home advantage
home field/court advantage (perhaps more North American than British)
This is, of course, just a phrase and as such not a complete one-for-one equivalent to your saying. As an analogy, this phrase is used in many situations unrelated to sport.
Macmillan gives a literal definition:
home-field advantage cf home-court advantage
home-court advantage
noun [uncountable] American
the advantage that you have over an opponent when a sports contest
takes place at your own sports field or court
Wikipedia, again with a literal definition, gives more equivalent phrases, mostly sport-specific variants:
In team sports, the term home advantage – also called home
ground, home field, home-field advantage, home court, home-court
advantage, defender's advantage or home-ice advantage –
describes the benefit that the home team is said to gain over the
visiting team. This benefit has been attributed to psychological
effects supporting fans have on the competitors or referees; to
psychological or physiological advantages of playing near home in
familiar situations; to the disadvantages away teams suffer from
changing time zones or climates, or from the rigors of travel; and, in
some sports, to specific rules that favor the home team directly or
indirectly.
Looking at the most general phrase, home advantage, examples of use outside the context of sport follow, all found with a Google Books search. (A word of warning: there is some very questionable English in these examples, but that doesn't detract in any way from the phrase home advantage itself.)
Lead markets only exist if an innovation design first preferred by a
country has an advantage over foreign market innovations in their home
markets, which can over-compensate [sic] the home-advantage of foreign
firms.
Lead Markets: Country-Specific Success Factors of the Global Diffusion of Innovations, Marian Beise (2001)
Globalization provides firms of developed countries with the
opportunity to locate plants in developing countries enjoying host
country advantages in wage costs in addition to their 'home
advantage' as stated in the introductory chapter.
Competitiveness and Development: Myth and Realities, S. Mehdi Shafaeddin (2012)
Even if his people wanted to try and bring him home, the Grey's [sic] had the “home advantage.” His government's secret space program was very advanced, decades beyond anything the public would suspect in terms of technology...
Moonbase: D.U.M.B.s (Deep Underground Military Bases) - Book 4, David Sloma (2014)
If you take him to your home for the all-important first time, you have the all-important “home advantage” of being on your own turf and in more control of the situation.
How to Pick a Lover: For Women Who Want to Win at Love, Wesley L. Ford (2009)
The last example also uses the phrase on your own turf, which may also be useful to you.
It also takes the forms on home turf and on home ground.
The Free Dictionary gives the following definition and examples:
on (one's) home turf
- In the place or area where one is locally established.
The team will be playing the championship match on their home turf this weekend, which they're hoping will give them a bit of an
advantage.
We'll be hosting the state-wide high school science fair on our home turf next month.
- In a field, profession, or area for which one has a deep affinity or familiarity.
After a string of unsuccessful action films, the director is back on home turf with a biting new historical drama.
I tried a few television roles, but I'm really only on my own home turf when I'm doing stand-up comedy.
Edit: Credit where credit's due, just noticed another earlier answer uses the phrase your home turf in passing.
beard the lion in his own den
Again, not a proverb, and by no means an exact equivalent to your phrase, but an idiom with the literal meaning of attacking a beast in its home, used to describe confronting someone or something on their own territory, and hence relevant. It's often used for visiting an authority figure, perhaps going to a school principal's office or meeting a judge in their chambers.
The phrase implies that the course of action thereby described is, at least, bold, perhaps brave and very possibly foolish, as well as being intimidating for the person entering the lair.
However, the emphasis in this phrase is on the courageous interloper, the foreigner entering the lair of the beast; this distinguishes it quite clearly from the phrase in the question, where the basic meaning is of (increased) strength on one's own territory. Unlike a dog, a lion is necessarily ferocious to begin with - that the confrontation is on the lion's own ground conveys the particular audacity of the invader.
beard the lion in his den (or lair) (phrase)
Confront or challenge someone on their own ground.
She bearded the lion in his den with a revelation-packed bombing campaign, attempting to beat him into coalition.
This was somewhat like bearding the lion in his den; and so it needed delicate handling.
Deciding to beard the lion in his den, I visit Dr. Gerald Imber, a Fifth Avenue plastic surgeon.
In the end, it came down to the fact that this wonderful Moorefield team was just a bit too young for the task in hand, bearding the
Nobber lions in their picturesque North Meath lair in a keenly
contested Leinster JFC final on Sunday.
The phrase is also heard as simply beard the lion, without any mention of a lair or den; this form does not in any way lose the sense of a move into the home territory of another - the whole phrase is implied, much as with plus ça change.
The verb beard isn't especially common, and so it's worth looking at its definition too.
beard (verb) [with object]
Boldly confront or challenge (someone formidable)
he was afraid to beard the sultan himself
Both definitions are from Oxford Living Dictionaries.
