Does bitcoin mining power add up and how does this affect the difficulty? I read that if my hashpower remains constant, and total network hashpower increases, after 2016 blocks difficulty will increase. Now as far as I have understood, difficulty increases if blocks are mined before 10 min and I find no co-relation of this statement with previous one.

Say current total hashpower is 100,000 MH/s. If 2 people have joined network with hashpower of 50 MH/s. Total haspower is 100,100 MH/s. There are large pools having 5,000 MH/s or even more on current difficulty, mining at block/10 min, chances are very low that that these new miner with much low hashpower can calculate block @ &lt;10 min.

This thing make sense if all machines in mining pools (say 50 MH/s), work on different blocks, then new miners can get block possibly in less than 10 min. But if hashing power is added i.e. 5,000 MH/s is used for finding block, then such minor additions should have no effect on difficulty.

So what exactly is going on here ??
Mining is a lottery, not a race.

Think of mining as digging for gold in your own piece of land. Everyone has an equally large piece of land, but some people can dig faster than others (=hash power).

One in every billion grains of sand contains gold. Despite that very low fraction, there are still plenty of gold grains out there. There are so many grains of sand out there that even just in your own piece of land, there are plenty of good ones.

However, the gold is randomly mixed with the pieces of sand, so every grain of sand you dug up has an equal chance of being good. Certainly those who dig through more sand faster stand a higher chance of winning, but even the very first grain you look at has a chance of being gold.

So how long does it take for a gold coin to be found? On average, as long is needed for all miners together to go through one billion grains. So does it matter if someone only adds 1% of the digging power to the total? Sure, he now has a 1% chance of finding the next gold grain. That isn't much, but on average that will absolutely reduce the time needed for a solution by 1%. And the difficulty (the ratio of sand to gold) will go up occordingly.