This advantage of knowing how your traffic is doing and where it is coming from also can also become a problem when you spend minutes and hours of day looking at your analytics details. At such a state the 1st instinct is to check the alexa or compete rank of any website that your come across. Most of social wannabe do it. At times pros also do it.
The point is – that it is OK to measure but it is counterproductive to spend time checking various metrics during every hour of your web time.
If you run a big business then you can outsource this task so that you can focus on building your business. If you run a large website then you can automate functions like getting a daily, weekly or monthly traffic report by email. If you are worried about the downtime then 1st step will be to invest in a good hosting and also use services like Pingdom and Sucuri.
If you run a social media agency then also spend time as and when required and use tools shared above but spend more time building your business then checking the details.
Think about checking various details (traffics, referrals, server logs etc.) may look like work but it does almost nothing to grow your business.
So avoid the death by metrics. When you do it, you will do a great deal for your work and also be at peace.