Here's my attempt that going in depth into the mastery trees. I'll try to give my opinion on each and every option, and tell how it relates positively, or negatively to Chogath.
I'll quickly summarize each tree though.
: While Chogath can go offensive, as a jungler you're more here for tanking and being like a second support to the team. We find ourselves generally putting 9 points into offense because we still do some damage, but not enough to merit more points.
: The defense tree is very strong, it's unreal how good this tree is to a lot of different positions. As both a tank and a jungler Chogath will excel at abusing as many points as possible in this tree. While you could put all 30 points into this tree and be fine, there is a point where you start going overboard and would probably be better off going into offense or utility.
: While Chogath would enjoy a lot of these masteries, it's just very hard to compare the benefits of going in the defense tree. Lastly when compared to dropping 9 points in offense or utility, it's better to have the offense later in the game as the utility masteries only really give Chogath increased buff duration (which you start passing the blue buff to your mid or top, and the red buff to your ADC when the time is appropriate) and summoner cooldown reduction (while this is good, flash shouldn't be used carelessly and smite already has a pretty short cooldown and doesn't gain much from this tree).
This is a very solid mastery if you were to use the summoners accociated with it. For information as to which summoners you should use, head over to that section of the guide.
Exhaust: Reduces the armor and MR of the foe you use this on by 10. This is great for early game ganking as it drops their resistances to help you do practically true damage.
Ignite: AD and AP is gained while the summoner is on AD. It helps last hit in lane, but won't help much as a jungler.
Ghost: Increases movement speed when you use ghost by a great amount. Worth using if you take ghost.
Garrison: I'm not a fan of this summoner in dominion, so I wouldn't use it.
This mastery gives you attack speed which can help clear the jungle to have vorpal spikes go off more.
This mastery gives 4% cooldown reduction to Chogath, a very good mastery since between philosopher stone and frozen heart you only hit 30% CDR.
This applies bonus damage to minions and neutral monsters that you auto attack. We skip this mastery because you get enough extra damage on your vorpal spikes.
Chogath doesn't need AD per level as he's a champion that deals his damage through magic skills.
Chogath doesn't really need the AP per level that he gets from this mastery, but it opens up the spell penetration mastery, Arcane Knowledge, which will be discussed later.
Increases damage to turrets by 5%, it's really not a mastery worth it on a jungler. If you were to push down the tower as a melee champion, this mastery wouldn't make a big difference.
This mastery increases your damage by up to 2%, it's really such a small amount that it's neglegable. There are a better use of 3 points than to get this mastery on a tank.
Because Cho is more of a magic damage dealer, we don't want the armor penetration.
% magic penetration is a great statistic to get for free, especially on a tanky champion like Chogath who isn't going to build much into this statistic, it helps him ignore that extra bit of magic resistance.
Critical damage? Not on Chogath. You can forget this mastery.
Attack damage on a champion like Chogath isn't really worth the investment. The boost from your vorpal spikes are going to give you more than what you need over raw attack damage.
Flat ability power isn't going to give you much, your skills don't scale enough for the small amount of AP to make a difference.
As a tanky character, you won't find yourself building too much AP. So this mastery is ignorable.
You don't get critical hits, so this mastã¼à¼€y isn't worth investing in.
Armor penetration isn't need on Chogath, the majority of your damage is magic, between the magic and true damage your physical damage is pretty ignorable.
As a tanky jungler, you really won't find yourself building ability power too often. So a % boost to your AP is an ignorable mastery.
Chogath doesn't need the offensive points to get this far, and even if he did the point in this mastery isn't that needed. As a tanky champion you're not building for the damage that you deal.
This is a very good summoner if you use the summoner accociated with the mastery. As a jungle Chogath we would definitely take this to get the extra gold for the smite mastery, since you'll be taking smite no matter what.
Cleanse: Increases the disable reduction by a second, it's not anything you would be carrying on a tanky champion.
Heal: Passively increasing health by 5 per level, again this isn't a very useful summoner for a jungle champion.
Smite: Extra gold on a jungler? Yes! This adds a lot of gold and should be grabbed on a jungler.
