As a couple folks already stated you also need to think about what your tracking needs are. Here in the Midwest it is all 'on leash' and it should be in this part of the country - due to land ownership patterns etc (generally smaller acreage). Also philosophically I'm only interested in fatally hit deer, not baying live deer. The fist thing I tell a hunter when we take a call is that we are searching for a carcass not a deer... if the deer is not fatally hit, we won't catch up to him....sometimes this disappoints some "trophy hunter" types. The reality is no matter what kind of dog you have if he is on leash the handler is the limiting factor, not the dog, so you aren't catching up to a live one anyways unless the deer is in pretty bad shape.
Additionally, on my and my family's wounded deer, as well as a few experienced hunters I've tracked for, we don't have problems.... we know where the hit is, give the deer ample time etc etc, the dog has no problem.... it is when you start taking cold calls for hunters that you find how stupid or inexperienced people can be, and also when you need the power dog. By "power dog" I mean the combination of cold nose, prey drive, intelligence, and experience to track a deer days after the hit with significant track disruption/disturbance. The downside to a power dog is that you can spend way too much time on nonfatal hits.... early on we used to... every hunter that calls hit the deer "right in the chest".... then contacts you two days later after him and 6 buddies walked all over and messed up the trail. A power dog can still track this deer and we went on many a mile long track half the night for no reason before we wised up. Now we carefully screen calls. The first red flag is when the hunter says he hit the deer "right in the chest" - I tell them first off that "that isn't the case or we wouldn't be talking right now" - if they get offended then I refuse the call
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The "two day old three mile recovery" makes for a good story in a book, but any experienced bowhunter knows that if you act appropriately after a hit that isn't the norm. Successful recoveries of non-pushed deer from fatal arrow wounds that aren't textbook hits generally involve a 300-400 yard track to a wound bed or several beds, then the deer gets up and travels 50-100 yards and dies. This characterizes 90%+ of the "hit him too far back" type recoveries we have.
These types of tracks are no-brainers for any decent dog.... and if you only track for yourself or guys you trust these will be the majority of "oops" hits you deal with. Were I or someone I trust to hit a deer in a very low percentage situation - say high in the back, or in the shoulder with minimum penetration - I'd do the track for a reasonable distance to assure it is a non-fatal hit, then call off. But I'd know going in that we were just doing our due diligence on a likely non-fatal situation.
In the normal "oops" type fatal hits on deer a power dog isn't necessary - kind of like commuting to work in a Ferrari. An SUV or a pickup truck might be a better choice for any variety of reasons.
Jerry said it perfectly above: "On lead dogs require situational consideration as well. The very first being how the dog will be used. If the dog is for personal use where most every track is hot (under 8 hours old) the selection of breed is less critical. I could teach a cat to track hot lines, lol. All I can offer for advice here is DO NOT get a big dog. I have run them all in 34 years of handling blood dogs and being dragged through heavy brush by a massive dog is NOT fun. A dog under 40 pounds is a good choice."
He has much more experience than I do - and this is spot on from what I've seen.
My wife and I are way over-dogged for 95% of the tracking we do. And we have had to learn how to deal with the unknowns on other peoples tracks so we know when to call it "nonfatal" and quit. I never got the dog originally because I was losing deer I hit myself - I got him because I wanted the "hit him too far back" type shots to be easier to find - and they are - for a decent dog these are 15-30 minute tracks as opposed to 4 hours to a day for a human blood tracker.
Again we love our dog, and would 100% take a teckel of the same blood lines again (and will) because we love the whole package, he is a perfect fit for US, but as I said before he wouldn't be for everyone - teckels, no matter the coat type, and no matter what some breeders say, have some idiosyncrasies.... like any dog breed... that make them a great fit for some folks, but not others.
One thing we need to continually work on (and work harder on than we do) is getting Oskar out and doing things... some teckels might be happy on the couch 10 months a year but our boy wants to HUNT! Additionally I feel a bit guilty that we have the dog ability to do so much more than we do and don't use him for it - our breeder hunts rabbits and 'coon and runs foxes in addition to tracking with her dogs. The owner of our dogs father (an Austrian hunter) uses his dog for all kinds of hunting, I've seen pictures with recovered roe deer, badgers taken from underground dens, foxes bolted from underground and shot, and ducks retrieved in small water hunting. Teckels were built for earth work ("dachshund" means "badger dog" in German) - these guys were not "born to track" they were "born to dig" and hunt underground, and virtually nobody, including my wife and I, use them for ground work in the USA. Such a versatile hunting breed has become "a blood trailing specialist" here, and we in the US have done the breed a bit of a disservice by that. On the other hand using these dogs for hunting of any kind helps preserve the original (hunting) bloodlines and keeps them from all going the way of the pet and show breeder.
Anyway, sorry for the digression.... all this again to say "Find the right dog for YOU"
R