Some physics, maths and facts about jump's difficulty.

Part 1: 3Lz vs 3F

JUMPS
There is already a lot of content in the skating community regarding this two jumps. You'll find some of the most useful at the end of this thread in case you are new to this.

This part is just a physics approach to their preparation and technique.

FLIP

Entry:
Usually entred from a mohawk or three-turn. Always entries rotating in the SAME direction than jumping. This way the skater gain angular momentum that will HELP them to rotate faster and complete the jump

Take-off: inside edge and toe-pick

Following the entry, the skater picks on the ice taking off before 1/4 rev.
The toe pick helps the skater to convert the kinetical energy from the entry into potential, while the inside edge makes them keep GAINNING rotational energy

LUTZ

Entry:
Always entering from a backwards glide, rotating in the OPPOSITE direction of jumping.
This makes the skater get NEGATIVE angular momentum, wich makes the jump so much harder to complete.

Take-off: outside edge and toe-pick

While approaching the take-off the skater must continue that glide till the end, this is what gives the clear outside edge.

That means they will not only have LOST all the helpful angular momentum, but also they must COUNTER the opposite one

Remember: the deep edge indicates how much momentum they will have to counter as that means how much they kept the glide till the take off

Finally, they pick on the ice to convert the kinetical energy into potential and leave the ice before 1/4 rev.

Here a visual side by side of the ice marks from both jumps.

Keep in mind what I've just said about the angular momentum and directions of rotation of the edge at the entry. Same for the Flip but opposite for the Lutz

(Courtesy of @chiburahakkai )

Just observing the different preparation and take off technique we can see the lutz is clearly harder, but let's see some research about how well top skaters perform them.

STATISTICS
I took top 25 skaters from ISU total combined score ranking, both men and ladies, making a total of 50 skaters. I replaced the juniors with top skaters from before 2018, as they dont have a career long enough for significant data.

And I counted how many 3Lz and 3F they have attempted and failed on international competition, and compared those rates to determine which jump they probably find harder.

(Details and disclamers at the end)

And the final results are:
Out of those 50 skaters 29 have higher fail rate on the 3Lz, 15 on 3F and 6 around the same (diff.<2%).

Here a graphic in case you want a visual representation.

However, I thought the most representative skaters of real difficulty are those who perfectly perform both, so here the current (17-18 season or later) senior skaters who have received (close to) no edge calls in their careers.

Chart, as an example of what I made, and graphic.

A clear mayority of them fail more 3Lz than 3F, the only 2 who dont, also have more 3F attempts than 3Lz.

This is a point I couldnt reflect, but if a skater has more 3F attempts despite it having a lower BV it is probably they find it easier and it is a matter of consistency.

So overall, both physics and skaters' statistics indicate the difficulty of both jumps is far from from being exactly the same.

Another point about this jumps is whether edges are fixable or not, as it's a big reason for getting negative GOE on this jumps, so here some examples.

FIXING TECHNIQUE

Patrick Chan: 3F

Had 2 ! and 2 e calls in 2008 and 2009. Didnt got any other for almost the next decade.

Here one of his ! calls at GPF 2008 side by side with his 3F at Olympics in 2018

Keiji Tanaka: 3Lz

Textbook flutz in his first seasons on international level and very few attempts. Reworked his technique and hasnt had an e call since 2014, just some ! from time to time.

Here an e call at jr worlds in 2012 and his 3Lz at Cup of China this season

Boyang Jin: 3F

Had a slight edge problem when he was junior, worked on it, had a ! call in 2016 and nothing more

Here his e call at JGPF in 2012 and his flip at the Olympics

Mao Asada: 3Lz

She worked so hard on correcting her flutz, and even managed to jump it with textbook outside edge on practice.

Couldnt find a front view at competition on her last years, so here Sochi 2014 vs GP France 2016. And GP France 2010 vs Japan Open 2015 practice

Yuzuru Hanyu: 3F

Believe it or not, one of the worst flip techniques, with almost 100% rate of e calls, on his first international years. Most male skaters with that rate just drop the jump and make up those points with quads. He worked on it and hasnt got an e call since 2014

Here a front view of it at 4CC 2011 and 4CC 2017

I also wanted to show the back view and had to use his EX from GPF 2011, as it is so blurry I added some lines too. Side by side with 4CC 2017 replay.

These are just a few relevant examples of fixing edges, but most skaters that receive systematic calls either reworks it or drop it if they get quads stable enough.

Fun fact: all of this 5 skaters have higher fail rate on 3Lz than 3F. Yes, including lippers. Yes, including Hanyu

Not all of them got textbook edges, but in every case the improvement is very clear.
Also, it seems a skater's body isnt the biggest factor, but rather technique, and it is fixable to at least keep the jump competitive. Especially effective if it's reworked early in their career

DISCLAMERS
1- The method I used for stats is just an approx way of compare the difficulty. It works on a general picture, but dont take the exact numbers too seriously

2- In fact it's biased towards 3F as I didnt reflect BV, # of attempts or combos so prob the gap is even bigger

3- I didnt post the stats of every skater because this thread is not about a particular skater, but top skating as a whole

4- I know some of the pictures comparing edges are so blurry, specially the old ones, so I encourage you to look for those programs if you dont see it clear

If after reading this thread you still doubt whether Lutz is clearly more difficult than Flip feel free to DM me or comment asking whatever you need.

Same if you want to check the numbers yourself or have questions about the method, DM me and I'll be happy to tell you.

Some better explanations of techniques:

Flip: https://twitter.com/chiburahakkai/status/1019876717148508161?s=19

Lutz: https://twitter.com/chiburahakkai/status/1020616883257540608?s=19