Change antenna so bluetooth beacon works in all directions equally well?
Yeah looks like there's some nulls like you identified so the received signal would be weaker if one of those nulls fell on your receiver.

The age-old antenna that might fit your needs is a half-wavelength dipole antenna (2.15 dB greater directionality than a perfect isotropic source). It's a linearly polarized omnidirectional antenna, but there are nulls above and below in line with the radiating members so it's not perfect (radiation pattern looks like a donut).

Alternatively (and way cooler), since your source orientation will be unknown, you could use a circularly polarized antenna! There are many premade ones since it's popular with the remote control community. Specifically, you could use a cloverleaf antenna pioneered by the legendary IBCrazy (1.2dBi supposedly) and a transmit/receive pair would only cost you around $10. It still has a null directly above and below the antenna but is pretty darn close to omnidirectional.

The benefit of circular polarization is that:

1) It will work at any orientation of the receiver relative to the transmitter. Theoretically, with a 90 degree rotation between a horizontally polarized and vertically polarized antenna (due to your ball's orientation for example) there would be zero signal received. In reality there will always be some reflection or cos(theta) power that makes it, but you could easily lose reception.

2) It will reject multipath better in a concrete jungle since the rotation of the circularly polarized signal flips on each bounce (right and left handed rotations, like corkscrews through the air). Circular polarized antennas reject the opposite polarity at -3dB when it receives the wrong rotation. This will manifest as an increased range since your receiver won't be swamped by garbage reflections (although the gaussian distribution of BLE already helps with that).

So to summarize, if you have a base station with a fixed antenna I'd recommend a circularly polarized antenna setup. If your receiver is mobile, you can get away with a linear polarized dipole but remember to try holding it at different angles if you lose signal. Also, if you generally know the area your ball will be located in, you should consider using a higher gain receive antenna to give you a longer range. In the RC community you can easily find high gain antennas at your frequency: regardless of the source polarization you could use a helical antenna since it will still receive a linearly polarized signal (if you stick with your dipole) but there will still be some loss.

The ultimate solution would be two transmit antennas hooked to a splitter and then oriented to cover each other's nulls. However, you'll get an insertion loss (less transmitted power aka less range) and now you're poorer... But at least you know where the giant ball is.

http://www.antenna-theory.com/antennas/dipole.php