Barrier: 20 extra shield amount is good for an early usage, but really seems like a lackluster point compared to the rest. This isn't a useful summoner on a tanky champion.
Since we're playing Chogath we will be getting a lot of regeneration from our passive. So the extra regen from this isn't very necessary, and compared to the other points in the defense tree, it cannot compare.
Health per level is a very good stat to get on a champion like Chogath. The health is going to build up overtime for free, and as a tank what more could you want? Oh you have to level this to get Veteran Scars? Icing on the cake, we'll talk about that mastery later.
Reduces damage taken from monsters. VERY good for a jungler, and it opens up Bladed Armor, which is a very VERY good mastery for junglers, but we'll talk about that in a bit.
Armor? Armor! This is a helpful mastery for a jungler, however we only put two points in it because of all the points we put into the first row.
Magic resistance is a helpful statistic for tanks, however as a jungler, we'll be dealing with armor for the most part, the APs will stick to mid lane so we have time to build our own MR, we don't need our masteries to give it to us.
Deals damage to monsters that hurt you, as a tanky champion who built for durability, this is going to help you clear quite a bit. This is a very solid mastery to pick up.
As a champion who deals mostly with neutral monsters, reducing champion damage isn't going to help you much. You don't do much trading like lane champions, and if a champion were to go all-in you most likely wouldn't be standing with 2 health. While in theory it COULD help you, it's such a long shot that I would say that it's not worth investing in this mastery or it's higher point.
Reduces slows by 15%, as the giant target that Chogath is, this helps you negate a lot of kiting that people may do with you. While it won't make kiting impossible, it's always nice to make the slow less effective.
30 flat HP for free? This is one of my favorite masteries, so my biased says to always get it. It's a great mastery to give you some good health right from the start of the game.
5% damage from turrets, while it sounds nice, it's so niche and random that you'd be better off investing in anything else. It's really just something that you don't need to invest mastery points into, but while your buy more items, you will be able to tank turret shots better overall.
Reducing damage from champion basic attacks is just like unyielding, it's useful, but not useful enough to merit the use of your mastery points. It's something you'll build into.
Reduces the duration of CC. Vital to all tanks, a VERY solid mastery. It's not something you can just build more than one of, so all the extra points help with your task to becoming the tank of your team!
4% maximum health increase. On a champion like Chogath this is going to stack with your passive stacks as well as any health that you build on your champion. This is a great mastery to put points into as the second to last row isn't the best.
Getting points based on the number of opponents is not the beset mastery. But what you have to realize is that out of the points available it's going to offer you stats that will be useful when they kick in. Say you're counterganking, well you're going to get some magic damage tops or jungles, and some physical damage. Well this is going to cover both of those instances, instead of dumping the points into just single armor or magic resist. It's also a great mastery for invasions, as the early extra armor and MR may save you from a bit of early damage.
5% on bonus armor and resistances just isn't enough to dump 3 defense points so late, there are much better masteries to put points in. Even with 200 EXTRA armor you're only getting an extra 10 armor. At this point 10 armor makes such a little difference that it just shows how worthless this mastery is.
10% less time spent dead really doesn't mean much to you. You don't want to die, dying is bad. You don't want to waste mastery points for lessening a bad thing. Just don't do it!
10% less damage from critical strikes isn't really worth it. It's such a small portion of the damage you'd take, that it isn't worth such a late point in your mastery tree. Remember, the majority of your mastery points are there to help your early, not necessarily your late. (There are exceptions, but this isn't one).
3% reduced damage taken from EVERYTHING? Hell yes. As a tank 3% less damage from everything is just too good to pass up.
A great mastery for summoners that are used on your champion. However, for Chogath we tend to wanna go 9-21-0, if we put a point in this for our flash we would lost out on our magic penetration in offense, or our damage reduction in the defense tree. It's not really worth losing for just a 15 second shave off of your flash cooldown.
Revive: Grants bonus health for reviving, but since you wouldn't take revive on Chogath, this is a very neglectable benefit.
Teleport: Reduces cast time by 0.5 seconds. Doesn't really help much even if we ran teleport.
