Basically DLP projectors do as mentioned above a great job of sports.
When DLP first started many years ago it was RGB or RGBW. This worked fine but the color wheel speed wasn’t high enough and a small percentage of viewers saw what was called rainbows. It happens when you dart your eyes across the screen rapidly and you get a flash of red blue green rather than them mixing to make the color it is supposed to be. Only the RGB make colors and they added the W to boast the lumen output for business type projection (power-point) where a lot of white is needed because the room is not dark enough. So it was brightness at the penalty of loss of color.
To fix the rainbow problem or at least make it many times better they repeated the RGB pattern to be RGBRGB and in effect doubled the wheel speed. Then they started looking at potential for secondary colors and came up with RGBCYM and then because business projectors needed brightness spec to sell they dropped the M and replaced it with W and you see many RGBCYW projectors now. At first RGB and RGBW all had equal pie segments on the wheel and then they started making RGBCYW where the RGB segments were much larger than the CYW segments. These RGBCYW got nicknamed business crossover projectors as they did power-point great but also did very well with sports and even movies.
It is also not as simple as what color wheel is best, because the room and the screen factor in and very important is screen size also. As the screen gets larger the lumens (brightness) per square foot go down. If you have a small screen say 100-110” and the room is painted darker colors and outside light is kind of blocked then an RGBRGB will have loads of lumens to make sports pop, and will also have great color accuracy and CR when you want to watch a movie in the dark. On the other hand if the room is brighter and the screen huge 200” say you would have no chance with a 2000 lumen RGBRGB and a 4000 lumen RGBCYW might look better.
One more thing to think about is with lamp life (hours of use) the brightness goes down.
And if that isn’t enough to drive you to drink all these projectors have normal and eco power modes where eco makes the lamp last longer, and they also have 1-10 brilliant color settings and a selection of 6 or more modes that favor color or brightness you can select from. Having owned both RGBW, RGBCYW & RGBRGB I can tell you the brightest modes of the RGBCYW produce a pretty poor image even for sports. So you may have an RGBRGB that max out at 2000 lumens and a similar RGBCYW that claims 3000 lumens, but it really doesn’t look that good once you get past the 2000 mark. IMO 2000-3000 is for power-point only or to give people the idea they are getting more for their money.
Lumens alone is not the whole story when it comes to sports. Yes the images are bright and full of color but there still is a need for convincing blacks and dark colors.
I’m a fan of bright projectors and darker gray screens in rooms with very dark ceilings and dark walls. Then keep outside light (windows etc) out and then add back in my sports bar lighting as task lighting on the viewers end of the room and directed away from the screen. Doing all this I can sit and eat a pizza and have a beer and feel like I have more than enough light that I’m not sitting in the dark with my buddies and my 110” image looks like it is a giant flat panel TV with the projector set on a brighter setting. Then after the game I turn off the task lighting set the projector to its best movie setting and it feels like I’m in a commercial movie theater.
My goal was to have the best of both worlds out of one projector one room.