Short version, giant hodograph, high critical angle. Longer version...When you're looking for a strong tornado, you look for that big right turning hodograph. There's also a decent amount of academic literature now that discusses the link between critical angle and strong tornadoes. That's the angle between storm motion, and the low level shear. The closer to 90, the more likely you are to have an environment favorable for producing a strong tornado. Think about a boat, flowing down a river. That's the storm. Ok, now, imagine you tie a giant rope to that boat, and yank the back of it at a 90 degree angle. What happens? It spins. Or you fall into the river cause you thought you were stronger than a multi-ton boat in a current. Anywho, combined with a low LCL, large cape, AM cap, discrete cells...you have a problem on your hands. Hodographs let us plot wind speed and direction with height. It's an easy to read way to measure speed and directional shear together. When you combine those, we find that a large, right curving hodograph, signals that the *wind field* in an area is supportive of tornadoes. I feel compelled to add at this point...when we see a large, right curve, we're expecting a right-moving supercell. A "right mover", moves to the right of the mean flow. Hodographs are an easy way to determine this (and remember it). Large hodograph, in right quadrant, with right curve, equals right mover. Right movers tend to produce stronger and more frequent tornadoes due to some fancy dynamics.
For tornadogenesis, we focus on the curvature of the hodograph in the first 2-3 km of the atmosphere. This is telling us about low-level shear. This is another area of tornadogenesis research that has become more clear in the last few years. It is part of why some supercells produce tornadoes, and others don't, and it is how the SPC can say now, x region will likely see supercells capable of "all hazards", where others will see a large hail threat. Basically, you start with a mid-level mesocyclone, and then that storm pulls in some additional rotational energy which enhances low level rotation. You can detect that on a hodograph through its low level curvature. You may also have noticed folks talking about the low "ground scraping" LCL's. That is, in essence, the cloud base. The closer that is to the ground, the easier it is for that strong low-level rotation to actually get to the ground. Skew-T's, and hodographs, tell us all of this information.
At the end of the day, hodographs are one plotting method used to tell us what's *possible*. The reason we use hodographs to prog wind profiles in severe setups, is they allow us to *easily* and *quickly* identify how risky a particular setup is, for a certain area. Thus when you read something "looks bad", it's because that chart or graph, is designed to allow us to easily interpret what we're viewing and come up with solutions. We could just look at the wind barbs on a Skew-t, or winds on pressure surfaces, but hodographs give us a better snapshot of what's happening at different heights, when it comes to shear and spin.
A tip for the future: don't overcomplicate chart analysis. When you forecast, you're considering many parameters. What's the starting setup? Do the models correctly capture this? Which capture it best? OK, what are the models that understand the situation to start with saying WILL happen in the future? How are they changing their forecasts with time? What do I know about the local area that could affect this setup? Do the models STRUGGLE with this setup, or area? What does this setup remind me of (or if you're me and have a bad memory, what does this remind a computer database of)? In all of that, you're going to look at many different charts, tables, plots, and figures.
Trying to get down deep into the weeds of a single hodograph in a scenario like this, isn't something anyone has time to do (or I suppose...should have time to do). Same is true for a Skew-T. I see folks overcomplicate them all the time, and you can come up with plenty of interesting things from them, some of which are useful. At the end of the day though--for a skew-t, what I'm going to look at....: what's the temp profile, what's moisture look like, is there a lot of CAPE, ok, where's that concentrated (aka, what's the profile), is it surface based, what's the wind, any significant advection occurring, anything else jumping out at me? If it's particularly noteworthy, what are possible analogs of that setup? Ok, got it, NEXT. Thus, for a hodograph--long curvy rightward turning hodograph = bad. The bigger, and stronger the curve, in general = more bad. .