Fantasy Football – a classic Portfolio Optimisation problem
England out the World Cup, German colleagues, customers, collaborators (actually not just Germans, Americans, Scots,…) and so called friends all sending me mocking e-mails and texts.
“I hear OXO are making a new product. The packaging is white with a red cross and they're calling it the laughing stock.”
How could I channel my frustration? NAG Blog to the rescue.
In my last blog I promised to reflect on my early career at NAG which isn’t that long ago compared with some of colleagues.
My commute to the NAG office is longer than I’d like, but there is a positive side…
· Valuable thinking time
· Audio books - I recently enjoyed “No One Would Listen” by Harry Markopolos. The exclusive story of the Harry Markopolos–lead investigation into Bernie Madoff and his $65 billion Ponzi scheme.
Back to “thinking time,” on one commute into Oxford I’d been pondering the previous day’s internal training course. I was recalling my senior technical colleague’s wise words. That wise colleague was David (some of you will have met him). He had given an internal training course to the Sales and Marketing group. His presentation was a simple introduction to the topic of Optimisation and he had touched on modern portfolio theory even explaining the efficient frontier.
Some of you may be lucky enough to have heard this talk before….
Imagine an English ice cream manufacturer. He might run a very profitable business, but recognise that his business is very dependant on long sunny, dry summers. Wishing to diversify and minimise his risk he chooses to start another business thus protecting himself against a cold, rainy summer with an umbrella company.
Subsequently he went on to talk about stocks and shares and the benefits of diversification. This struck a chord with me. I learnt early on in my adult life the importance of diversification. Remember GEC that became Marconi. Where did Marconi go wrong? As a result of shares options I had a portfolio dominated by Marconi and consequently suffered a very large paper loss. Oh, why didn’t I meet David earlier? He went on to speak about how diversification can be achieved by holding a selection of stocks from a spread of geographic regions, industry sectors etc.
Of course this whole training course was aimed at helping us understand NAG’s Optimisation Routines . For those of you wishing to learn more about NAG’s optimisation routines you should refer to the NAG Library Manual and the appropriate chapter introduction.
Anyway, as I drove back into work that morning I had that light bulb moment. Fantasy football is like portfolio optimisation! Well, you can imagine how I sprinted into the office from the work car park eager to share my discovery with David.
Me: “Remember your lecture about optimisation and portfolio optimisation? Fantasy football is like this, isn’t it?”
David: “What is Fantasy Football?”
·You have a set of rules.
· You have a limited pot of money that you can spend to pick a squad of 15 football players.
·You then have to pick X Goal Keepers, Y defenders, …
· You can only pick Z players from any one team
· Players win points by
o Keeping a clean sheet
o Scoring a goal
oAssisting a goal
· Players lose points by
o Getting red or yellow cards.”
o Getting red or yellow cards.”
Pause for thought.
Me: “These are constraints aren’t they?”
Patronising nod from David
Me: “And this is an Integer problem, isn’t it?”
Laughter. David: “Well, at least you were listening last week. Now, go and get on with your work.”
Me: “No, you don’t get it. You’re going to help me program this up and we’ll see how the NAG Optimisers perform! I bet they won’t beat me. I’ve won the office fantasy football competition two years in a row. I would be interested to see how it performs though.”
Two or three days pass. I find a way of getting all the historic data from “The Official Fantasy Game Of The Premier League” into an Excel spreadsheet.
A week later I manage to persuade David to code up one of NAG’s optimisation routines to optimise my portfolio of football players. What does this mean? Well one is supplied with a list of players. Each player has a value and their previous season’s points total is listed. So one might choose a strategy which optimises a squad of 15 players based on a maximum spend of £100 million. A more risky approach might be to assume you will always have 11 fit players so you pick the 4 cheapest players and then look to maximise your return from an optimal 11.
Fortunately NAG supplies Visual Basic Declaration Statements and C Types with its DLLs. This makes these libraries easy to use for VB programmers who could easily code up one of NAG’s Optimisers to pick a Fantasy Football side. Yes, NAG’s Libraries are easy to link to Excel and we include a simple Portfolio Optimisation example on our website.
Let me explain this screen shot.
The two teams that were picked entirely by NAG’s Solvers were David’s “Too Hot” and Sven’s “Old NAG’s Best 15.”
· “Too Hot” was based on picking the four cheapest players (with the highest return) and then the “Optimised 11”
· “Old NAG’s Best 15” was based on optimising the entire 15 i.e. taking no account that only 11 players can be picked and used in each match.
In my next blog I’ll share with you how “Too Hot” and “Old NAG’s Best 15” finished the season.