Is it safer to leave a bike somewhere where there are a lot of people like Walmart parking lot or somewhere with less people like at a park?
Locked in both cases but which case is more likely to get stolen?
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The question is about crowds of people, but I'll answer from another perspective, dealing with crowds of bikes. I'd say you're better off locking your bike up in a location that has many other bikes nearby, rather than locking up in a location where your bike is the only one. First of all, crowded bike stands tend to be where lots of people are, so you get some protection from the crowd itself. The location is also obviously popular with other bike riders, so the incidence of someone who'd actually notice something amiss at the bike stand is likely higher. Finally, you typically get protection from the other bikes as well - no lock is impenetrable to a determined thief, but so long as your lock is better than the one on the bike next to yours, you'll be a less attractive target for theft. A crowded bike rack presents options for a thief, so as long as you're not the lowest hanging fruit with a poorly secured, expensive bike, you'll be a less likely target.
A well locked bike is relatively safer in a crowded place.
According to markelinsurance.com in "Bicycle Theft in the U.S."
In the section "6 easy ways to help prevent bicycle theft"
- Lock it in a high-traffic area. Cyclists shouldn’t just look for a well-lit area to secure their bike. Ideally, a bike should be locked in an area with a constant flow of people walking by so a person attempting to steal a bike would be noticed quickly.
Number 4 must go with the first three which are:
If a thief acts like the owner of an unlocked bike a crowd won't keep the bike safe. Sawing through a good lock on an appropriately locked bike will attract more attention than an appropriately locked bike in isolation.
In a remote area, you'll give more opportunity to a thief to make their work unnoticed.
In a crowded area, it depends on how you secure your bike. If it's a bad lock, it can be defeated quite quickly and discretely by an experienced thief. If it's a good lock (and you attach the key components of the bike), maybe you'll deter unequipped thieves, but some thieves won't care about being noticed: they count on the fact they can do their work faster than the arrival time of law enforcement, assuming that someone will call.
So I would say, it less unsafe to leave a bike in a crowded place but it shouldn't be considered safe. That's about theft risk. In less crowded areas, the vandalism risk is much higher.
The key aspect for me to evaluate the risk of a bike being stolen is rather: is it worth the effort for a thief? A fancy bike in front of a Walmart might be worth the risk while a crappy bike in a park might not interest anyone, except those who will 'borrow' the bike for a journey (those are more likely to be discouraged by a good lock).
You give a lot of credit to random people in crowded places to notice unusual things. Often times bike racks (if they're actually provided) are out of the way and won't be noticed by the average Joe coming or going.
Your best hope is that that bike rack is in a place covered by the security cameras and you can convince the management to show the video to the cops so they can identify who took the bike.
From personal experience, passers by don't provide any protection. My son (and his friends) went out for the day drinking at various pubs along the river. At the last stop they locked several bikes to the railings with one cable lock that the owner didn't realise he no longer had a key for having dropped it in the river when he rode in to the river earlier in the day. I came along with tools and smashed the lock apart... by the side of a busy footpath and right outside a busy pub and 200M from the main city police station, mid afternoon on a Saturday. And no one even paid attention to a few minutes of vandalism while breaking the lock apart.
Your best bet is lock the bike up in an area with lots of bikes. Use a better bike lock than everyone else. Make your bike look worse than everyone else's. Put a grubby carrier bag over the seat, if you can bear it get the frame dirty (mud is good) and get the brightwork un-bright.