Feature Requests: Remove redundancy and add new time control

Greetings, Lichess users:

The comment of @Nordlandia in item # 14 aroused my curiosity. I thought: "Since I failed to get the attention of any Lichess developer in this forum, I will try my luck at Github".

I entered the Github site and I published the same suggestion that appears in comment # 1 of this topic: "Remove "Custom" from Quick Pairing and replace it with Classical 30+x, where "x" represents a variable increment equal to 0 or 15 or 30...

Interestingly, I received a response very similar to @tpr's comment in item # 6. A Github user named IsaVulpes argues that 30+0 is very similar to 15+15. However, when I make my own calculations, the results deny that 15+15 = 30+0.

For example, I used data provided by @Morozov in comment # 11. He states: "The average game of chess is 40 moves".

You observe these results:

https://imgur.com/CfyWOkP

The difference between 15+15 vs 30+0 is 5 minutes. This number is not insignificant. During the final phase of a game, 5 minutes of extra time to think about your movements makes a world of difference.

When we compare 15+15 vs. 30+15 or 15+15 vs. 30+30 the differences are even more significant: 15 and 25 minutes respectively.

Conclusion: comments that disqualify a time control Classic 30+0 (or higher) do not have mathematical arguments to support them.

At 60 moves 15+15 is equal to 30.0. At > 60 moves 15+15 gives you more time. At < 60 moves 15+15 gives you less time.

First I agree 100% with the suggestion of adding a new default time control for classical that includes an increment. Second in response to tpr, I believe most games last around 40 not 60 moves.

First off a lot of respect for @Ugalde for putting thought and effort into this. Aside from that I think we ought to consider more than just the average number of moves in a game and take that as a basis for increment.
The fact itself that a game can or can't be won by mouse racing will have some effect on a players behaviour.

E.g. I am down a knight but up on time 5 min to 1min and the position is somewhat complicated. My choices are: try and play the position or play the clock. If there is increment, playing the clock won't work that well.

If I am a piece down at move 40 in a 15+15 increment game, then I resign.
If I am a piece down at move 40 in a 30+0 game with my oppo,e,t at 1 min, then I might play on to move 80.

Personally, I'd like to see the idea of a 4x4 grid implemented (it was suggested on Github, I believe). That way we can have a couple more variants offered for both Rapid and Classical. One concern raised regarding the idea is that it would reduce the pool of users for each variant and increase wait times for games--but I experience virtually no wait time at all right now. It would not bother me to have to wait 10 to 15 seconds for a partner. It might bother some, but a bit of a wait (potentially) seems worth it if it means gaining several more time controls to choose from.

Another opinion:

• 10+10 (my preferred)
• 5+5 or
• 1+1

Or anything with increment really

Yes 4x4 has been suggested a very long time ago. @GSP0113
https://lichess.org/forum/lichess-feedback/add-rapid-with-increment-to-the-quickplay-buttons?page=1
In fact this idea existed from the day quickplay buttons were introduced. However it has been yeeted due to aesthetic concerns.

I'd also like to see quick-pairing buttons for 960 or Crazyhouse. Considering some increased popularity for 960.

See - https://github.com/ornicar/lila/issues/5739