in football. Obviously ability too has a big bearing - so, Man Utd probably have about the same luck as anyone else - it’s just that they play a lot better and create more chances so whether they have a good day ‘luck-wise’ or not they’ll still probably win. It’s struggling teams like us who need luck on our side, especially in the early part of the season can have a big bearing on confidence (and I would say confidence is a bigger factor in influencing results than luck).
R —- This is true, and I meant to make this clearer. As you get better the odds of any single game are more in your favour. So United against us would be an 80/10/10 split, for example. What I’m trying to get at is how we determine what will happen on any day, and, if we can’t, then is it not chance?
J—— However, I don’t think luck HAS to be the defining factor. Had Sanchez started off with lots of good luck, things might have been different, but the fact remains that he didn’t, and he didn’t deal with it well at all. A good manager should probably be able to ride the bad periods, account for bad breaks, and come out ok at the end of it. In retrospect, we needed the luck to go our way because Sanchez wasn’t adept enough to keep things going if they didn’t. The worse manager you have, the more luck starts to come into play. Coleman had quite a lot of luck during his time here I thought.
R ——Agree with all of that.
J —– I dunno, perhaps it’s useful to think of it this way - luck DOES play a part in football - but - the worse the manager/tactics, the more you’re relying more on luck for in order to do well. And conversely, if you have a really good manager, he can set a team up that needs a lot of bad luck in order to do badly (although it’s still possible). Ultimately, things like the bounce of the ball are in the hands of the gods. But managers do have the opportunity to give themselves a better chance.
R —- Agree with that too. A manager can make the team better so that instead of a game being 50/25/25, it can be 60/20/20, which in the long run will give it an edge. I guess this is sort of my point, the difference between an average team with luck against them and a bad team with quite good luck might not be at all apparant. As you say earlier, this can lead to all kinds of complications. I think this is what has happened to us this season.
J —— (PS. Not sure about your probabilities. For example, for your first one (7-0-0) if you want a 50% chance thing to happen seven out of seven times, then that’s 0.5 to the power of seven, which is 0.625%. It’s the same chance as flipping a coin and getting seven heads in a row - in other words, pretty unlikely.)
R —— Yeah, I think they must be off, as I mentioned, they don’t add up to 100 which is a sure indicator of this! I *think* the general point holds though.
I suppose what I’m trying to say is that if we assume a team’s true ability is x points, the variation that could be down to chance alone is probably pretty high.
As you say, a true 90 point team will rely a lot less on this because it will be attacking more, and will have most of the ball, etc, etc. It might end up with 80 points or it might end up with 95, but it’ll probably be there or thereabouts.
What I’m interested in is the teams around us, all of whom may well be 35 point teams. I believe that chance can make a 35 point team look like a 20 point team or like a 45 team, and that variation will cause us to misattribute differences to managerial performance, etc, etc.
Anyway, thanks, Jamie, this is definitely an exploratory post and I really don’t know what I’m talking about… yet.
weltmeisterclaude
12 Mar 08 at 11:50 am
“The difference between an average team with luck against them and a bad team with quite good luck might not be at all apparant.”
That’s something I agree with, definitely. I think it’s the kind of thing that might not even itself out, even over a whole season. That’s one of the reasons I think, in an ideal world, managers should be given at least two years before they can be properly judged. That and the fact that it takes time to shape your own team. With Sanchez there was the problem of massively low confidence, fan unrest, and being in the bottom three, so his sacking was understandable. But, for example, the sacking of Allardyce at Newcastle was ridicuous IMO.
(PS. Probabilities - I think the thing is, in your table 7-0-0 is the most likely, when in fact there’s a much bigger chance of 3-2-2 or 4-1-2 etc… anyway, for the other reason we’ve stated, perhaps the 50-25-25 thing starts to lose some value! Neither am I sure what I’m on about by the way…)
JamieR
12 Mar 08 at 12:03 pm
ah shit, that’s right isn’t it? What I’m assuming is that because a home win is most likely, winning all seven is the most likely eventuality. Which clearly isn’t the case. I have asked Joseph Buchdahl for his thoughts - hopefully he’ll correct me!
weltmeisterclaude
12 Mar 08 at 12:06 pm
Not sure about probabilities but I do think that there are very few genuinely good managers out there and therefore luck plays a big part.
Most managers are ex players likely to seek their first job at about 35 and will be looking to work for perhaps 25 years.
Of today’s breed how many qualify? Ferguson, Gradi, Hodgson, Redknapp, Keegan? How many others have kept working that long?
Why so few - because all the others were sacked with a reputation so low that they couldn’t get another job.
So some have some success, most have none at all but very few sustain success. Because they’re not capable of improving teams.
Tony Gilroy
12 Mar 08 at 2:35 pm
I think you’re right. There are a minute proportion who are known to be able to do a very good job, and a vast middle class who might or might not get things done, and then, the underwater bit of the iceberg, those who have already been found wanting and already consigned to manager hell (or Sky Sports).
This is something that has long surprised me: if I took over a football team the first thing I would do is pay well over the odds to a proven manager. I don’t know how these things work, but if I had £20 million I’d spend whatever it took to get my man, with the proviso that he’d have whatever he didn’t want in salary to spend on his team.
Put another way, if you’d said to Star Manager A last year: “here’s £30 million”. Name your own salary, and your transfer budget is whatever is left over plus whatever you can sell your players for.
Would that work? Would anyone agree to it? Would it have worked better than the Sanchez approach?
Purely speculative, of course. But I like having these wonderings.
weltmeisterclaude
12 Mar 08 at 3:01 pm
I think you’d find the salary would leave little left over for expenditure.
But that makes it more likely the manager would fail?
Yes but he’d have a prosperous retirement.
Tony Gilroy
12 Mar 08 at 3:32 pm
Yes, it wouldn’t work. But until quite recently even the best managers were paid less than their players (I think), which clearly was not correct.
weltmeisterclaude
12 Mar 08 at 3:44 pm