Tuesday, August 02, 2011

Skew's Your Daddy?

Sporting Index have finally published their 2011/12 League One points total spreads.

Interestingly, whilst Charlton are typically 4th favourites to win the League One title with the traditional ‘fixed odds’ bookmakers (behind Huddersfield, Sheff Weds and Preston), they are firmly placed 2nd in the Sporting Index hierarchy with a spread offered of 75-77.

This may seem somewhat anomalous, although the reasoning may infact be rather more subtle and got me thinking about a different way of assessing ‘value’ in the spreads market.

Although bookmakers (of either type) will occasionally ‘take a view’ on the outcome of an event, the vast majority of the time they are solely focused on laying a balanced portfolio of bets.

In short, they must assess what the ‘average opinion’ of punters regarding a given market will be. To quote John Maynard Keynes’ famous quote about a beauty contest (in which the winner was the person who selected the faces that others considered the most beautiful):

“It is not a case of choosing those [faces] that, to the best of one’s judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.”

Whilst the ‘actual’ probability of an outcome is highly correlated to what ‘average opinion’ thinks it is, ‘average opinion’ is often wrong.

By coming up with an accurate assessment of ‘average opinion’, no outcome (unexpected or otherwise) can hurt the bookies materially, and they can thus simply sit back and earn the inbuilt profit margin/spread.

If you fancied a fixed odds bet on Charlton to win League One (8/1 is generally available), then one of either two things is guaranteed to happen: either Charlton will win the title, or they won’t.

Whether Charlton win the title by 20 points, or finish in 13th place again is irrelevant to the payout received, or loss suffered.

Since the bookmakers are most concerned about ensuring a balanced book, the fact that we are ‘only’ 4th favourites simply reflects the weight of money.

In short, rightly or wrongly punters have been more inclined to fancy some of our Northern rivals over us.

Indeed I think they may be ‘right’ but not for reasons that are immediately obvious or necessarily concerning (to us as Charlton fans).

Unlike the fixed odds bookmakers, the spread bookmakers have a more complicated assessment to make before publishing the total season points spreads (or frankly any type of spread) which they hope too reflect ‘average opinion’ (thus ensuring the balanced book that they also crave).

Firstly they need to consider ‘skew’. To what extent will observations greater than the upper level of their spread (77 in our case), be more likely than observations less than the lower level of the spread (75)?

If ‘average opinion’ perceives there to be a skew (either way) then the spread bookmakers will receive unbalanced bets, which will force them to adjust their spreads (to attract punters to take the opposite view, achieving balance).

If enough bets were accepted and the actual outcome reflected the original perceived 'skew’, then they will likely generate a loss on the market.

Second, they need to consider ‘kurtosis’ or the degree to which the total number of points achieved is likely to be highly bunched around the average, or has scope to be very divergent (‘fat tailed’ or providing ‘optionality’ in statistical/finance speak).

By definition Charlton will achieve between zero and 138 points, but bookmakers and punters alike must operate within reasonable bounds of ‘confidence’ in order to be willing to make and lay bets alike.

Whether in the worlds of finance or bookmaking (a form of finance after all), it is fairly standard to manage risk within a confidence level of 95%.

In this context in other words, they will ask themselves what ‘average opinion’ considers the range of Charlton’s total points to be, in 19 out of 20 seasons.

I believe the spread bookmakers have placed us 2nd in their hierarchy because Charlton’s likely total points are very ‘fat-tailed’ to the upside.

In short, I believe Charlton are the only side in League One for whom I cannot make the following statement with at least 95% confidence: “They will not generate more than 100 points.”

Moreover, I believe that the spread bookmakers have correctly identified that the ‘average opinion’ of punters would conclude likewise based upon our considerable summer transfer activity, hence the spread has been set commensurately higher.

This activity however needs to be assessed in the context of considerable uncertainty about Chris Powell's ability to mould a winning team.

It is worth noting however that he may not be the manager for the entire season, an important consideration perhaps capping downside if things go awry.

This does not however suggest that the fixed odds bookmakers are wrong to consider Huddersfield, Sheff Weds’ or Preston’s chances of winning the title to be greater than ours. As mentioned, the two sets of bookmakers are looking out for different things.

