This is the third consecutive year I’ve spent the Independence Day Holiday Weekend with a group of CFA students/friends in Las Vegas. The acronym CFA stands for Chartered Financial Analyst. You may not have heard of the program. But there’s an extremely good chance that the men and women in charge of managing your pension plans have this designation. It’s become the Gold Standard in the business – and I’m fortunate enough to work with the University of Toronto School of Continuing Studies and help some of our city’s best and brightest climb the CFA mountain.
The CFA Program is about refining the qualitative and perhaps even more importantly, the quantitative skills of those already in the financial services industry in order to make them better. Part of the core training is teaching candidates how to value investment products in order to “buy low, sell high.” And I’ve always believed that many of these skills are transferable. That is, much of what I teach in the CFA Program can be applied to sports gambling – I’ve been testing this thesis with reasonable success over the past several years.
One of the wagers you can make at this time of the year, with the NFL season still two months away, is the number of total wins that each team will achieve. I was particularly intrigued by what was showing with respect to the Pittsburgh Steelers. Last year, they had an 8 – 8 record. There were two different sports books, one at Treasure Island, the other at the Wynn, that showed the following lines:
I’ll explain – in next week’s column – exactly what these “quotes” means. But first I wanted to do some number-crunching to determine the most probable number of wins that Pittsburgh would achieve in 2013.
My thesis is that Pittsburgh would be lucky to be as good in the coming year as it was last season. Losing Mike Wallace means that their offense will not be as explosive. Losing James Harrison means that the defence will not be as intimidating. Their two best players, Ben Roethlisberger and Troy Polamalu are injury prone and getting older. My gut told me… very strongly… to take the under. But first some number-crunching: In the world of investing, it’s always better to look before you leap!
In the past 10 years, 56.6% of the time teams have won eight games or fewer. So the “naïve” model would suggest it is more rather than less likely Pittsburgh wins fewer than 9 times in 2013. But there’s something even more interesting. In the past ten years, forty teams have won exactly 8 games – so it’s a statistically significant sample size. I tracked how many games those 8 wins teams won the following year. 73% of the time it was nine or fewer.
Then what’s going on? Why is the line 9 or 9.5? I believe it’s because the betting public is exhibiting one of the classic behavioural biases that distort good decision-making. It’s called “anchoring and adjustment”. Bettors are looking back at the past six years where 4 out of 6 times the Steelers won 10 games or more. Only one problem: Markets are (or should be) forward-looking.
Right then, I knew I was going to bet
the under. The only question was: At Treasure Island – or the Wynn? (To be continued…)
(Last week, I argued that the Pittsburgh Steelers are far more likely to win fewer games this year than they did in 2012. The question was: If I were to make a wager, which sports book would provide the best pay-off!)
I’m going to repeat the betting lines that were posted at two Las Vegas casinos the July 4th Independence Day Weekend:
This is how to read the Treasure Island line. If you put down/invest $7 and Pittsburgh wins 8 games or fewer, you win $7.35. (Essentially, you multiply 7 x 1.05.) If Pittsburgh wins exactly 9 games, you get your $7 back. But if Pittsburgh wins 10 games or more, the casino keeps your money. The Wynn proposition is simpler: 10 wins or more means you lose. 9 wins or fewer means you win. But at Wynn, if you wager $7, you only stand to win $5. (Essentially, you divide 7 by 1.4.) But how to decide between the two?
The framework espoused by CFA Institute can help. It’s called “expected return” – and to ground my decision in factual analysis, I went back over the past ten years to determine the “naïve” probability that any team will win a given number of games. This is represented by the Historical Column. The Adjusted Column allows me to superimpose my beliefs about this football team – not unlike the latitude the Black-Litterman allows an analyst in constructing the efficient frontier.
|Number of wins||Historical Percent||Adjusted Percent|
|0 – 4||15%||10%|
|5 – 6||18%||16%|
|13 – 16||8%||6%|
See the adjustments? I think it is very unlikely that Pittsburgh will be terrible (0 – 4 wins) or outstanding (13 – 16 wins.) When I look at their schedule, it seems most likely that they’ll go either 2 – 4 or 3 – 3 inside their division. Then I’m projecting 5 – 5 outside it, which would get them either to 7 – 9 or 8 – 8… and in either case, you’d win your bet at either casino. However, I also see it slightly more likely than the historical norm that they’ll win 9… which would mean a push at Treasure Island, even though you’re still winning at Wynn.
Okay. So we could flip a coin. Or we could simply multiply out the probability of each event by its payout, to determine which is better. We’d solve in the following way, using the Treasure Island bet first: There’s a 62% chance Pittsburgh wins 8 games or fewer which means we would win $7.35. There’s a 10% chance we would neither win nor lose. There’s a 28% chance we would lose $7. So we set it up as follows: Expected Return = .62 x $7.35 – .28 x $7 = $2.60. The Wynn bet: Expected Return = .72 x $5 – .28 x $7 = $1.64 and it’s a no-brainer. You’re taking your money to Treasure Island, because if it works out, the holding period return is 37%!
Postscript: The Pittsburgh Steelers finished 2013 with an 8 – 8 record.