Why warm up?
To prevent injury and improve performance.
Exercising whilst your body is warm has been proven to help prevent injury and improve performance during your workout. Why? Because when your body is in a sedentary state, most of your blood is channeled towards your internal organs in the mid section of your body. When your body 'warms up' what it is doing is redirecting much of the flow of blood, and therefore oxygen and nutrients, to the main muscle groups, raising their temperature, in turn making them more flexible and 'ready' to be efficient for exercise. Joints also become more lubricated allowing a fuller range of motion. Your heart rate will increase as your heart is doing a lot of work redirecting the blood to where it will be needed. Basically, your exercise is not fully efficient until your body is in this warmed up state.
Skipping warm ups.
So when you skip a warm up, usually because you feel you'll get more benefit from just jumping straight into the main event, you won't receive the extra benefit from the immediate higher intensity as your body is not in the right state to receive the full added benefit. So not only is all that extra intensity energy wasted until your body is warm (energy that would be better saved until after you are warm), it's applied to your body as a sudden abrupt force that could potentially cause unwanted strain on a cold unprepared muscle, or poorly lubricated joint, resulting in injury.
How should I warm up?
A seperate routine? Or during the workout?
By the end of the warm up, your heart rate should be raised, you should feel warm to hot, and your breathing and muscles should feel prepared for exercise. Your joints should also feel lubricated and move easily without labour. The best warm ups are a gentler version of the activity you are about to do, so with HIIT routines, seeing that what you will actually be doing is bodyweight moves, you can actually warm up in the main activity itself simply by starting less intense and gradually building it up as you go. Or you could do a separate routine altogether if you prefer with lower impact moves. The 4 Minute Max Outs has both options covered. It's up to you how you want to do it. Either approach is fine.
Let your ability or how you are feeling decide.
What decides it really is your own ability level or how you are feeling on a given day. Listen to your body's feedback. Given that people warm up at different rates, fitter people tend to need less of a warm up as their body adapts to the onset of exercise much quicker. In this instance, warming up by gradually increasing the intensity in the actual routines is fine. People who are less fit, or perhaps feeling a bit stiff and achy already, would be better starting with a lower impact routine before the main workout. The 4 Minute Max Outs has a warm in routine separate from the Max Outs that is deliberately designed as a very quick, low impact, routine that can be repeated by the minute so you can take as long or as little as you need to get warm. You can even do it after getting out of bed in the morning. It will help wake you up, get your circulation pumping, and help ease out any joint aches you may have from the day before. Although the moves have to be performed fast, they are lower intensity moves that are to be done standing on the spot or in the basic squat hold position. They require no jumping or feet movement at all. So you can warm up virtually anywhere before you find a suitable place to do that quick 4 Minute Max Out.