Are Oldham matches Giffen goods?

A Giffen good satisfies the rather odd property that as its price increases, demand increases. It so happens that if you run a regression of Oldham's attendance on entrance price since 2000, the coefficient (given the particular regression model selected - I'm talking about the model I'm sticking in my thesis right now before I submit in 4 weeks) on entrance price (both logged) is 0.215, with a standard error of 0.096. So price goes up, attendance goes up!

The classic Giffen good is potatoes in Ireland during the famine. The classic explanation is that potatoes were a large part of the Irish diet, so that when their price increased, the Irish substituted away from other foodstuffs in order to ensure that they had enough potatoes to satisfy themselves, hence demand increased, perversely. There's an argument the same is true for football - it's a big part of a hard-up football fan's leisure diet, and so if the price goes up, other things must go out of the window (bit of shopping with the wife, the odd cinema trip), in order that he can get to as many matches as possible.

It's plausible, but I think more likely it's that football attendances in general are on the up, and Latics are caught up in this general trend. Football stadia are generally perceived to be safer these days, and football is more acceptable a thing to do, than say in the 1970s or 1980s. Also price is a very uninformative variable - it's constant for long stretches of the sample size, increasing in four increments from £14 to £20 over the sample. It strikes me it's more likely this is coincidental than causal. I sound very like my first ever econometrics tutor, John Ashworth in Durham, who argued strongly against the existence of the Giffen good...

No, no and Bradford

Well, Oldham didn't send their fans home overly happy on Saturday, only drawing 1-1 with their Yorkshire neighbours Huddersfield. Furthermore it seems a very poor turn-out from Huddersfield led to the attendance being only a paltry 7,000, as opposed to the 9,500 gate predicted. So that's a no and a no.

Moving on to Bradford, another Yorkshire neighbour, to whom Latics travel this afternoon. It turns out Latics have won their previous five matches against Bradford home and away, and given Latics occupy 4th position, and Bradford 22nd, one might reasonably expect a Latics win. Sure enough, my model suggests Latics have a 52% chance of winning, with Bradford only a meagre 23%. Of course, such models struggle to take into account the late season desperation which tends to surround matches involving sides in the relegation zone, and leads to them out-performing relative to their league position.

Given further that Latics have failed to win their previous two matches away against teams in or near the relegation zone, this suggests a draw. I'll be disappointed if that happens, but I can see it happening. Probabilities for individual scores run something like this: the most probable score is a 1-0 Latics win, with 13%, then a 1-1 draw following with a 12% probability. I'd go for that myself. There's a 2% probability on Latics repeating their 4-1 win at Bradford last season.

Come on Oldham!

Also, if Scunthorpe win their match away at Northampton today, and Nottm Forest fail to win at home to Rotherham, Scunthorpe will be promoted. A Scunthorpe win has a 47% probability, a draw or Rotherham win at the City Ground at 37%, suggesting that, assuming these two events are independent of each other (!), that there's actually only a 17% probability of Scunthorpe securing promotion today. By next week though I'm sure it'll be confirmed...

Predicting football match outcomes...

Well, it took long enough, as these things always do, but now I have a model that predicts football match outcomes. The predictions of the model I'll assess in the weeks to come if I get a moment, but I'm rushing towards a thesis submission in May, so time is getting tight.

Nevertheless, the predictions this model provides are very much in line with what the bookies think, and in line with the predictions of Finktank, the Dectech enterprise that publishes predictions on football matches each week in the Times. What is this model? It's a very simple model which describes the process determining the number of goals each team scores in a match as belonging to a Poisson distribution. The Poisson distribution matches incredibly well the arrival of goals in football matches, and so if X is home goals in a match, and Y is away goals, then both can be described as Poisson processes. It's likely of course that there's some interaction between these two processes, and in this case, a bivariate Poisson distribution of (X,Y) would be sough.

Making predictions on such bivariate models is a trivial extention of what I've done already, but I haven't the time to do that yet. Maybe in May. Once the season's finished...

