Very good advice from Black Jack. Here’s an alternate perspective which kind of expands on Mantis9’s final three recommendations:
Taking Hick’s Law one step further, forget techniques and trust your training in terms of their execution. Develop flow-state and continuity in your movement instead. If you want to reduce reaction time, study and understand rhythm. If you understand the opponent’s rhythm, you can undermine to his sense of timing.
Distancing is pivotal to space/time referencing in this regard. As an example, the subtle difference in distance between kicking and punching ranges is an elastic factor in developing good distancing. As you spar, take note of the rhythmic change of your partner as he prepares his attack whatever that may be. People instinctively know from experience how far they have to be from something in order to hit it, grab it, or pick it up. Each rhythmic shift is indicative of their own sense of distancing and how that spacial reference accomodates a given tactic. Each tactic has a pre-emptive signature that you’ll be able to recognize as you work through various set-ups and attacks during 3/4 speed free-sparring. You’ll notice that the rhythm must compliment the distance in order for the bridging tactic to be effective. Practice moving away from his single attacks at first (jab, cut-kick, or other probing tactic) while he’s enroute. That just means not being there to block or counter (moving just out of range).
Once you can read the rhythm in his advance, practice countering the single attack with your own strikes, clinch, etc. In the same training session, experiment with that concept in regard to combinations, but with combos, don’t evade. Instead, counter with jams, bridging, shot, or whatever tactics the rules of the game allow for.
Continue experimenting with rhythm as you add layers of complexity and diversity to the drills. You’ll develop good conditioned response to the intuitive prompters that are necessary mechanisms of the opponent’s dynamic in their entering and attacking phase. Once you can read his rhythm to the point where he abandons his attempts to get close while he’s in the process of advancing, you’ll know you’ve locked onto his rhythm.
Increase the speed at this point and take your lumps until your sense of rhythm adjusts. Vary your own rhythm and footwork to compliment that of your opponent. Once in a while, step way out of range and exhale as you drop your hands, go flat-footed, and reset yourself from a point of stillness. As you inhale again, rhythm and hands up. You can also experiment with your own attacks on the inhale. You’ll find that this tactic invariably lends you attacking entry if the oppoenent doesn’t adjust his rhythm in kind. In other words, if he doesn’t adjust his cadence, he’s relinquished the pace and lost the initiative while you go from a defensive attitude, to taking the intiative. Yin to yang, yang to yin.