Fag Packet Calculations

Following on from my post on how to calculate the score probabilities using Poisson, it is my intention (at some point) to go through and describe a detailed method of how to calculate each team's attack and defence ratings, and the home advantage.

Unfortunately I'm quite a lazy person, so I wouldn't hold your breath for too long. I will get around to it (I'm sure) but at this stage I just couldn't tell you when.

Anway, when I do finally get round to it, I will attempt to show you how to calculate the following:

• Home attack ability
• Home defence ability
• Home advantage
• Away attack ability
• Away defence ability.

With these elements calculated, we can then derive the home team goal expectancy as:

    µhome = A1 x D2 x H
    (where A1=Home attack ability, D2=Away defence ability and H=Home advantage)

and the away expectancy as:

    µaway = A2 x D1
    (where A2=Away attack ability and D1=Home defence. Note there is no home advantage for the away side!)

... But, as I say, this is all quite an undertaking and, quite frankly, I can't be arsed at the moment. I did, however, come across something on my laptop that I must have copied quite some time ago. It's from The Times Fink Tank (I believe I offered this as a good link some time ago), and in this short article some "fag packet calculations" are provided to help the feckless arrive at attack and defence ability figures, along with a home advantage figure. These can then be used in a Poisson calculation.

In all honesty, I have absolutely no idea how accurate or inaccurate these rather broad brushstroke calculations are (although I'd be surprised if they do work well), but I thought that, for those who cannot wait for me to get off my backside and show how I do it, or for those that may find the full answer a bit too difficult, then this "dummed-down" version might just be the ticket.

So please note, this is not mine. It is from the Times Online (although I cannot tell you when). I haven't asked permission to reproduce this here, so if they complain I will have to take it down. In the meantime, here it is:

I am going to use tomorrow’s big FA Cup fourth-round tie — Liverpool v Everton — as an example.

First, you need to understand home advantage. A study of 3,257 games suggests that the average team away from home against average opponents score 1.1 goals, while at home they score 1.49 goals. This produces a critical number for the DIY Fink Tank. If you divide 1.49 by 1.1, you get 1.36. For every goal you think your team would score away from home, they would score 1.36 at home.

Right. Next step. And for this you just need the league table. You are going to calculate how many goals your team score and concede per game at home and away, and how many your opponents score and concede per game. This allows us to get ratings for both sides in attack and defence.

Let’s say you are a Liverpool fan. At home in 2007-08 and 2008-09 the team have scored 60 goals in 30 matches — an average of two per game. We want comparable ratings for both sides, so for the moment we are going to pretend that both sides are away from home. So divide that two goals per game by 1.36. You get 1.47. Jot it down.

Now look at Liverpool’s away goals. They have scored an average of 1.43 goals. Taken together with the home average of 1.47 goals that means Liverpool score an average of 1.45 per game. That is their attack rating. You can do the same for Everton. Their attack rating is 1.21.

Repeat the exercise for defence. The only thing you need to remember here is what to do about home advantage. Don’t forget that when Liverpool concede goals away from home it is the other team who had the home advantage. So the goals scored against Liverpool when they are away need to be divided by 1.36. For defence, then, we get a rating of 0.6 for Liverpool and 0.86 for Everton.

What now? For Liverpool multiply 1.36 by Liverpool’s attack rating (1.45) and Everton’s defence rating (0.86). You get an expected number of Liverpool goals of 1.7. For Everton multiply their attack rating (1.21) by Liverpool’s defence (0.6). You get 0.73. So 1.7 plays 0.73, an average scoring game with Liverpool in the driving seat, essentially expected to win by a goal.

Home Team
Attack: HGF = 2.00 / 1.36 == 1.47 + AGF = 1.43 (avg == 1.45)
Defence: HGA = 0.65 + AGA = 0.88 / 1.36 == 0.64 (avg == 0.64)

Away Team
Attack: HGF = 1.85 / 1.36 == 1.36 + AGF = 1.21 (avg == 1.28)
Defence: HGA = 0.95 + AGA = 1.12 / 1.36 == 0.82 (avg == 0.88)

Home attack X Away Defence (1.45 * 0.88 ) == 1.27
Away attack X Home Defect (1.28 * 0.64)    ==  0.81

Goal difference is 0.46. Therefore (48.16% probability for Liverpool win)

If you had a computer and a spreadsheet you could now use something called the Poisson distribution to get the probability of a Liverpool victory. The graphic shows how probable different scores are and it follows this common distribution.

But you are in the pub, so maybe it is difficult to work an Excel sheet and perhaps you don’t know what the Poisson distribution is anyway.

Here is the quick cheat method. Liverpool’s expected goal difference is 0.97. Multiply this by 21 and then add 38.5. You can do this (expected goal difference times 21 plus 38.5) for almost any side to get the probability of victory. It gives you a 59 per cent chance of a Liverpool victory. Not a bad estimation at all.

There you have it. The Fink Tank on the back of an envelope.

_________________________________________________________________________

Traded the Morocco v Tunisia match (much more entertaining than most of the pundits had forecast) and also the Southampton v Leicester match. Bit annoyed with myself on this last match as I could see how well Leicester had started the match, but I was hesitant in doing anything about it and then Leicester scored. If I hadn't prevaricated, I would have made a really healthy profit. Still, the evening was okay, so I suppose I should be thankful for that.

Football: £54.54 | Tote: |  Total P&L:  £54.54 

 

Football Showing 1 - 3 of 3 markets

Market Start time Settled date Profit/loss (£)
Football / Southampton v Leicester : Over/Under 2.5 goals 23-Jan-12 19:45  23-Jan-12 21:45  19.34
Football / Morocco v Tunisia : Correct Score 23-Jan-12 19:00  23-Jan-12 20:57  29.82
Football / Morocco v Tunisia : Over/Under 2.5 goals 23-Jan-12 19:00  23-Jan-12 20:45  5.38