The ideal range for sparring is where just out of range of a lead leg kick by your opponent. This means for opponent to kick or punch you, he or she must move his or her body toward you (or get you to move closer). This range gives you more time to react to an attack, but it also means you are also probably out of kicking and punching range for your attacks. To get with range, you must learn to lunge.
When sparring, time is critical. The more time it takes you to move, the more time the opponent as to react to the movement. You must learn to move not only quickly, but to be able to block or attack effectively while moving.
Stepping is slow; stepping forward with the rear leg is very slow, just as rear leg kicks are much slower than lead leg kicks. Stepping with the lead leg is quicker than stepping with the rear leg, but it is still relatively slow. For example, from a standard fighting stance, to step with the lead leg to bridge the gap and reverse punch the opponent’s head, you first lift the front foot, then you step it forward as you push off the rear leg and shift your weight forward into the reverse punch. This is a lot of movement (four distinct movements)so it takes lots of time to complete and gives the opponent time to react. The opponent sees the front foot lift and know something is about to happen. When the front foot begins its step, the opponent now knows a step is happening and an attack will probably follow. It mind reacts quickly to movement.
The fastest way to advance, or retreat, is to lunge. In the lunge, the rear leg is the first to move. To lunge forward, the rear leg explodes forward, and, as it does, the front foot lifts and is propelled forward by the rear leg. The weight is also propelled forward and behind the reverse punch. Everything occurs as one movement. The only indication the opponent has of a movement toward him or her is your whole body appears to be getting larger as you get closer. It takes a few milliseconds before the brain detects movement and those milliseconds may mean the difference between you scoring and the opponent moving away or blocking the punch. Also, during the lunge, the front leg may kick, since it is pre-chambered by the motion of the lunge, or the rear leg may continue its forward movement into a kick.
To lunge backward, the movement is the same except the front leg begins the lunge by exploding backward. In a backward lunge, say to avoid a front kick, you rear leg cannot be used for kicking, but the front leg may fire a kick immediately after it starts the lunge. Then after the rear leg lands, it may immediately explode into a forward lunge that may lead to a front or rear leg kick. The further aid you in setting up for a counter attack, you may lunge backward at angles to the attack so the attack slips by you. This puts you within range for any type of counter attack.
Therefore, to increase your chances of scoring, stay just out of range of a lead leg kick, and use forward lunges to bridge the gap. If the opponent lunges, lunge backward and counterattack, and maybe then counter with a forward lunge and counterattacks.
To increase the speed of your lunges, practice them a lot and work on exercises that build explosive leg strength, such as doing dead lifts and leg presses, running up and down stairs, working on a stair climber machine, doing plyometric jumps, practicing all your patterns using very low stances, and using low stances in all your training exercises. Sparring matches do not last very long so, while it is good to have, endurance is not much of a concern. Being able to do a hundred kicks in a round, which may or may not score, is not as important as being able to explode into a few kicks that do score. Therefore, instead of concentrating on endurance exercises, concentrate on explosive strength exercises so you will be able to bridge the gap in an instant with a lunge.