Would recommend some sort of runner on the stairs.

Please post a picture. We don't know what this stairway looks like. Is it open or enclosed? Straight or switchback? What is on the stairs now? Are they already nice wood stairs or have you removed (or are planning to remove) existing carpet and they're just plywood underneath?

Pics please posted here in comments

Especially if you have kids running around the place, or older people who may not have the best footing, I would recommend a well-secured runner on stairs.

We have a dog run access to our walk out basement so a no brainer no carpet anywhere in that basement or the stairs with 3 huge dogs .

Our basement is currently under demo so I don't think a picture would do it justice. It's a closed staircase with a switchback and full carpeted. I'm going to add porcelain tile to the staircase and just wondering if a runner would be needed. I've attached a photo of the porcelain tile and the staircase style I'd like without the carpet runner.

Porcelain can be quite slick - your manufacturer may have information on the coefficient of friction of your tiles, however, and it may be fine. More information on floor safety is here: https://nfsi.org. I can understand Patricia's priorities because of her situation, but safety-wise, I would worry about someone hurrying down the stairs, pivoting on that angled bit, and slipping.

Edited to add, a different vendor shares that your selected tile is treated for slip resistance. https://internationalwholesaletile.com/product/woodville/

Those are pretty nice stairs. Do they have to be redone because of water damage? Porcelain is not what I would choose for stairs in any case. Is the porcelain going to be on the basement floor as well?

IMO tile on there is not a good plan if there is a change it might get wet . Waht is the reason for the tile ? Is it to go with something else . I need a bit more info .