We actually switched server hosts due in part to issues like those you describe. On our old host, their "solution" to DDoSing was to "null-route" our IPs, meaning any traffic directed to our game servers, website, VOIP server, etc. would be directed to nothing for 8 hours. As you can imagine, being DDoS'd was absolutely devastating to us.
We pay a relatively high amount of money for the dedicated servers we use now, but it's absolutely worth it. Many of the events listed in the picture above weren't even noticeable to us. For those that were, it was usually no more than a minute or two of slowness before the automated system fixed it. I had my friend go into detail in this comment about how exactly they handle DDoS mitigation.
That's awesome! It's a really good feeling when you find a reliable ISP. Not having to deal with these issues is why you pay them for the service.
A null-route is not a goddamn solution grumble grumble. Excellent info from your friend. I definitely learnt something today!