I use Google Maps and Waze a lot on my phone, and they show completely different routes to get to the same place. One day driving to work, one map says it's 35 minutes and the other says 45. What's the math behind this? Are they using different algorithms or is it just a traffic thing?
It's more complicated than just a traffic difference, but it's not really that mysterious either. The two apps do use different algorithms to calculate routes, yeah, but the real issue is that each one has different data about how traffic is flowing at that moment. Waze, for example, collects information from users who are using the app - like, you're sending to the server how many kilometers per hour you're going, if there's congestion ahead, accidents, speed traps. Google Maps does something similar, but it also uses massive historical data about traffic flow and information from mobile carriers.
Beyond that, each one prioritized different things in their algorithm. Waze tends to suggest routes that avoid congestion even if they're longer or go through smaller streets - like that more creative route you wouldn't have thought of. Google Maps is generally more conservative, trying to balance time with the most direct route. And there's another detail: they update their data at different rates too. If you're in a place where traffic changes really fast, one might have more up-to-date information than the other at that exact moment.
That's why you saw that 10-minute difference. It's not a mistake, it's that one was seeing the traffic situation differently than the other. On a day when traffic is predictable, the two usually give pretty similar numbers anyway.
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