Anyhow, in the meantime, what does the model predict?

Take the currently running Liverpool v Man U match. Finktank thought beforehand Liverpool had a 43.4% probability of winning, with the probability of a draw at 29% and a Man U win at 28%. The bookies favoured a Man U win over a draw, suggesting that Liverpool had a 36% chance of winning, the draw at 31% and the Man U win at 33%. The simple double Poisson model I've run (on all matches before today this season in the Premiership) suggests that Liverpool have a 37% chance of winning, the draw at 30% and Man U at 33%.

After 65 minutes, the match is locked at 0-0, and the first half was a very tight affair, reflecting these evenly matches odds. A contrast is given for the Arsenal v Reading match, which is a home banker if anyone ever saw one: Finktank see the Arsenal win at 70%, the bookies at 61%, and my model at 71%.

So what about the match I'm most bothered about? That is, Carlisle United vs Oldham Athletic. As things stand, the model can't take into account form. If it did, it would put a stronger probability on Carlisle, as Oldham are in terrible form, with four consecutive defeats severely hampering their promotion hopes. Nonetheless, Oldham have a 39% probability of winning, Carlisle a 32% chance, the draw at 29%. What's the most likely score? The probability of a 1-1 draw is 13.3%, followed by a 1-0 Oldham win at 12.6%, with finally a Carlisle 1-0 win at 11%. There's a 10.6% chance of a scoreless draw. All these orderings are the same as Finktank for this match, although Finktank put Oldham slightly stronger favourites at 41%. As part of my summer research I'd like to look into what exactly Finktank construct their forecasts based on, since they're not massively different from that of a "simple" double Poisson model.

I'm biased. Three or so years back, Oldham recovered from a poor run of defeats to post a battling 1-0 win at Gillingham. I think Oldham will do that today. No, I hope.

Finally, Finktank suggest you should believe their score predictions because they've beaten the bookies on a lot of occasions. Personally I think you should trust the output of a model by whether or not it predicts the score well. So I'll let you know how I do.

Second place!

Well, somewhat predictably, after having beaten two top sides in close matches, Oldham succumbed to a "lesser" team, or a team they might have been fancied to beat. Of course, Millwall are resurgent under a very good manager, and so the result isn't all that outlandish, but nonetheless disappointing, as the Latics lost 2-1 at home to Millwall.

My model predicted 6042, and the gate was actually 6181, so at least I was only about 140 out in my prediction.

Movements forward have been made in my bivariate Poisson model, so hopefully by Tuesday evening (pancake Tuesday!), I'll be able to predict the result of the Port Vale v Oldham match. Quite an important one really, another defeat will leave us playing catch-up big time. A win is needed badly. Come on Oldham!

Thinking about betting again...

...not to mention Christianity and econometrics, I'm not convinced any more by my arguments of earlier about betting, and whether it's right as a Christian.

My point earlier was that if I could identify clear inefficiencies, then there may be a case where betting on an outcome is not an unwise use of money. However, my work at best will identify inefficiencies in the betting market compared to my model, not compared to the actual probability of a goal being scored. Without being able to see the future, it's impossible to assess truly whether or not betting markets are efficient.

However, I'm finding it a lot of fun modelling, or trying to model, goal arrival in football matches using duration models. I'm not making a lot of progress, as I've had to try and get my head around Stata, but hopefully I'll make some progress soon.

Another point I've been pondering on a little, and was given a little insight yesterday on, was that of econometrics assuming everything is random. Well, the assumption that we model everything as a random variable. This does not conflict with the idea that there is a God behind it all, and that in fact outcomes happen with a probability one as far as God is concerned, because He intends them all. To us, as they unfold, they can appear probabilistic, and it is the best way to model them, both in economics and econometrics, as random variables. In econometrics, some true underlying data generation process is always assumed, which we aim for but can never know whether or not we achieve it.

Genius...

...high time I found a good bit of Latics action on youtube:

http://www.youtube.com/watch?v=luTeSaUHlvM

Having missed the majority of these matches, it's good to see a compilation of the goals so far this season!

