How is hashrate calculated when all you know is luck/shares/difficulty?
Mining bitcoin, you got block header which consist of 80 bytes message from a pool or from bitcoin core server, etc.
Then, you use nonce 0x1 with this header, and hash this header. this process is one hash.
cycle nonce from 0x1 to 0xffffffff with this header. these process complete a work full hash out.
It needs 4.295 G time hashes to complete brute force search on one block header, or 4.295 GH to hash out a work.
It is unlikely to found an extreme small hash value from hashing a work. So, you produce another block header (called local work) to hash it again. repeat doing this brute force process to search an extreme small hash value from a work.
Hashrate is a speed measurement of hash times done in per second. eg. 4.295 GH/s mean your device can do 4.295 G hashes in 1 second to process a work, eg. use bitcoin network benchmark 10 minutes control measure:
21.5 GH/s can process or hash out 5 works in per second. 10 minutes, process 3000 works.
1 TH/s can process or hash out 233 works in per second. 10 minutes, process 139,800 works.
1 PH/s can process or hash out 232,829 works in per second. 10 minutes, process 139,697,400 works.
It is more chance to found a work which produce an extreme hash value if you can process more works.
All pools, solo miners get block header data are different due to data input time or different transactions contained in block header, they all work on their different block headers, so, no competition between them. You should not be fear of big pool. There may be some competition within the pool if the pool use a single header data for all clients without coordination.
It is a luck if the work you process can produce an extreme hash value. But, it also depend on your miner process capacity. I prefer using how many works can be processed in per second as a benchmark.
Largest pool at moment, Foundry USA got 28992 PH/s process capacity or their mining device can do 28992 Peta times hashes per second. I saw one header was solved in about 1 minutes by the pool. How many works this pool can process:
1 minute, she can process 405,010,702,080 works or 405 G works
2 minutes, she can process 810,021,404,160 works or 810 G works
5 minutes, she can process 2,025,053,510,400 works or 2,025 G works
10 minutes,she can process 4,050,107,020,800 works or 4,050 G works
But, sometime, it can be not solved in more than 1 hour.
Other pools use different block headers. If your block head is good, you can solve a block before big pools.