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Terms:
There are all kinds of ways of categorizing skis depending on where you ski and your type skiing.
> You will see "All-mountain skis generally have what we call mid-fat waists that range from 80-110 mm." all over the place. I couldn't find the source.

Length:

Shiffrin who is 5' 7" (170 cm)uses 155 skis for slalom.

Nastar.comMasters-level men have more options, ranging from a women's-length 155-cm ski to a World Cup-length 165-cm ski

Size Charts for Skis | skis.com
Sizing video | skis.com
Weight is more important than height. Men's Ski Sizing

Weight (lb)	Starting Length
110-119	147
120-129	150
130-139	154
140-149	159
150-159	164
160-169	169
170-179	174
180-219	176
220 +	180

If height is greater than 6'2" and weight is less than 170lbs start with a base length of 174cm
Ability Modification

Beginner	minus 3
Intermediate	no change
Advanced Intermediate	plus 3
Advanced Expert	plus 6

Skiing Style Modification

Cautious	minus 3
Average	no change
Aggressive	plus 3

Skiing style compares to others in your same ability level. Experts can be cautious, while beginners who like to ski fast would be considered aggressive. Width:
My 20 year old skis which I've been skiing for 15 years were 73 mm.

Bottom Line is:
Tom McBride says "Narrow skis allow for quicker edge-to-edge transition (quicker turns) and are often lighter weight, but will tend to be thrown around more on ungroomed stuff. Stay from extremes."

At 2009 Volkl Mantra | Marker Bindings, evo and a couple of other places they say
"All-mountain skis generally have what we call mid-fat waists that range from 80-110 mm."
Most other places they say all-mountain starts around a 95 mm waist.
It's subjective. My take after spending a couple of days reading guidelines is:

• All-Mountain skis
  • East (hard snow) 85-94 mm
  • West - California (packed powder heavier) 90-100 mm
  • West - Rockies (CO) & Wasatch (UT) (light powder) 95-105 mm
• On piste - Frontside - Carving
  • Carved quick turns 76-85 mm.
    Some say < 75
  • GS turns 85-95 mm.
• Off piste - Big mountain 101-120 mm
• Beginners should get narrower skis

Alpine Ski Design - Realskiers

Category	Waist	Best Terrain
Technical	65mm - 74mm	100% Groomed, ice to corduroy
Frontside	75mm - 84mm	80/20 Groomed/Off-Piste
All Mountain East	85mm - 94mm	75/25 Groomed/Off-Piste
All Mountain West	95mm - 100mm	60/40 Off-Piste/Groomed
Big Mountain	101mm - 113mm	80/20 Off-Piste/Groomed
Powder	> 113mm	100% Off-Piste

REI Skinnier skis are better for carving turns on groomed runs, while wider skis provide better flotation in deep snow.
All-mountain skis with 85mm-95mm are best for a mix of groomed and powder.
Ski Mag Narrow waists (under 85 mm) are quick and grippy, built for groomed or icy slopes..
Wide waists (100-plus mm) surf the deep. Anything in between should be versatile for all.

Sidecut radius and the mechanics of turning--equipment designed to reduce risk of severe traumatic knee injuries in alpine giant slalom ski racing | British Journal of Sports Medicine

Solomon.com Skis for performance on groomed slopes generally have a narrow waist width to encourage high angled edges and grip when turning. They also make shifting from edge to edge easier, so you can make quick turns more efficiently.
These rigid skis allow you to use the edges even on the most difficult, steep and icy runs. Choose a sidecut radius suited to your technique and preference towards tight or wide turns.

Bode Miller "When it comes to ski width, Bode says buck the trend: While wider skis tend to be en vogue at the moment, Miller cautions against them. In addition to putting stress on the bindings, he says, skis that are too wide can also negatively affect performance. "Ninety-five, ninety-eight percent of the skiing should be done on a ski that's 70(mm) underfoot. It's the way the physics and the energy transfer from the body to snow tends to work the best."

Older men should consider skiing on ladies ski. Softer flex.

Taper: Subtract the tail width from the tip width, and you have the taper. The greater the taper, the easier the ski will be to skid. (Big rockered skis, for example, often have a very narrow tail for easy steering and smearing.) A low taper number means the tail sticks to the turn, making the ski better for carving on hardpack.

Sidecut / Radius:
More sidecut will give a smaller radius.

You need to understand that a given radius does NOT mean that the ski will always want to turn in that arc. It depends on the edge angle and weight and speed of the skier. A higher edge angle will give you a smaller radius.
I couldn't find what edge angle is used in calculating radius.
See turn radius in ski physics

General guide:
<16 m – short – carving and all mountain skis
17-22 m – medium – all mountain
22 m – long – powder

Giant Slalom gates are supposed to be set at about a 27 meter radius (for teenagers and adults) according to FIS regulations, but many NASTAR and other non-FIS races may have tighter turns which are closer to about 20 meters in radius.

