The pattern of any antenna can be divided into Vertical and Horizontal components (these are not the only choice sometimes we use LHCP and RHCP, etc). For V and H we're looking at the Theta (up/down) and Phi (left/right) electric fields.
(we analyse antennas as transmitters, its easier, and they work the same when receiving)
Now the yagi will create some V and some H radiation on every direction, but the radiation is mostly H and mostly in front. For a well designed yagi, if we call the front Hpol radiation intensity 0 dB, then I estimate: sidelobes of -10 dB. Exactly sideways -15. Backlobes -15. Exactly behind it there is a hole, -20 dB. This is an azimuth cut, moving around in the Theta=0 plane. So far so good.
Now plot the Vpol radiation. The amount of this is strongly dependent on the feed and matching, how well balanced the coax is, whether the mast resonates at that frequency. I am going to guess for a typical Hpol yagi installed on a metal mast and Gamma fed, the Vpol radiation will be -15 dB in front, compared to the Hpol in front. Going around the antenna though, I don't expect it to change much. As the mast, cable etc are radiating, it will be roughly omnidirectional.
As an aside, If the yagi were floating in free space with only a tiny transmitter connected to the feedpoint, the Vpol radiation would be much less, perhaps -40 dB compared to Hpol.
So to answer your question - well first the front to back ratio needs to be carefully defined to make sense. I would start with this: The ratio of total power radiated to the back, to total power radiated to the front. Because when you look at F/B ratio, you're interested in the rejection of all signals from the back, not just horizontal ones. Perhaps there is a more complete definition out there.
It doesn't help the amateur to talk about the Vpol F/B ratio, but you could certainly define it and calculate it. For an Hpol antenna, Vpol F/B might be close to 0 dB.