Ok, I saw seven of the forty odd goals in this clip (Cheltenham away and Forest home)...

Back to work...

...today, two days after most of the rest of the world. But only two days until the weekend, when I go up to Wolverhampton and watch Oldham play Wolves. And in the meantime I can work on football related bits of my Ph.D, which always helps when I'm not feeling overly motivated.

Today I'll spend a good portion putting together a dataset of match details from Premiership and Championship matches going back to 2002, in order to base a model of goal arrival on this dataset. First I hope to replicate some results from another paper (Dixon and Robinson) by using their model, a Poisson regression model, and then I hope to use a slightly different type of model to estimate the probability of goal arrival at any point in a football match. The aim is to access the efficiency of betting markets, and with Karen Croxson, who has tons of data on betting markets, I intend to do this. Should be fun.

Some more reflections on a great day...

...since I'm a Ph.D student and hence I have the time to slack for a bit...

Understandably, the Forest fans were very disappointed and infuriated. Even if both penalty decisions were correct (as I naturally think they were), it's pretty galling to have two penalties given against you in one match, and to have that compounded with two sendings off is a pretty bitter pill to swallow.

Check out this generally very good blog, where the guy clearly sounded off on getting home from the match. If only I could do trackbacks on this thing, and even knew what they were, I'd do one here - I like getting publicity for my site - I got about 100 times my usual site traffic yesterday after putting a link on the JKLatics discussion forum... but to the blog, I think I'd have done the same had I driven over 50 miles and seen my team lose 5-0. When Jack Lester came on, it reminded me of being driven (by Jack Scott actually!) to Grimsby over ten years ago now, when Lester scored a very quick hat-trick and Latics lost 5-0. Thankfully he didn't do the same yesterday.

Considering the various statements knocking around on discussion forums and blogs, I'm inclined to still say pretty much what I said yesterday, which I think most Forest and Oldham fans would agree with: Oldham would have won without the two sendings off and penalties. Forest were shocking before the referee's decisions hampered their cause.

But can they even begin to blame the referee? If the ref is faced with a very bad, red card-able offence early in the game, is faced with two clear fouls inside the penalty area, the latter denying a clear goal-scoring opportunity, he has to make the same decisions again that he made yesterday. It's frustrating, I'd have hated to be on the other end of it, but that's what happened. It's pretty improbable that all those things happen in one game, but when it rains it pours I guess, and it's a bit of a downpour for Forest right now. But they have the quality to fight back, and I'm sure they will end up in one of the two promotion spots come May. I hope we're in the other one!

Before I stop though, it's nice to read all the various reports (especially ones that aren't just copy and paste jobs from some press release...), so (apologies to Forest fans...), PFA website (Calderwood fails to note we dominated before the sending off too), Oldham Athletic mad (a great website that helps me a lot with my attendance model), Manchester Evening News, and finally the BBC report, which appears to think the 43th minute came in the second half...

Another interesting challenge...

...Oldham Athletic will be charging just £2 for adults, and £1 for kids in their next two home matches. These are matches against Brighton and Hove Albion, and Northampton Town, matches which otherwise would not attract a very high attendance at all. It's a great idea, I'm totally for it - get a full house in, hopefully get some kids hooked on Latics, especially if the team can carry on playing as they have recently (unbeaten in nine league home matches, seven wins).

But it creates havoc for modelling and forecasting. On the other hand, it's a known break. One of the biggest problems with forecasting is structural breaks, if the break affects the mean of the time series being forecast. Before the break, it's generally quite hard to predict one will happen, and then if it can be predicted, the size is another matter entirely. If a break happens, next period when forecasting, one needs to know whether this is simply an outlier, measurement error, or an actual break.

So here, I have quite a lot of information: I know something will happen that can only be described as a break - the two previous big discount matches (Grimsby (free) and Torquay (fiver)) have attracted substantially larger attendances. I further know it will only last for two matches, it is not permanent, but it's not a one-off either. And I'll know the reason why the break has occured.

