When you log a workout, it gets translated into the 4 categories. This translation occurs via a simple "weighting algorithm", which says "for every 10 minutes logged of exercise X, a user receives Y minutes of cardio, Z sets of Strength and B Variety points". Not all exercises have the same weighting. For example, 10 minutes of golf would give you far less cardio than 10 minutes of spin class. Over the course of the week, your 4 category stats are combined with those of your partner. You can see this total in the "Your Matchup" page.

At the end of the week, your team's totals for each category is compared to your opponents' totals. The team that wins the most categories, wins the week's matchup. It is important to note though, that Days, Strength and Cardio are worth twice as much as Variety. 
Take the following example:

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Here, you can see that Team B won the competition because their three category wins combine for 5 points, while Team A won only 1 category and therefore got 2 points.

A note on "Variety"... Variety is individual. So, if you do yoga and your partner also does yoga, your team still gets 2 Variety points. You are not penalized for having overlap with your partner.