I think Idra said it best:
The tank's damage was also changed from 50 to 35+15 vs armored, but this is essentially irrelevant in ZvT, they will now kill hydras in 3 shots instead of 2, but hydras are not usable vs terran because of their poor mobility and ridiculously low hp.
What he is getting at is: although they are now better against Siege tanks, the fundamental problems that exist with Hydras have not changed. If you didn't feel you were able to use them as the basis for your army before, then you shouldn't now.
On the other hand, if you were having success with Hydra's prior to the patch, they certainly haven't gotten worse.
Short answer: Scout, detect the roach build before the Roach Warren, and change your build as necessary. Alternatively, start with marine/marauder and change to your hellion build if you detect a non-roach build.
Long answer: Let's assume you detected the Roach Warren 10 seconds after it went up.
If you detect the roach warren early enough, you can immediately throw a tech lab up (25 seconds) on your Barracks and build one marauder (30 seconds) in the same amount of time it takes the Zerg player to build their Roach Warren (55 seconds).
- 0: Roach Warren goes up.
- 10: Roach Warren detected.
- 15: Barracks starts building a tech lab; 2nd Barracks starts to be built.
- 40: Tech lab complete; Marauder 1 started.
- 55: Roach Warren complete, Roach 1-3 started.
- 70: Marauder 1, new, larva, Roach 4 started.
- 82: Roach 1-3.
- 95: Barracks 2, tech lab started.
- 100: Marauder 2. Marauder 3 started.
- 102: Roach 4.
- 120: Tech lab complete; Marauder #4 started.
- 125: Marauder 3. Marauder 5 started.
If at this point you see 4 roaches on your doorstep, you'll have 3 marauders complete (assuming a rush takes 23 seconds from when their 4th roach came out).
- 4 roaches = 32 DPS, 580 HP
- 3 marauders = 40 DPS, 375 HP
Statistically-speaking, the roaches will win without stim. If you researched stim, it'll be very close. If you had a bunker, you'd be fine.
Now, if they wait until they have 6 roaches:
- 85: Roach 5 started.
- 100: Roach 6 started.
- 112: Roach 5 completed.
- 127: Roach 6 completed.
- 150: Marauder 4 completed.
- 155: Marauder 5 completed.
Given the rush of 23 seconds, 6 roaches would appear in between your 4th and 5th marauders completing.
- 6 roaches = 48 DPS, 870 HP
- 5 marauders = 66.65 DPS, 626 HP
You're slightly better off. Without stim, it's close. With stim, you win. With a bunker or two, you are fine.
Note that this is all theory. Going for a hellion rush and having to bail out on it is not good news. Wasted time, resources, and a sense of panic can cause you to falter in this position. Even if you're able to stick to the example above, you won't be in an excellent position. You'll be forced into trying to scout to detect when the Zerg player changes their build to counter it and you'll be in a position where you're constantly reacting rather than being proactive and causing the Zerg player to react.
The best solution is to detect the roach build before the Roach Warren drops and get a head start.
If you watch a standard roach opener, you'll notice that rather than expanding after their 13/14 pool, the Zerg player is forced to save the minerals, wait until 18 to throw out the roach warren, and build up minerals for roaches rather than an expansion. When you don't see that expansion after the pool, it's a good sign that Zerg is going with a roach build. This is especially true if you do not see an upgrade happening at the spawning pool right after it is done. The upgrade happening at the spawning pool, in combination with an extractor being built early, usually hints at a baneling bust build instead.
If you swap over early, you'll be in a much better position than you would be if you waited for the Roach Warren to start building. You'll be proactive, the Zerg player will be reacting, and you'll have the upper-hand.
Best Answer
I realize some of my answers are a little long, so I made a TL;DR version
I'm going to ask you a few rhetorical questions and I don't want you to be offended, but they are things you need to be thinking about.
In my opinion these were the three major mistakes you made. By 7:30 it had become your opponents game to lose before a single shot was fired.
Looking at your BO I saw:
If you can cut the produce of the factory, and done an MM timing push at 6:30 (which is the usualy MM timing push) you would have easily won the game. At that time your opponent had 5 marines and 1 tank (no siege mode). The normal MM push there is 4-5 of each Marauders and Marines. You would have steam rolled him.
If you had done so your answers would have been:
Instead, you chose to go 4 unit producing structures off 1 based (which you can't really afford as Terran). This meant that your Barracks sat idle, you didn't produce Marauders and you didn't have a good timing push. Its because of this I asked my first 3 questions.
You don't really seem to have a plan.
Strangely this wasn't what lost you the game. Not having a plan, while hard to over come, is not crucial, especially since your opponent didn't really have one either (there is no good reason he builds that second Barracks). The problem became your response to what your opponent was doing.
At 6:30 you saw a Factory with a tech lab, two Barracks and a Starport being built. The second Barracks is really the red herring here, so let's ignore it for 5 seconds. What does: 1 Barracks, 1 Factory, 1 Starport mean? In TvT this means Marine/Siege/Viking.
In response you throw down an Engineer Bay (for Turrets, which you build) and a Starport for Vikings, and continue to build Marines (and a single Marauder). Which of these things is supposed to counter Siege tanks using Vikings for sight? Well Viking vs Viking is key, but what about the Siege tanks?
By 11 Minutes you'll have built 2 Vikings and 3 Marauders with another one of each on the way. Ultimately there is nothing you can do about the Siege Tanks and they roll your Marine heavy force. They box you in and that's game.
In theory you probably could have done something clever with Dropships around 9-10 Minutes and caught him with his pants down, but really you don't do anything to stop him.
Before you play your next game (before you even load up Starcraft) I want you to have an answer to the first three questions I asked. And next time you scan Factory/Starport I want you to think "Great! My timing push should arrive right before he gets Siege Tanks!"
A plan is like a story, it has a beginning, a middle and an end. Turtling and finding the right moment to attack isn't a story, its like a blurb you'd find on the cover. Let me tell you the story of Bio into Biomech:
It sounds scary doesn't it?