In order to find League One betting opportunities which provide highly attractive risk/reward, I am seeking opportunities to buy or sell spreads where I’m on the ‘correct’ side of any skew (so that I’ll make money more often than not), and where the tails are ‘fat’ in my direction (providing the scope for disproportionate profits compared to losses).

Assessing skew is not easy, but as a proxy I’ve done the following. I simply sat back and used ‘gut feel’ to assess what I thought would be the average points generated by each team if the current season was played out thousands of times (some might refer to this as a ‘Monte Carlo Simulation’).

If this ‘average’ is materially more or less than the actual spread (say by more than 5 points), perhaps because the spread has been dragged higher or lower by the bookmakers concerns about ‘fat tails’, then I would be comfortable that I’m on the right side of any skew.

Looked at another way, it is simply my best guess for the way the table will actually look at the season’s end – obviously feel free to disagree for the purpose of your own analysis.

I’ve copied the Sporting Index spreads next to it, and marked those bets that would be attractive on this basis only (ie. not yet enough for me).

Huddersfield 85 75-77 BUY
Sheff Utd 77 69-71 BUY
Charlton 77 75-77
Preston 74 67.5-69.5
Sheff Weds 74 72-74
Scunthorpe 69 64-66
MK Dons 67 69-71
Notts County 66 56-58 BUY
Orient 64 66.5-68.5
Colchester 64 58.5-60.5
Exeter 59 62-64
Brentford 59 68-70 SELL
Carlisle 59 60-62
Chesterfield 58 57-59
Wycombe 58 53-55
Yeovil 57 54-56
Bury 56 51-53
Bournemouth 55 63.5-65.5 SELL
Hartlepool 55 58-60
Oldham 55 54-56
Rochdale 55 62-64 SELL
Walsall 52 52.5-54.5
Tranmere 54 54-56
Stevenage 50 51.5-53.5

In order to assess ‘kurtosis’ or the scope to find attractive ‘fat tails’, I’ve listed below my expectations for the range of total points each team would generate with the above mentioned 95% confidence.

Again I have put the Sporting Index spreads alongside – I believe a suitably attractive bet on this basis would be one where the reward/risk ratio is at least 2:1 ie. the gap between the upper/lower bands and the bet midpoint is at least 2:1, and I have again marked these accordingly.

Huddersfield 65-95 75-77
Sheff Utd 55-82 69-71
Charlton 62-100 75-77 BUY
Preston 55-82 67.5-69.5
Sheff Weds 58-88 72-74
Scunthorpe 55-77 64-66
MK Dons 52-80 69-71
Notts County 50-80 56-58 BUY
Orient 50-75 66.5-68.5 SELL
Colchester 48-70 58.5-60.5
Exeter 50-72 62-64
Brentford 50-75 68-70 SELL
Carlisle 52-74 60-62
Chesterfield 42-64 57-59 SELL
Wycombe 38-64 53-55
Yeovil 41-61 54-56 SELL
Bury 38-58 51-53 SELL
Bournemouth 48-75 63.5-65.5
Hartlepool 50-68 58-60
Oldham 40-60 54-56 SELL
Rochdale 38-65 62-64 SELL
Walsall 41-61 52.5-54.5
Tranmere 42-62 54-56
Stevenage 38-55 51.5-53.5 SELL

As you can see, the size of the ranges is not constant and in some cases (eg. Charlton, Notts County) considerable.

Some teams have considerably more ability to surprise (to the up or downside) based on factors such as the managerial turnover, playing budget, summer transfer activity, risk of administration etc..

To use an alternative analogy, if you took a sample of a hundred 40-year olds, 50 of which drank 35 units per week and 50 of which were tee-total, the average life expectancy of each group would only be different by a couple of years (too many other factors are relevant too).

However I would state with far greater than 95% confidence that none of the first group would live to 100 (the booze consumption isn’t high enough to kill them in the near-term, but would be near-guaranteed to do so in the end).

In short the range of life expectancies would be much narrower (although the former group would have more fun).

As can be seen above, some bets which were interesting in terms of skew (eg. SELL Bournemouth) are not attractive any longer because the realistic ‘optionality’ is not sufficiently attractive.

Similarly some bets which were not interesting in terms of skew (eg. SELL Orient) are attractive in terms of optionality.

Likewise in Charlton's case, there is scope to make a lot of money but the entry point is not appealing enough to offset the likelihood of small losses (the ‘skew’).

