Monday 18 February 2013

Fibonacci Fibbing

There were some big differences of opinion about the Under / Over total for last night's NB All-Star game. The totals line ended at 294.5, although Betfair had markets for 291.5 and 297.5 as well. Before the tip-off, the Over had traded as low as 1.8 and as high 2.22. As my Twitter (@calciocassini) followers will have seen, any price north of 2.0 was great value to my mind. While the game has become less and less defence oriented in recent years, 295 points has only been reached once, last year, in regulation, although three other times the total went over after overtime. 

You always need to be careful with these ultimately meaningless games that are more about the show than competition, but the fourth quarter is always played seriously if the game is close. Even with little defence, four quarters of 74 points is a lot to ask, 6+ points per minute. After 6 minutes, the total was 34 points, (with 1.55 traded), and after one quarter just 57 points were on the board. The scoring pace picked up in the second quarter with 77 points putting the total up to 134 at half-time leaving 161 needed for the Over to come in. The most points ever in an All-Star half was the 157 scored in 1988.

After three quarters the total was 212 points and a four point differential, so the rest of the game was always likely to be a little more competitive. With 83 needed for the Over to come in, the only danger was overtime, but in the end it was a comfortable win, and I hope some Twitter followers got the 2.16 or close that was available.

Pinnacle sometimes has some good articles on betting, but this one on draws is not one of them:
Betting on draws isn’t the most glamorous form of soccer betting, but it could be one of the most profitable. We investigated betting in a set numeric pattern on draws with odds of 2.618 or more to see whether the Fibonacci betting system is a magic bullet for soccer betting profits.
The essence of the Fibonacci Strategy – published in 2007 by Fragiskos Archontakis and Evan Osborne- is simple: bet on a draw, and if you lose, bet on another one. Repeat this process until you win. There are only two additional – and vital – rules to follow:
Only bet on draws when the probability is above 2.618
Increase your betting stake in a way that follows the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21 etc.
The idea is based upon a theory from 1989 that the draw is the most difficult for bookmakers to predict, and therefore can be exploited. The idea is that as long as you continually increase your stake, any win will overcome your previous losses.
The Fibonacci Strategy in practice
Looking at data from the 2011/12 Premier League, there were 93 draws in 380 games – therefore 24.5% of all games ended in a tie. Interestingly, the odds for a potential draw in all 380 ties were above the 2.618 threshold suggested as the lower limit by Archontakis and Osborne. This means there should be – on average – a payout every four games. This means the winning stake would be the fourth Fibonacci number: 5, with a total bet each time £10 (the winning stake added to the failing three stakes before it: 1, 1, and 3). Considering the average odds for a draw over the season were 4.203, this means that the average winnings would be £21.02 (£5 stake multiplied by the odds), with a profit of £11.02 when the stakes have been subtracted. Over 380 games, this equates to a theoretical profit of £1786.7 – all from an initial stake of just £1.
Fibonacci Strategy Drawbacks
However, there are numerous practical limitations that prevent the Fibonacci sequence from printing money. For a start, many games are played concurrently, meaning there’s no option to increase your stake to the next Fibonacci number if a draw doesn’t occur, as the games will finish at the same time. Instead, bettors might consider applying a Fibonacci betting sequence to individual teams. However, this means that long streaks without draws could cause huge holes in bettors’ bank balances. Looking at the longest Premier League streak without a draw (Manchester United in 2008/09), the Red Devils went 20 games without drawing, before finally succumbing to a 0-0 tie with Arsenal. Because the Fibonacci sequence increases exponentially, bettors would have to have bet £10,946 on that final game to follow the sequence. Including that bet, anyone following the betting system would had to have staked £28,656 – a huge amount for a system that usually provides winnings of just £21.02. The odds for a draw on that game were 4.1 however, which would have provided winnings of £44,878.60, or a profit of £16.222.60. With Fibonacci, the increased stakes also provide impressive returns.
The Fibonacci Sequence explained
The Fibonacci sequence is one of the most widely known numeric sequences in mathematics, characterised by its simple formula:
N3 = N1 + N2

This indicates that (after the two starting numbers), each additional number in the sequence is the sum of the two preceding numbers. For example, the Fibonacci sequence begins 1, 1, 2, 3, 5, 8, 13, and 21. Looking at the start of the sequence:
N1 = 1, N2 = 1, and therefore N3 = 2
N1 = 1, N2 = 2, and therefore N3 = 3
N1 = 2, N2 = 3, and therefore N3 = 5
N1 = 3, N2 = 5, and therefore N3 = 8 
This is all terrible 'advice', and no magic bullet. If your draw selections aren't going to be profitable to level stakes, then the fanciest staking plan in the world isn't going to help you. And even the best of draw selection systems is going to hit long losing runs, it goes with the territory, and what the author is doing suggesting that the odds on a draw are possibly going to be below 2.618 is beyond me. It happens, but only in highly unusual circumstances - think end of season Italian games.

As an example of the length of possible losing runs when backing draws, the XX Extended Draws are in profit this season after 204 bets by 22.3 points (to level stakes) but in there was a sequence of 21 consecutive losses. Aggressively increasing your stakes after a loss is not going to work. Who would have staked £17,711 on that 22nd selection of Getafe v Sevilla at 3.5?

I also take issue with the statement that betting on draws is not glamorous. Is it a coincidence that eight of the  top ten in the FTL are draw related? What does 'glamorous' even mean in a betting context? For me, the glamour is the money in my balance, and if the draw is overlooked by others, well that can only help.

Updates on the FTL once the Monday schedule is complete.


RIchard said...

martingale by another name isn't it? i've always felt that the reverse martingale type plans are best, or at least more fun, for sports betting ie increase stakes on a winner, reduce stakes on a loser. though clearly it depends on what sport and the winner/loser ratio.

WhyAlwaysMe said...

Backing draws is quite a limited strategy in my opinion. I believe the common argumnet put forward is that the draw can be 'value' because it is not a popular bet. However this conveininetly ignores effieient market theory - on Betfair the odds are generally accepted to represent a 'true' price in liquid markets. In other words if the draw gets too big the big pro players will come in and take up the slack. So the draw can be unpopular among small bettors but also well supported in the market.

But I have another reason for not being keen on the draw, which is the limited upside. If you look at historical odds the draw is always going to conform to a narrow range, there will always be a ceiling. For the vast majority of games the range will be between 20% and 32% for the draw, so however good you are you are always playing in this narrow band. About the best you can hope for is an advantage of 2 or 3% realistically and that's if you get everything right.

If you are on a winner system it is possible to identify winners prices at 33% that are close to 50%. The margin of safety is much bigger on the win because you are operating in a much bigger band than with the draw.

I hope I am getting the point over - if you are playing the draw you do have to be super accurate because the bands are so narrow.

Don't get me wrong - beating the market by 2 or 3% is very decent if your model is that accurate. But personally I prefer a bigger margin of safety than that which is why I would always look to the winner markets on football betting.

James said...

I shudder when I see the word Fib-onacci. It goes completely against the Capital Growth Model.

You should never increase your stake after a loss, only after a win, simply because you have more money and can risk a larger sum.