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For the advanced timings data, you need to use Spigot: spigotmc.org.

To use the Timings parser, please type /timings paste in game, console or RCON. It will then give you a link to view it on this page.

The old Paste option has been removed for now as it is not needed.
Connection Handler (previously labeled Player Tick) is a wide wrapper of many things involving processing a players incoming data to the server. This value being high does not represent a bug itself in "Connection Handler", but usually will include timings data from plugins too.

If you are seeing high values here, it could mean you have more players online than your server can support. It is important to remember that Minecraft gets slower every version update, and while you may of been able to support this many players in the past, you might not be able to anymore.

If you are using the player-shuffle setting (has a value other than 0) then that can cause extra lag here, and you should ensure that setting is 0.

Look for other timings such as PlayerMoveEvent, PlayerInteractEvent, PlayerBlockBreakEvent and PlayerBlockPlaceEvent.

Those having high timings will also be counted in this event, but they will be the problem.

There is very little other than player-shuffle (and a future setting) to reduce Connection Handler alone. You must simply lower your player count and ensure no plugins are being slow in the events listed above.
Full Server Tick is the best representation of your servers performance, in the Pct Tick Column. If this value hits 100%, then your server is unable to keep up and will begin losing TPS. There is no magical solution to improving Full Server Tick, it is merely provided to see a better summary of your overall server performance and you can improve it by improving other timings on your server such as entities and plugins.
Spigot introduces a major feature called Entity Activation Range that lets you specify ranges away from a player that an entity will enter "inactive" state, meaning it will slow down its activity. Any inactive entity will reduce its performance cost by up to 95%! This can be a major savings in terms of performance on servers that have lots of entities.

With Entity Activation Range, it is no longer necessary to use ClearLagg to wipe out every entity on a schedule, as you can instead set the Misc setting for your world to be lower, such as 4. This will make items on the ground not cause you any lag!

Additionally, setting the animals setting lower to such as 12, will greatly reduce impact from animal farms. And finally, you can safely lower monsters to about 24 without any real noticable impact.

Lowering these settings will lower the "Active Entities" summary at the top of this report, and will give a much better TPS.
Scheduler accounts for all time spent processing Repeating and Single Synchronous tasks created by plugins. 100% of the timing spent here is due to a plugin, and you need to look at your plugins to identify what is making this timing total to this.

Async Tasks do not count on this entry. See all Task: Entries for your plugins to find a culprit.