Your battle appears in the lobby. Nobody can connect to it. That used to mean an evening with your router's admin page. Now it mostly doesn't.
The fix: leave the relay on
Hosting from your own machine means other players connect to you, and most home routers won't let them in. Coilbox now checks this for you. On the Host a battle panel, look at Game port: if it says your port isn't open, players outside your network can't reach you directly.
That's what Server relay is for. Leave it on Automatic and, when your port isn't reachable, the battle is routed through the lobby server's relay instead. Players connect to the relay, the relay passes traffic to you, and nobody touches a router. If your port is open, Automatic hosts directly and the relay stays out of the way. The panel shows your latency to the relay, and the line at the bottom tells you which route this battle will take before you click Host.
One thing to do first: under Windows Firewall, click Allow them through the firewall. Otherwise Windows asks while your game is starting, which is the worst possible moment.
If you'd rather host directly
Enable UPnP or NAT-PMP on your router, or forward UDP port 8452 to the local IP address of the hosting computer. The Game port section shows the exact port and address to use, and the port can be changed if 8452 is taken. Forwarding is done in your router's admin interface, not in the game.
Or don't host at all
There are official SPADS autohosts — permanently-running servers that host battles for you. Join one, set up your game through its commands, play. It's what most players use anyway.
While we're here
If a multiplayer game desyncs or crashes, check first that everyone is on the same version — Coilbox handles this automatically, manual installs may not. If the versions match, please report it on GitHub with two attachments: your infolog.txt from your Recoil data directory, and the replay file for the match. Those two together are usually enough to find the cause. A report without them generally isn't actionable, however detailed the description.