Nastar.com Tight, 18-meter sidecut GS skis may be the rage, but perhaps not the fastest choice for everyone. The higher the edge angle you create while turning, the bigger the sidecut you can handle. If you get a lot of angulation, you can actually have too much sidecut, which makes the skis feel hooky. While most masters racers prefer a GS radius under 25 meters, an 18-meter radius may be too tight for you, depending on your line and the amount of edge angle you can create.
There's one more consideration among masters racers: age. The older the racer, the shorter the length and tighter the radius their skis tend to be.
Masters-level men have more options, ranging from a women's-length 155-cm ski to a World Cup-length 165-cm ski with a radius from 12 to 13 meters.

The older you are the more likely you’ll prefer the shorter ski because it doesn’t require as much « bossing » and as we age we can use a shorter ski to compensate for diminishing strength, reflex speed and fitness levels.
For the 55 to 64 year old crowd, you’ll likely prefer the longer end of the spectrum and for the 65+, you should start your search towards the shorter end.

Senior Ski Team (SST)Whistler/Blackcomb

A rough guide to sidecut radius and types of ski is given below:
Skis - Ski Equipment - Mechanics of Skiing

Radius (R)	Type of Ski	Description
10m - 12m	Slalom	These skis will make small aggressive turns when carved, intended for small slalom race turns.
14m - 20m	Allround, Freestyle, Beginner, Powder	Most types of ski generally have radii within this range. These skis are generally a bit more stable at higher speeds than slalom skis, and are well suited to general piste skiing at the speeds that most people ski at.
20m - 30m	Giant Slalom, Freestyle, Powder	Giant slalom skis make larger turns when carved, and need to be used at higher speeds to work properly. They are intended for larger giant slalom turns, at speeds towards the top end of what people generally ski at on an open piste. Freestyle and powder skis can also have radii within this range as they are not used to carve aggressively, and are not intended to be skied with the same speed and aggression as giant slalom skis.
30m +	Super-G, Downhill	These skis are only really used by racers as the speeds needed to use them properly are too fast and dangerous for most pistes.

Stiffness And Flex Pattern:
Wagner In general, a firmer-flexing ski is more stable and powerful under a strong skier; if too stiff, the ski is difficult to drive into a new turn, especially in trees, bumps and powder. *A softer ski provides easier turn entry and exit and is more forgiving for a lighter skier. If too soft, the ski feels unstable.

Camber/Rocker:

• Cambered skis produce more pressure on the snow at the tip and tail since they have to flex further to achieve this curve.
• Rocker skis offer superior float in the soft snow and increased ease of turn initiation with less chance of "catching" an edge. This is great for skiing deep powder. The effective length on hard snow is less since the tip and tale are not contacting the snow.
  As skis in general get wider, rocker helps keep the new shapes maneuverable for a wider range of skiers.
  Any ski with a very short effective edge (either reverse camber or lots of tip and tail rocker) will be unstable and slippery at higher speeds. In choppy, variable conditions or ice, a ski with a short effective edge will not hold an edge as well as a ski with a longer effective edge
• Full rocker makes easy transitions, with better edge grip than rocker and better maneuverability than camber.
• Hybrid - camber with front and tail rocker - The edge engages the snow closer to the foot and allows the skier to have an easier time conducting pressure to the point of engagement. By having the foot closer to the point of engagement (and disengagement with tail rocker), the skis can enter and exit from their turn radius with greater ease. The risk of “catching an edge” is greatly reduced.

Ski Weight Chart for Alpine & Backcountry Skis | evo
'Explained: Three Key Specifications for Buying Skis - Width, length, stiffness | Welove2skiWeLove2Ski

• 70's - Most skis had about 4 mm of side cut (Difference in width from tip to underfoot)
• The late ‘70s and early ‘80 more sidecut for racing skis (Mahre Brothers) 7 mm sidecut.
• 1988 - Fat (115 mm) skis for power skiing
• 90's more sidecut and shorter recreational skis
• 1998-2015 Professional Racer Bodie Miller pushed the sidecut and short skis even further.
• 1993 - Shaped Skis
• 2000 - My Shaped Skis were 74 mm at the waist
• 2010 - Rocker design (curve up at the tip and tail) became popular.
  Wider (100-105 mm waist) all-mountain skis became the fad.
• 2016 - Many are saying you should stick to narrower (85-95 mm waist) if you are skiing primarily groomed slopes.

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