Upgrading from 55-250 for sports.

Hello, i'm currently deciding about buying upgrade lens from my 55-250 for sports photography. I was close to buying Canon 70-200 F4 but recently i started to photograph indoor ice hockey but i'm mostly photographing outside. So is there anything else that could be better lens at that price point ?

By definition, a sport lens is a fast lens and nothing is
more expensive than light.

So, compromises are preprogrammed in the equation
you propose. Higher ISO is among them since you will
need both shorter SS and bright ƒ stop to control DoF.

I too shoot hockey and I use a 180~400 ƒ4 and a body
that grants a greater DR.

You have serious ambitions that maybe a lucky find on
the used market could satisfy.

This is kinda old now, so you've probably moved on...
Here's how I work out what I need.

I'm shooting indoor sport. In Australia, NZ and South Africa we're all pretty big on playing cricket and netball on tight-netted courts, roughly 30m x 12m (100x40ft). 
As a professional, I can access any location (provided I don't interfere with any off-court officials) so my ranges are 24-300 which perfectly covers action from one end to the other.
Venues are generally poorly lit, so I need to know exactly where my acceptable noise level is on my ISO. Unfortunately that means I need to shoot in either 2.8 or 3.5. f4 just doesn't cut it in my conditions.
I have shot with monopods (for both stability and to bear some of the weight on a 4-6 hour shoot), but image stabilisation is fairly important for a handheld lens over a distance.

So here's what I have:
Canon 24-70mm f2.8
Sigma 70-200mm f2.8 w/ Stabilisation
and I have a Sigma 120-300 f2.8 w/ Stabilisation on my eBay watchlist for when sport starts back up.

As a professional, I really enjoyed using my Rebel t6i with EF-s 18-200 (approx. 28-320 with crop). In fact, I still carry the Rebel with me because there's not much wrong with it.
But I could no longer deal with a lens that has a variable f3.5-5.6 because the low light was punishing me. I presume if you're shooting with 55-250 then you're also probably using EF-S lenses? In that case, seriously look at something like an 18-200.

But if that's not long enough:
Sigma do an 18-300 f3.5-f6.3 with stabilisation.
Tamron have an 18-400 f3.5-6.3 with stabilisation, but I've never used a Tamron lens so I can't recommend or advise against them.

But if your images are either too dark or too noisy then you have one option; go with f2.8 lenses and the ones I have (regardless of brand) are your only real options at f2.8