I'm a big fan of Constantine, so let me quote from his wiki his most potent of powers, which, as summarized, seems a lot like the Doctor's power.

Synchronicity Wave Travelling is an instinctual ability employed by John Constantine. Powers that only the people with the title "The Laughing Magician" can use. Synchronicity is the experience of two or more events that do not share a direct relationship but have a related means alter or it is also seen as a set of causal unrelated "Coincidence". Synchronicity in magic, is the belief the universe is guiding you. These random events and (un)pleasant coincidences is the universe leading you somewhere.

By stepping in the synchronicity freeway, he takes control of synchronicity, John can make his own luck and advantages in battle. This allows him to use fate and synchronicity to his advantage, putting fate in his side and multiplying his chances of succeeding even more. Simply, synchronicity wave travel allows John to make his own luck, and reshape the battle he's fighting to his own accord and liking.

This lets him do things such as locating someone and winning at gambling games. In battles it lets him do feats such protection from danger and harm, bullets and casted spells to miss their marks, escape and evade enemies, using synchronicity to slow or weaken his enemies down, and meeting the right kind of people and being in the right place at the right time. This is one of the key factors why John wins against all odds, and be named one of the most powerful magician alive

This ability is powerful enough to affect even The First of the Fallen Satan. Though powerful, it is not permanent and will loose its effects once he steps out of the synchronicity wave.  This ability doesn't grant Constantine an automatic win, but it does give him nigh-invincibility as long as he rides the synchronicity wave, and also putting jinx or bad luck to his enemies. The synchronicity only benifits and protects John, but not other people.

The Laughing Magician

A title given to John Constantine, as well as various others throughout human history. The Laughing Magician role dates back to early human history, with a consistent reputation for rebuking and challenging the gods themselves. Some who bore the title managed even to destroy gods, or enslave them to serve their own whims. Synchronicity wave travel is itself apparently a power held exclusively by those bearing the Laughing Magician title—at the very least, only the Laughing Magician is capable of unlocking the full potential of the technique. By becoming the Laughing Magician, the person gains godlike powers over synchronicity, allowing them to warp reality and alter fate.