Most interestingly, three bets qualify as attractive on both metrics ie. SELL Rochdale, SELL Brentford, and BUY Notts County.

One bet in particular is extraordinarily attractive, namely SELL Rochdale.

Highly-rated manager Keith Hill has moved on (taking two key players with him), and thus rookie boss Steve Eyre must try to emulate last season’s extraordinary performances with one of the tiniest budgets in League One.

Nonetheless, their highly impressive exploits last season ‘only’ generated 68 points, so an entry point of 62 (just two wins fewer) seems more than justified.

Brentford finished last season strongly under ex-Addick Nicky Forster, and have also taken a punt on a leftfield managerial appointment, Uwe Rosler.

At 68 points, one can enter the bet at a level seven points greater than the total they managed last season, more than discounting any squad improvement that may have occurred.

Finally, Notts County have eccentric boss Martin Allen in charge and whilst he remains somewhat unpredictable, the Magpies (like Charlton) have undertaken a considerable summer rebuilding job which remains ongoing.

However I believe the capacity for surprise is firmly to the upside, and at an entry point of 58 points, I feel very comfortable.

For these three teams, it’s time to ”..back up the truck..” as they say in the US. I believe the spread bookies' expectation of average opinion is wrong - if the spreads begin to move in my favour before the season even starts, then I will know I'm onto something.

As for Charlton, I think there is potential for the season to be extraordinary (akin to 1999/2000) but this is not my average expectation, hence the apparent anomaly. It seems both types of bookies agree.


At 10:35 PM, Anonymous CharltonChris said...

Great post NYA, thanks.

At 9:11 AM, Anonymous stuart said...

I can only really comment on the spreads on the premiership but your analysis does not hold up there (any more). A few years ago it was possible to make money by buying or selling a team who were likely to under or over perform in the short term before reverting to mean/expectation over the season. I think how sporting used to calculate their spreads was to have an expectation for each game and then deduct/add points per game from the annual spread after each game depending on the result of that game. So last season after say 10 games villa’s spread would have dropped and Blackpool’s would have risen and you could then cash your winning bet by buying back the spread. If the bet had gone against you it was simply a case of waiting for the team to revert to mean (see below)

In reality over the season dropping points against teams you don’t expect to lose against is balanced by winning when you didn’t expect to as you revert to the mean. Again this is demonstrated by villa finishing 9th and Blackpool being relegated. So now sporting tend to keep their spreads fairly static regardless which isn’t their guess of average opinion of average opinion but their best guess of expected points.

This would suggest there is a money making opportunity if you can spot the team that will under/over perform over the whole season but with such a scrutinized league, and such a correlation between wages and performance that’s unlikely. In addition the 2 point spread I think is too large a margin for the bookmaker.

If the time was available I would like to track sportings prices over a season to see if my hypothesis is true

As I say I don’t know whether this applies in the lower leagues as I have insufficient knowledge

At 1:03 PM, Blogger Kings Hill Addick said...

Very interesting. I've always considered spread betting to be a great way to lose a lot of money, even though it's the profession that Mrs KHA is in.

I agree with your analysis but still think it boils down to you (or me) accurately predicting the future, even if in this case it's only about identifying possible exceptions.

I like the idea that one gambles small sums on many positions that come in big if the right set of circumstances exist. Taleb talks about avoiding the potential massive loss to make a small gain. Even if the probability is significantly in favour of a small gain, if there is any risk, at all, of a massive loss I would be uncomfortable with it. I probably have more experience of the risk/reward relationship in personal finances and protection than spread betting, but I get the concept, and I tend to be on the slightly more cautions side.

It would seem that the club, itself, however, is operating to this exact principle. Something you have discussed before. Bring in players that will almost certainly do ok, but hope that one (or more) of them improve way beyond expectations. I don't think anyone really believed that Darren Bent would be sold for £16.5m when Curbishley brought him in, even if the Ipswich coaching staff kept saying it, but it was hoped that he would develop, and expected that at the very least he would 'do a job for us'.

I am not going to put any money on it, but I am extra ordinarily confident this season. I agree that if Powell doesn't build a winning team with these players someone else will come in will do so. I think 100 points is possibly a little beyond us but I wouldn't be at all surprised if we exceed 90 (80 if Powell is removed after a poor start).


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