I’m pretty much a fish at sports betting. I enjoy dabbling in it a little, and end up coming out a little bit ahead by taking advantage of free bets and similar promotions, but I don’t follow many sports closely enough to beat the juice on my own. So, when this year’s Women’s World Cup rolled around, I decided to try something a little bit different.

Nate Silver’s “data journalism” site FiveThirtyEight has been one of my favorite things on the Internet since it kicked into high gear following its acquisition by ESPN last year. In a world where numbers in the media – and probabilities in particular – are often twisted and abused by the dishonest and the mathematically-challenged, it’s great that there’s at least one outlet dedicated to presenting statistics in a way which is both accessible and accurate.

So, when I saw that FiveThirtyEight was offering statistical predictions for the Women’s World Cup, I decided that I would put their model up against the wisdom of the crowds by comparing their numbers with the lines being offered on Bet365.com. Anywhere the odds of a given result as predicted by FiveThirtyEight exceeded the odds being laid on Bet365, I would put a few dollars down. Here’s what I learned in the process.

Math: it works!

The most evident and most important observation was that, from early on, it seemed apparent that FiveThirtyEight’s model was actually really good. A few bets that were longshots on paper came through for me, and it didn’t take too long for me to feel confident that I was going to turn a profit on the tournament. Of course, a single soccer tournament is still a fairly small sample size, so it’s possible that both Nate and I were lucky this time around.

Still, I came out about $100 in the black over the course of a few dozen bets, most of them for $5 or less, making for a pretty solid ROI. While I can’t say for sure that FiveThirtyEight’s model would turn a profit in the long term, it performed well enough that I’ll probably repeat the experiment for a little more money the next time around.

Moreover, the bets that I ended up making based on the model followed some noticeable patterns. There were a few teams that seemed consistently underrated, including the USA who, of course, went on to win. More interestingly, however, there were a couple of more general trends I picked up on; these have helped to convince me that the model was actually pointing out a weakness in people’s overall betting habits, not just getting lucky. It’s also made me eager to try out a similar betting strategy in future events where I don’t have a model telling me who to bet for.

Underdogs in the group stage, favorites in elimination

During the group stage, the overall pattern was that the odds being laid by Bet365 were fairly consistently overestimating the favorite and underestimating the underdog relative to what FiveThirtyEight was predicting. Therefore, I found myself making a lot of bets either on draws, or on upset wins for the lower-ranked teams. The odds being offered during this stage were often substantially different from FiveThirtyEight’s predictions as well; a team given 22% (3.5-1) odds to win by FiveThirtyEight might have been paying as much as 4.5-1, for instance.

Once the group stage was over, however, the trend reversed itself. There were, first of all, far fewer matchups where FiveThirtyEight’s predictions didn’t match the betting line, and those differences were smaller. When there was a difference, however, it was almost always the case that FiveThirtyEight’s model was telling me to bet on the favorites, who seemed now to be underrated, while the betting lines on the underdogs were too optimistic.

If you think about it, there’s a fairly obvious psychological explanation for why this might be the case. Many bettors probably don’t follow international women’s soccer very much outside of the World Cup, so a lot of bets on group stage matches would likely be getting placed based on teams’ positions in the world rankings rather than personal observations of their skill. The problem with betting based on standings, however, is the statistical principle of “regression toward the mean.”

In a nutshell, regression toward the mean occurs any time you have a system with results which depend on a mixture of fixed and random factors (skill and luck, in other words). Particularly good and particularly poor performances tend to result from a combination of the two; thus, the best-ranked teams will tend to perform a little worse in the future than they have to date, and the worst-ranked teams a little better, because the luck component of their performance so far can not be expected to hold. In effect, there is a sort of invisible “pull” towards the middle of the rankings as variance evens itself out in the long term. If unsophisticated bettors are not taking that regression into account, then you have the situation that the top teams’ chances are being overrated and the worst-rated teams may not be getting enough credit.

By contrast, once we reach the elimination stage, the formerly lowest-rated teams who have made it through must necessarily be running hot: otherwise, they wouldn’t have survived the group stage. These teams haven’t necessarily improved any, but bettors who have been following the tournament so far will have recently seen them doing better than expected. Of course, the top-rated teams are also coming off wins, but since those wins were expected, they won’t skew people’s appraisal of those teams as much as the upsets enjoyed by the underdogs.

Thus, the same people who were underestimating, say, Cameroon in the group stage because of their poor position in the world rankings (currently 53rd, following the World Cup), might then overestimate them in the elimination stage, having just seen them clobbering Ecuador (6-0), beating Switzerland (2-1) and putting up a good fight against eventual finalist Japan (1-2). This is a trend you might expect to see repeated in other tournaments and playoffs as well, with the smart money being on the underdogs early on, but on the favorites towards the end, especially when the number of data points for any particular matchup is highly limited, as it is in international soccer.

Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.