All in all, it makes for an interesting experiment. Will the attendances be as large as the Grimsby or Torquay matches? A method for capturing a break is to add a dummy variable estimated over some observations in the sample, and extend this dummy into the forecast period. Usually in time-series, the dummy is for the last few observations. However, here as we have some idea from these matches how big the break might be, it makes sense to use this information.

Extending the Grimsby dummy gives a forecast of 11,670, and extending the Torquay dummy just 6,856. I think somewhere inbetween these two examples is more likely. A combination, weighting Grimsby at 0.6 since £2 is closer to £0 than £5 gives a forecast of 9,442, but I think a higher weight should be used, since zero prices have wierd effects. A weight of 0.75 on Grimsby provides a forecast of 10,230, which pleases me.

Come on Oldham!

Is life a random walk? And Oldham's fortunes...

Yesterday, in his first Clarendon Lecture in the Economics Department at the University of Oxford, Peter Phillips suggested that a time series could provide the conclusion that life is a random walk. Well, I guess given he talked about estimating numbers for models on particular data series and questioned what these numbers mean, that in fact he wasn't really trying to substantiate in any way the claim that life is a random walk.

Of course he's fitting an econometric model to the world, and that doesn't necessarily shed any light at all on the true underlying data generating process. It was data on the number of species in exitence, going back 600 million years. Of course I don't think that life is a random walk, I don't for one moment believe that the various underlying processes generating this 600 million year data set really suggest everything is random.

Nevertheless, that's what people who deny the existence of God are forced to believe - it's all random. However, through the existence of a man who lived 2000 odd years ago we have God's revelation to a disbelieving world, captured in a book that's internally consistent as to exactly what this Jesus chap was up to. God isn't random, He has a plan, and He's made it known to His world. Will you take a look? Check out here if you want to.

On to Oldham Athletic. I was dissatisfied with my model, and applied an ad hoc solution, contrary to how I believe econometric modelling should take place, although consistent with the idea that the best ways to do econometrics are not the best ways to forecast. Originally the forecast was about 5,700, but with a variable to capture the visit of local rivals, the forecast was raised to 6,179, which I still thoughts too low. However, the model was giving forecasts in the right ball-park, whereas I was way out: the actual attendance was 6,001. Again much lower than I'd have expected, but continuing the trend this season.

But Oldham won 2-0 against local rivals, continuing their good form in the league now to 1 defeat in 12 matches, and 7 wins along the way. Surely soon, if this form continues, attendances will rise?

A local derby...

...provides another challenge for my Oldham Athletic attendance prediction model. Simply fired through, the model gives a prediction which my eye says is far too low: 5,696. Certainly, based on attendances in the league this season thus far, this seems too high - attendances have barely broken the 5,000 mark. However, Bradford travel only 22 miles to get to Oldham, and the attendances at the previous two matches between the sides at Boundary Park have been 9,381 and 6,982.

So what to do? Are Bradford a special case, counting pretty much as Oldham's closest rivals right now, with the absence of a Wigan or a Stockport in the same division? Unfortunately the tag of closest rivals actually goes to Huddersfield Town at 16 miles away. Furthermore, Huddersfield do appear to bring better travelling followings than Bradford, in my limited experience and memory.

Nevertheless, Bradford and Huddersfield do pretty much count as our only rivals this season, and are rivals that bring large visiting contingents - unlike, for example, Bury. As such, why not a Rivals variable?

Inserting that, and the model predicts a slightly more satisfying 6,179. I still think it's a bit low, but then this season gates have always been pretty low. Bradford aren't on the best of runs (although they've signed a very good player in Tommy Black this week), while the Latics head into this game unbeaten in seven home games and after two consecutive away victories. So maybe, all that accounted for, a gate not much over 6,000 is about right. We'll see.

Oh and while I'm here I might as well predict the result I guess. 3-1 Oldham. No rationale for it. Come on Oldham!