This is the first post in my Amazing Race Domination series. The other posts in the series are:
- Who Dominated Amazing Race 29? A Computational Approach
- Do Underdog Teams Always Win the Amazing Race?
- Number-Crunching Amazing Race Seasons 1-29: Who is the Most Dominant Team?
- Predicting the Amazing Race Winner with Random Forests
Amazing Race: Singles Edition
The 29th season of Amazing Race definitely shook up the well-worn formula with the strangers twist. Pairings were determined before the first leg, resulting in a lot of drama for some (Brooke and Scott, Mike and Liz) and great synergy for other (Tara and Joey, London and Logan). The pairings couldn’t have been arranged any better, and overall, season 29 was very entertaining.
Brooke and Scott were definitely unexpected winners. Coming into the finale, the strongest team was Tara and Joey, and it seemed as if they had the competition already wrapped up. In fact, Brooke and Scott’s first win was the leg prior to the finale, whereas Tara and Joey had three legs won, most out of any teams in the season. Brooke and Scott obviously didn’t dominate the race – but you have to keep in mind that you only need to get first on the last leg to actually win. The third-place finishers London and Logan were almost always lagging behind the other teams, though out of the 11 teams they’re probably the most synergized.
A question I want to answer is, which team actually dominated Season 29? In other words, who performed the best if we consider performance in all the legs of the race? Some might say Tara and Joey, since they won the most number of legs. Matt and Redmond also present a strong case, coming in second a lot of times. Team Fun, Becca and Lloyd, is also in the running. In order to dominate the race, a team must have performed well in all of the legs, not just the final one. To quantify domination, I introduce a very simple index, the aptly-named domination index.
Intuitively, the domination index should be an average of the placement of a team in every leg that they participated in. However, to be able to compute the average fairly, the placements in each leg must be in similar scales. Consider legs 1 and 6. On leg 1, there were still 11 teams in the running, so the placements range from 1 to 11. On leg 6, only seven teams remained, so the placements go from 1 to 7. As a specific example, remember that Brooke and Scott placed 4 out of 11 on leg 1 and 5 out of 6 on leg 7. It seems wrong to add 4 and 5 directly since the two legs had different numbers of teams still participating. So how can we put the placements in similar scales?
We can do this by linearly scaling a team’s placement on leg j to the corresponding performance index, which lies between 0 and 1, via
Intuitively, we can think of the performance index of a team in a leg as the fraction of the other teams which placed lower in the particular leg. A team with a performance index of 0 is the last team (i.e. 0% of other teams placed lower). A team with a performance index of 1 is the first placer (i.e. 100% of other teams placed lower). In general, a team with a performance index of x on leg j means 100x% of other teams placed lower on leg j.
Now that the placements of the different legs are comparable, we can now talk about averaging the placements.
We can now define the domination index as a rolling average of the performance index across the different legs. That is, for a specific team, we compute the domination index on leg j as
Intuitively, a team’s domination index on leg j is a measure of the team’s performance from leg 1 up to leg j. If, for example, a team had a domination index of 0.4 on leg 6, then it means that, on average, 40% of the team’s competitors placed lower than the team on legs 1 to 6.
Since the domination index is a function of the leg, we can explore its time dynamics for each team in the race.
As we can see here, Kevin and Jenn (the surfer and the model, respectively) only have domination index on leg 1 since they were the first ones out. Obviously, it’s 0 because they placed last. On the other end of the spectrum, only Brooke and Scott, Tara and Joey, and London and Logan have domination indices from legs 1 to 12, since they’re the only teams that actually completed the race.
Seth and Olive started out so high, with a domination index of 1, then sizzled out at leg 3 wherein they were U-turned by Tara and Joey. Liz and Michael and Vanck and Ashton have downward parabolic trends, starting out quite rocky, then finding their footing, and then eventually doing badly again. It’s important to note that all three teams I mentioned here got U-turned. This hints that doing great in the first few legs isn’t a particularly good strategy since it puts a target on your back.
Matt and Redmond and London and Logan display flat domination dynamics. The first team is a steady 0.7-0.8, while the latter is a steady 0.3. The ironic thing is that London and Logan were the ones that got to the finale, even if they performed quite poorly throughout the race. It just proves that you don’t have to be a dominating force in the race to get to the end – you just have to make sure that someone is behind you at all times.
Interestingly, only Brooke and Scott display an upward parabolic trend – starting out really well, doing not so well in the mid-race, then finishing out with a bang. The dynamics in their domination index sets up a good winner’s story.
And with that, let’s do a ranking of the teams according to their final domination index.
Ranking the Teams
With a large margin, Matt and Redmond dominated the race. They have a final domination score well above 0.7, which means that they placed above >70% of team throughout the race. Becca and Floyd and Tara and Joey are second and third, with the first team edging the second by a very, very small margin.
Seth and Olive appear quite high, which is interesting since they were eliminated third in the race. They placed really high on the first two legs, but got U-turned on the third which led to their elimination. This just proves that Seth and Olive are really strong racers, and a definite threat to win if they weren’t targeted early on.
Winners Brooke and Scott are at fifth place while the third-placers London and Logan are fourth from the bottom, which again prove that you don’t have to dominate the race to get to the end. It’s important to point out that these two teams were in an alliance throughout the race.
The domination analysis I performed is very simple and can be used to describe the racing skill of teams in a definite manner. If you’re interested to see the Python code I wrote to analyze the data, check out my Github. I used a bit of Beautiful Soup to extract team placements from wikipedia and pandas to wrange the data.
In the next article, I’m going to apply the domination index to see which winner and/or finalist dominated the most across the 29 seasons of the show.