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.

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!

Attendance vs Crewe

It's been a couple of weeks since the last home match, and with a couple more wins under the belt, one might expect a bumper gate in the home match tonight against Crewe, which kicked off about seven minutes ago. Particularly given one of the two wins was a crushing 3-0 win at local rivals Huddersfield. However, my model of attendances predicts a gate as low as 4,289.

A number of factors cause this: it's a Tuesday night; it's December, Christmas is coming and all that. However, it's the first home game for a while.

I can't believe the gate will be that low. I'm looking into forecasting using what is apparently a very good forecasting device, the exponentially weighted moving average. By altering the parameter on the weight from 0.1 to 0.9 I get a range of forecasts between 5,122 and 5,903.

I'm inclined to go with the naive forecast with parameter 0.1 to be honest, I reckon the gate will be just around 5,000. I could be proved wrong, and my model right however. I just hope Latics win!

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!

Econometricians dabbling with Christianity...

As I wrote my response to Ed Glaeser yesterday, I came across a number of interestingly titled papers, and before I knew it I was on a trail back to Ed Leamer, who Ed Glaeser is a colleague of, and whom Glaeser recommends all should follow when doing econometrics. It so happens I disagree with this on econometric terms, as my response should point out (if it doesn't, I'll be working on that!), and I also have bones to pick about Ed Leamer's understanding of God and Christianity, comments that spawned papers titled "Sinning in the Basement: What are the Rules? The Ten Commandments of Applied Econometrics " by Peter Kennedy, and "Applied Econometrics without Sinning" by my supervisor, David Hendry.

Kennedy's use of Christian language is an outpouring of a work by Edward Leamer in 1978, which described econometrics along the lines of the building where he was apparently taught it - on the bottom floor were the applied guys churning out econometric models, and on the third floor were the econometric theorists, teaching students about the ideals of the subject, without getting their hands dirty. He was intrigued by how both camps used the same language, but described the former as "sinners in the basement", and the latter as High Priests.

I'm quite unsure of where Leamer got this idea from. Perhaps it could be from the perception of that Christians, well Christian leaders, are somehow perfect, or at least should be (witness the consternation when they're found not to be, and found to be child abuses etc). Hence they occupy this third floor, pure and clean, not getting dirty with the world. Yet this is not the view of Christianity put forward by the inventor of the faith, Jesus Christ. Not only did he (described as our High Priest) get his hands dirty in the world by healing, dining with the masses etc, but he also remained sinless (where sin is defined, as it is in the Bible, as disobeying God). As a result, when Jesus died on the Cross, a death deserved for those who disobey God, he took that punishment, meaning that all who disobey God can avoid punishment, if they believe and trust in Jesus as their Lord and Saviour.

So Jesus knew that, in fact, all occupy the basement, to use Leamer's language. What does this mean for Leamer's model? Well it means not least that even econometric theorists get their hands dirty, and in Glaeser's words, behave opportunistically. Those, such as Leeb and Poetscher, in their 2005 paper, who claim model selection can never deliver consistent regression estimates and make strong claims about it, when their model set-up precludes consistent estimation by any methodology, be it simple regression, model selection or model averaging, are very guilty in this respect.

Only Jesus, and the Father and Holy Spirit, occupy the third floor for the time being. Thankfully, through Jesus heading down the stairs to the basement for a time, we can enter the third floor in time, though not yet - either when we die, or Jesus returns.

Turning to another aspect of Edward Leamer's theology, he writes:
"As you wander through the thicket of models, you may come to question the meaning of the Econometric Scripture that presumes the model is given to you at birth by a wise and beneficient Holy Spirit."
Such blatant use again of Biblical language suggests that this quote is motivated by some understanding of Christianity. However, again it is not the view of Christianity Jesus talked about, and if we're really interested in Christianity enough to write in econometrics papers, we should consider what its founder had to say.

Many of the words of Jesus recorded in the Bible could be used to show that Christianity is not something bestowed upon some people at birth, but not others. For example, in John 3:16 Jesus says "For God so loved the world that he gave his one and only Son [Jesus], that whoever believes in him shall not perish but have eternal life". Further John 20:30-1 says "Jesus did many other miraculous signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name." So being a Christian is about taking the decision to believe in Jesus and what He did, listen to Jesus and work out what believing and following Him means (through the Bible and Jesus' miracles), and doing it.

So just as econometrics isn't about having a particular model provided to you by some divine revelation, neither is Christianity, and in both one must be very careful to learn and to understand exactly what is going on, not what one thinks is going on, from one's childhood memories (econometrics = that undergrad class you had to take, Christianity = primary school).

Econometricians behaving badly...

Edward Glaeser has written a paper about econometricians behaving opportunistically, and how they violate all the assumptions economic theorists have been making for years now about the behaviour of individuals when faced with a set of incentives.

Basically, it's a fallen world, and as a result, people will present bad stuff and cover it up. But it's given me a chance to try and link together my faith and my work a bit, and I've written a response to Glaeser's work, hopefully outlining an alternative method of carrying out econometric analysis which, while not free from opportunism, provides a method for exposing it elsewhere, and providing a transparent way of doing econometrics, if carried out properly. In a lot of respects, econometricians attempting to behave themselves mirror Christians attempting to live in the fallen world before Jesus Christ returns. It's a tentative link, and I'm encouraged that Paul mixed his metaphors quite a bit in his letters to the Corinthians, as I think I've managed that. Have a read, see what you think. Do get back to me with your comments.

A challenge of another kind entirely...

Forecasting league attendances at Oldham has become reasonably simple - just below 5,000 is a good benchmark. However, the Association Members Trophy, now known as the Johnstone's Paint Trophy, poses another challenge altogether. This is because no-one really cares about the competition, and it doesn't provide interesting opposition as a rule, because the teams that participate are all from League One or below. Hence the best that could really be hoped for is Nottingham Forest. Oldham have drawn Chesterfield. Hardly glamorous, no offence to Chesterfield. I'm sure had they drawn Oldham at home they'd feel similarly indifferent. The dummy variable on these kind of cup matches suggests they knock something like 60% off the normal gate at a home game.

So from 5,000, that suggests there should be around 2,000, which sounds about right. However, estimating on data up to Saturday's pleasing 3-0 win over Brentford gives a forecast of 3,107, which is way too high. When Oldham made the semi-finals of this competition two seasons ago, the home game in the semi attracted only 2,881 people! However, that was probably because the club decided against offering substantial discounts for that game, which they will undoubtedly offer on Wednesday, and did in previous matches that season - the quarter final, against Tranmere, attracted over 4,000 people, while the second round match against non-league Accrington Stanley drew a crowd of 2,812.

Yet I still think 3,107 is far too high. Inserting dummy variables for a couple of outlying matches (Chasetown in the FA Cup last season, and Carlisle earlier this season), and inserting an intercept correction for the current season, provides a lower forecast of 2,675, which is better. Further, adding these dummies renders some other curious coefficients insignificant, and given their "wrong" sign, and plausible explanation (see paper), it seems sensible to get rid of them. These variables are a dummy for when the game falls on a Wednesday night, and the Days Since Last Home Game variable, which is the number of days since the last home game.

When got rid of, the forecast falls yet further into acceptably low territory: 2,504, and so this is the forecast I'm going with for the Chesterfield match.