Flash: When you take Flash it's always nice to have it up as early as possible. I have set up mastery set-ups where Cho could take this mastery, but ultimately I've decided it wasn't the best choice. If you want to set up in the utility tree it can work, remember no masteries are perfect and there are sections in the utility tree that Chogath can benefit from.
Clarity: 25% extra mana, Chogath shouldn't have mana problems, and even if he did, this summoner and mastery is not the answer.
Clairvoyance: Reveals champions seen by clairvoyance, we keep this summoner to the support, there's no reason to take this mastery for clairvoyance on your jungler.
Movement speed when leaving the jungle to get in place for ganks. It helps you place ruptures and get successful ganks off. It's a solid mastery for Chogath.
Mana regen to help you get more mana, and allows you to pass off your blue buffs to your mid with less regret. However, with Chogath's passive it really isn't a necessary grab, it's more of just a luxury grab for people who are too spammy on the usage of their skills.
Helps you recall a second earlier in Summoner's Rift. It's an alright mastery that's usually grabbed for filler. I wouldn't suggest it on Chogath as you're going to be in the jungle, and shouldn't be too worried about people popping up where you would recall.
Extra vision when wards are placed for the first 5 seconds. It's a point I never really found to be that useful. As a tanky jungler you're expected to be like the second ward placer on the team, but I still don't feel that this mastery is worth the point compared to the rest.
Lower cooldown on Flash and Smite? I think it's a very solid mastery to go into if you find yourself going down the utility tree. 10% cooldown reduction on summoners is cool as not much really lowers the cooldown on summoner spells.
Mana per level, while it isn't a bad stat, it cannot compare to the other options in the row, it's just not something you really need on Chogath. There are better options.
Reduces the cooldown on activation items, while this sounds good, it's not going to compare to the lowering of cooldowns on summoners. It's a solid pick-up on Chogath because you find yourself often with Randuin's Omen and Shurelia's Reverie, but it's just not enough to take mastery points from other grabs.
Extra gold over time is an interesting stat on a jungler. You should still be able to clear while having this statistic, but you're really dipping too far into the utility tree that you're taking too much out of the defense tree. It's an alright grab though.
When you go for 9 points in the utility tree, this is the point to get. Increasing the buff duration is a very useful thing, and the only thing that can do it is this mastery. It's a very solid point to get, and as a jungler you utilize this to more than the most on your team.
Lifesteal and spellvamp, when you have a passive that gives you the sustain that Chogath's gives, you really don't need a small amount of healing off of skills and auto attacks.
You do not need the biscuit as you have your passive and many health pots at the start of the game. It's really just a waste of a mastery point this far into the tree when you already have so many better options.
Extra starting gold gives you another potion, but with your passive you really don't need it, there are other places to put your mastery points than in this mastery.
This increases your experience gain by up to 5%, this is a great grab for if you are heading this deep into the utility tree. While I don't recommend coming this far, if you did this would be the mastery in this section of the tree to grab as getting your ultimate opens up a lot of possibilities such as a strong gank, countergank, or even a dragon.
Strength of Spirit
Extra health regen for the amount of mana you build, outside of frozen hear we don't really build much mana, so this really isn't a mastery you should even consider dropping points into.
A 60 second ward that you get at the start of the game. It's really something you don't need to consider as there are far too many options this far in for Chogath that you wouldn't even begin to consider Explorer, besides you wouldn't even want to grab Biscuiteer, the prereq to get this mastery.
5 gold for auto attacks you land on enemy champions based on a 5 second cooldown. Sadly you don't see many enemy champions in the jungle, so this is a heavily wasted mastery on Chogath.
If you were to go this far into the utility tree, may you be happy to find 6% CDR close to the end. While it's not the most important thing, as Chogath can build many items efficiently that give CDR, it's a nice grab if you're shooting very far for the utility tree.
Last, but not least, Nimble. Extra movements speed is a godsend on Chogath. While it's not something I would ever recommend as you are wasting a lot of durability building so far into the utility tree, if you made it to this point at least you can say you walked away with a nice boost of extra movement speed. It's a hard stat to build outside of boots, and Chogath can't get enough of it as it only helps allow you to get into position to use all of your skills to be the best disrupting tank as possible.