Can you elaborate on how to arrive at these levels of anonymity?
The numbers aren't metrics of any kind. They're just arbitrary "star ratings".
VPN is a 2 - good enough for trolling web forums, but instantly compromised with a subpoena
Mixers are a 4 - it requires a lot of work to analyze usage patterns; a subpoena lets you definitively associate a whole bunch of IDs but you still have a lot of effort tracing the coins back to an individual. But it's not impossible for someone with resources.
TOR is a 9 - It's easy to see that you downloaded TOR, and it's easy to see that someone using TOR did something, but connecting them is nearly impossible - the connections deliberately go through multiple countries and no centralized accounting is required anywhere, so even if one node is compromised it can't be traced farther. There are still some weak attacks (like timing attacks) which is the only reason it's not a 10.
What if we connect to the mixer via Tor and enough people are using it?
Connecting to the mixer isn't the hard part. Here's how it goes:
1. You buy 2.3456 BTC for cash from Alice.
2. Alice sends 2.3456 BTC to 1xxx01 (your dirty wallet)
3. 1xxx01 sends 2.3456 BTC to the mixer.
4. The mixer spits out 2.3456 BTC to 1xxx02 (your clean wallet, which you only use through TOR)
5. 1xxx02 sends 2.3456 BTC to 1xxx03 (your deposit address on BitTOR)
6. BitTOR credits your account for 2.3456 BTC.
7. You connect through BitTOR and your client sends a crypto sig to EN1 (exit node 1) to withdraw credits from 1xxx03 as you surf.
So what happens when The Man wants to find out who posted unauthorized pictures of the revolution?
They bust down BitTOR's door and find that 1xxx03 was the responsible party;
And look here, 2.3456 is a pretty easily traced amount all the way back to Alice. You're busted.
OK, so split the amounts on the mixer service - 2.3456 in, 1.3456 out in one transaction to 1xxx03; 1.0000 change back to you at 1xxx04. Now it's much harder to trace you back... But that 1.0000 change is someone else's dirty money. If you spend it anywhere that can be linked to you, you get dragged in for their crime. That's no good.
If you send it to 1xxx03, they can now add the coin values and infer back up the chain.
If you send it to 1xxx05 (another BitTOR account), you now have to be careful not to use those two accounts together in any way.
You can keep sending it through the mixer, but the end result is your inputs - fees = outputs. If few people are using the mixer, correlating them is easy unless you spend a LOT on fees and allow very long delays between inputs and outputs (to allow more mixing).
If the mixer's web page (where you get your deposit address) is compromised, you're busted.
If a decentralized mixer is partially compromised, your security goes down - each trip you take through the mixer increases the chances that your funds are cleaned by a compromised agent.
In short: It's complicated, and while mixers improve anonymity, they don't provide strong guarantees. It's better than shuffling your coins to a bunch of your own accounts and hoping no one realizes they all come from the same root (which is futile; that kind of trace is easy), but if I was betting my freedom, I'd want "very good", not "better".