Yes, size does matter, at least when it comes to Canada’s collective cup collecting contest, and we have a lot of cups to prove it.
Many have asked whether there’s a conspiracy with the prize distribution in Tim Hortons' Roll Up The Rim To Win contest. Earlier this week, The Huffington Post Canada released its unscientific findings that the odds favour those who buy bigger cup sizes, based on the 92 drinks we consumed over a week. The experiment sparked a lot of discussion and follow up by some of our fellow media outlets (see here and here and here).
But, as we noted in our survey, we had an admittedly small sample size — 92 coffees consumed mostly by staff in our Toronto office. So we asked for your input.
In total, 1,182 Tim Hortons customers responded to our national “roll call” to take tally of your results, accounting for 19,349 beverages. To gauge the win-loss ratio, we asked readers to tally the results of their last 10 drinks per cup size. We also asked readers to give us their overall win-loss numbers for 2013.
The national results (story continues below slideshow):
The larger the size, the more likely the odds of winning. Large coffees saw a win rate of 19.3 per cent, followed by extra large at 18.3 per cent and medium at 17.9 per cent. All are better than the one-in-six odds that Tim Horton’s lists as the official odds of winning a food prize. Small coffees — and there were more than 3,000 of these counted by our readers — came in with a win rate of 13.4 per cent.
Tim Hortons prints in its cups that there is a one-in-six chance of winning a food prize, or 16.6 per cent.
“I buy at least 3 times a day, only win on bigger cups,” said Mike Reed of Manitoba. “No one I know has won anything but coffee.”
Regional odds were interesting to note. In British Columbia, readers reported a 20.6 per cent win rate with large drinks and 12 per cent for smalls, while in Ontario, large coffees saw a 19.6 per cent win rate for large, 17.7 per cent for extra large and 13.2 per cent for small.
The national results are also unscientific, but an interesting addition to the hot debate about RUTR odds. Readers from all provinces reported to us, although our sample size came mostly from Ontario (54%), Alberta (12%) and British Columbia (11%).
In our original story, when asked about whether cup size changes the odds, Alexandra Cygal, senior manager of public affairs for Tim Hortons, gave a categorical "no."
The "conspiracy theorists are wrong," she said in an email. "Our prizes are distributed randomly across all eligible cup sizes so large cups don’t necessarily mean better odds."
By the way, if you think odds of one-in-six mean you’re due a prize after buying six drinks, a crash course in probability theory is warranted.
As Wai Kong (John) Yuen, a math professor at Ontario's Brock University told us earlier, "it only means that in the long run, if you buy a large number of coffees, say 600 cups, you are expected to win around 100 times. However, anything can happen if you only buy six."
Think of what happens when you roll dice. There's a one-in-six chance the die will turn up a six. The odds essentially "reset" on the next roll. Says Vadim Kaimanovich, the Canada Research Chair in Analysis and Probability at University of Ottawa, "The result doesn’t depend on what happened before or what happens after."
Readers who participated in our national “roll call” had lots to say about the contest:
- “My whole office went all month and nobody won a single prize. It's a scam!” — @mademediainc, Quebec
- “I won more free coffees in Kandahar on my 2nd tour then I ever do back in Canada.” — @DocVerrall, Alberta
- The binomial probability of having a record as crappy as mine is exactly 3.05% — @maxmoore306, Alberta
- Conspiracy? Been playing the game since inception, never ever won more than a free coffee or donut. Better than nothing? You decide. :) — @CalvinSwine905, Ontario
Share your Roll Up The Rim experiences in our comments section.
Summary of National and Regional Win Rates:
Note: 1 in six odd is 16.6%
Win percentage: 13.90%
Small win rate: 13.39%
Medium win rate: 17.89%
Large win rate : 19.30%
Extra Large win rate: 18.27%
Win percentage: 13.53%
Win percentage: 13.55%
Win percentage: 15.12%
Win percentage: 12.79%
Win percentage: 14.23%
Win percentage: 12.8%
Win percentage: 10.30%
Win percentage: 18.02%
Newfoundland and Labrador
Win percentage: 17.09%
Win percentage: 11.76%
Win percentage: 18.75%
Win percentage: 13.96%