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In computer networking, the contention ratio is the ratio of the potential maximum demand to the actual bandwidth. The higher the contention ratio, the greater the number of users that may be trying to use the actual bandwidth at any one time and, therefore, the lower the effective bandwidth offered, especially at peak times.
A contended service is a service which offers (or attempts to offer) the users of the network a minimum statistically guaranteed contention ratio, while typically offering peaks of usage of up to the maximum bandwidth supplied to the user. Contended services are usually much cheaper to provide than uncontended services, although they only reduce the backbone traffic costs for the users, and do not reduce the costs of providing and maintaining equipment for connecting to the network.
The "contention ratio" is the maximum number of other people you will have to share the connection infrastructure with. So a contention ratio of 50:1 would mean that the maximum number of people you could be sharing the connection with at anytime is 49 other people. If all 50 people were downloading at the same time then your download speed could drop hugely, in reality though this doesn't happen and you can enjoy much faster download speeds.
Specific examples by country 
In the UK, an RADSL (Rate Adaptive Digital Subscriber Line) connection used to be marketed with a contention ratio between 20:1 and 50:1 within the BT network, meaning that 20 to 50 subscribers, each assigned or sold a bandwidth of "up to" 8 Mbit/s for instance, may be sharing 8 Mbit/s of uplink bandwidth. With the advent of ADSL2+ ("up to" 20Mbit/s service), FTTC (Fibre to the Cabinet) offering 40Mbit/s services and even FTTP (Fibre to the Premises) offering 100Mbit/s, BT no longer work on "contention ratio" as a planning rule.
In the US and on satellite internet connections, the contention ratio is often higher, and other formulas are used, such as counting only those users who are actually online at a particular time. It is also less often divulged by ISPs than it is in the UK. The connection speed for each user will therefore differ depending on the number of computers using the uplink connection at the same time because the uplink (where all the low bandwidth connections join) will only handle the speed that has been implemented on that line.
One of the issues with a stated contention ratio is that it is not, on its own, adequate for comparing services. There is a huge difference between 1000 users each on a 2Mbit/s service sharing a 40Mbit/s pipe, and 50 users each on a 2Mbit/s service sharing a 2Mbit/s pipe. In the latter case two users trying to download at the same time means each get 50% of the speed. When there are a 1000 users it would take 20 users maxing out their 2Mbit/s link at the same time to show any congestion. However both of these would be quoted as 50:1 contention.
Contention ratios are essentially just planning rules which are used to design a network offering (typically) an Internet service. The perception of the quality of that service will depend on the actual usage of the users of the service. This is partly why rules such as 20:1 for business and 50:1 for residential users came about. The actual usage demands of users have changed over the years and for evening/weekend traffic residential users can be demanding a lot of bandwidth making 50:1 contention ratios inappropriate. Contention ratios also only really make sense if dealing with relatively consistent speeds. The fact a single back-haul in the UK could have users at 500kbit/s and users at 100Mbit/s makes normal contention ratio planning a thing of the past. In practice, a well run network aims to avoid links hitting limits, and upgrades the links when they do - this only works where the pricing model allows extra revenue to pay for the higher usage links and this is hitting some "unlimited use" tariffing models.