## DOTA 2 - How many matches for +1000 MMR?

A couple of days ago, I was curious to find out how many matches do I have to play to increase my mmr by 1K. As we know, typically a win and a loss changes our mmr by +25 and -25 respectively. So in order to actually increase our mmr, it requires us to play more matches than we intuitively think of since a loss totally nullifies the outcome of a win. Of course throughout the mmr mission, our winrate has to be higher than 50% to have a net increase in mmr.

As I was calculating the number of matches I need to play to increase my mmr by 1K at a particular winrate, the idea of creating a graph to visually feel the change of required number of matches at different winrates, came up. So I created the following graph by generating all the required number of matches for both +500 and +1000 mmr change. I hope this will help all the mmr ladder climbers realize how much time they have to put in for their desired mmr increase at the level that they perform (winrate).

On the X-axis we have winrate and on the Y-axis we have required number of matches. The blue and the red curve are for +500 and +1000 mmr increase respectively. The formula for calculating required number of matches is pretty simple.

mmr_net_change = mmr_per_match * no_of_matches * winrate
- mmr_per_match * no_of_matches * (1-winrate)

Rearranging this we get:

no_of_matches = mmr_net_change / (mmr_per_match * (2*winrate-1))

Here you can see the whole chart that I calculated for winrates in the range of 51% to 70%.

Hope you guys plan your journey accordingly.