English has a lot more vowels than most languages, so most learners need to re-train their ears to recognize the additional vowels. In both British English and American English, the difference between ball and bowl is small, but significant. It is easy for native speakers to recognize because their ears are trained to do so.
In ball, the vowel is a long vowel: that means that it sounds the same all the way through. The same long vowel occurs in law- /lɔː/ in BrE and /lɑː/ in AmE.
In bowl, the vowel is a diphthong, which means that there is a glide between two different sounds. The same diphthong occurs in low- /ləʊ/ in BrE and /loʊ/ in AmE.
You can see the difference clearly in this spectrogram of a British English speaker saying ball and bowl. In the first word, ball, the long vowel is the same all the way through. In the second word, bowl, the diphthong sound changes, starting at the red cursor line.
Regarding your comment about casual, fast-paced conversations: when people speak casually, and when they speak quickly, the parts that lose clarity are the function words: the little words that provide the structure for the language.
Take the word and, for example: the strong form is /ænd/, but most of the time we use the weak form /ənd/. As speech gets progressively faster and/or more casual, it becomes /ən/ and finally /n/.
Meanwhile, the important words- nouns like ball and bowl- are usually stressed, and don't soften up in the same way. The central vowel in a stressed word is about as protected as you can get.
You might get some de-stressing if the noun is preceded by an adjective (the red ball) or when it's part of a compound noun (a furball), and this might weaken the clarity a little, but not, in my opinion, enough to make it impossible to discriminate for a native listener with the same accent.
Best Answer
[The sentence is at 1:30 in the video, if anyone else wants to hear it.]
The "at" is really there, and needs to be there. When Jobs says it, it's closer to "eht". Listen for the rhythm in this phrase:
Every syllable takes the same amount of time.
You might be having trouble with the T sound. Are you making a puff of air at the end? If so, stop doing that. At the end of the word "at", your tongue should still be touching the roof of your mouth. It will sound almost like there's no T at all. This flows naturally into "the", where your tongue starts on the roof of your mouth.
"Decided" is similar, but when there's a vowel after "decided", you end up saying the D at the end. So "decided at" sounds more like "decideh dat". Don't force this -- it's a weak D. When your tongue moves from the roof of your mouth to the bottom, you'll make the D sound automatically.
That's how to say the phrase like a native. If you keep the puffs of air, everyone will still understand you; you'll just be slower.