Yes that's right, there was about 4 wild fights that we have, two are draws and two the lion kills the tiger. And there is one more I know of, where the lion killed the tiger that might be true. So in the five wild fights that we have, the tiger won none of them. I honestly don't know why you wouldn't expect the tiger to leave, some tigers I'm sure will stay and fight, but I wouldn't expect most to, I just don't see the species being that bold to do that. Even if some did stay and fight, what if they lost most of the fights, and instead of dying the tigers ran, but they left wounded and survived, they wouldn't ever come back into the lions territory again. This could be why it was known from that source that the tigers deserted the areas where the lions came in to. Even African lions vs each other many times will flee if they sense the other has a significant edge over them.
But I guess the question is, would most tigers win, and the lions would have to leave, based on the accounts we have I don't see that, it looks like either a knock down drag out fight, or the lion kills the tiger. I'd put my money on the lion as well out in the open, I think they possibly could run a tiger down to exhaustion, certainly an African lion could. But I'm not all sure the differences between the Asiatic lions and African lions, not sure if the Asiatic's patrol their territory as much as African lions. I found it interesting in that Pocock book, that Asiatic lions sagittal crest area of the skull is more developed than the African lion skulls, they seem to claim Asiatics skulls are very developed muscularly. Also interesting, and I had heard that but didn't see this source, it states the lions lower jaw is more rounded and doesn't sit flat on the table compared to the tiger. The lion may have the stronger lower jaw here, better for the pulling and tugging and fighting over the choice portions of meat growing up in the pride.
The other concern also is whether the lion would handle the tiger differently than it would an invading lion, being a complete separate species, the lion may have even a greater drive to take that species out and eliminate it from the competition as they are a threat to their prey source. So with that theory, the lion may be even more willing to fight another tiger compared to another lion. I cannot see the tiger as a species operating the same, nothing about their behavior suggest this, the circus acts are almost like a bigcat behavioral experiment, the lions had a distinct hatred for the tiger always wanting to fight them, many times the tigers avoided them and refrained from the fight. And yes most all the trainers agree that mixed them, they actually saw the lion win most of the time in one on one fair fights. Most trainers that back the tiger were not really mixed lion tiger trainers, and most all expressed a distinct admitted bias for the tiger. Alex Kerr, Mabel Starks, Charly Bauman, Capt. Dutch Ricardo, all said they liked the tiger, most of them also said they didn't like lions. You don't hear that from Beatty, who called lions devils and terrorist, he just admired their fighting ability over the years and willingness to fight. None of the other mixed cat trainers that backed the lion ever said a bad word about the tiger or disliked it, they also never said they like lions more.