Missing Fast Enough to Win?!

MATHEMATICS IN USPSA: CAN I MISS AND MAKE UP TIME!?

by: Josh Mazzola of Team AR15Targets

Let's talk math!  Now granted, math isn't everyone's favorite subject, but understanding its application is an invaluable part of improving your scores in the various action shooting sports.  In USPSA specifically, a large part of the game is mathematics.  Finding the balance, not only as a shooter between speed and accuracy, but mathematically between speed and accuracy is key to success.  We as shooters can all understand that balancing speed and accuracy means shooting fast enough so that we are "using" the entire target zone allotted to us, but what exactly do we mean when we say mathematically balancing speed and accuracy?  - Well, by understanding how to maximize USPSA Hit Factor scoring, we as shooters can better understand what the cost of shooting points down is, purely in terms of time; something which isn't as obvious in USPSA as in IDPA for example. 

Standard IDPA Target

In IDPA (which utilizes Time Plus scoring) there are 3 target zones per target; the Down 0, Down 1, and Down 3.  After shooting each stage, your total points down are tallied up and divided by 2.  This gives you a value in seconds which is then added to your raw time.  In other words, if you shot a stage in 10.00 seconds with 6 points down, your overall time would be 13.00 seconds (10+[6/2]=13).  This means that the cost of shooting a "Down 1", which for all extensive purposes is a Charlie on a USPSA target, is a penalty of 0.50 seconds.  It's important to note that the point values in IDPA never fluctuate, so a Down 1 will always equate to 0.50 seconds and a Down 3 will always equate to 1.50 seconds.  Mathematically, what this breaks down to, is that if a shooter can shoot a D0-D0 faster than he/she can shoot a D0-D1+0.50s, then it is mathematically faster for him/her to shoot all D0-D0's.  Very few shooters are able to shoot a D0-D1 more than 0.50 seconds faster than they can shoot a D0-D0, meaning that every time they put a shot outside the Down 0, they are almost always adding time to their score.  This is why you see the winners of most IDPA matches with very few points down.  To put it another way, if it takes a shooter 1.00 seconds to shoot a D0-D0 but only 0.55 seconds to shoot a D0-D1, then he/she is still better off shooting a D0-D0 because with the 0.50s penalty assessed, his/her 0.55s time is bumped up to a 1.05s time, 0.05s slower than his/her D0-D0 time.  Understanding this, we can deduce that accuracy is of extreme importance in IDPA and in order to be successful one must shoot very few points down.

Standard USPSA Target

In USPSA (which utilizes Hit Factor scoring) there are 4 target zones per target; the Alpha, the Bravo, the Charlie, and the Delta.  The Bravo and Charlie zones are actually worth the same point value, so we can eliminate the Bravo zone for the purposes of simplicity in discussion.  Opposed to in IDPA where points are a negative, in USPSA, points work in the shooter's favor.  The Alpha zone is worth 5 points, the Charlie zone is worth 4 points (3 points for Minor Power Factor), and the Delta zone is worth 2 Points, (1 point for Minor Power Factor).  With this in mind, the general maximum value of a standard target is 10 points (A+A = 5+5= 10).  The shooter's overall score on a USPSA stage is deduced by adding up the total points shot, and dividing that number by the overall time; the final number is the shooter's Hit Factor (HF).  What this means, is that
mathematically, the value of a point (in terms of time) is completely dependent on the stage and is not consistent like it is in IDPA.  We don't usually think about a dropped point equating to time when shooting USPSA, but by doing so, we can actually see how fast we should be shooting a stage and see if a shooter can actually "miss fast enough to win".

Example 1: Shooting a High Hit Factor Stage

A stage is denoted a "High Hit Factor" if there are lots of points available and the shooter can complete the stage relatively quickly.  A High HF is usually something around a HF of 10.0.  So for the sake of this example, let's say that the stage has 10 targets or 100 available points (10 targets X 10 points per target = 100 points) which shooterX can shoot in 10.00 seconds; 100 points/10 seconds = 10 HF.  In this case, we can deduce that a point is worth exactly 0.10 second (10s/100p = 0.1s/p).  So if the stage has a high HF, then shooting points down doesn't hurt very much, and in actuality, can be better for you than shooting all A's if you can increase your speed accordingly!  Now I know you're jumping out of your chair right now, but bare with me as I explain why.  If the shooter can shoot an A-A in 1.00 seconds and can shoot an A-C in anything faster than 0.90 seconds, then he is actually going to improve his overall HF by shooting A-C's (assuming the shooter is shooting Major PF).  If the shooter in the same example were to be shooting Minor PF, then his value of shooting a Charlie would be doubled from 0.10s to 0.20s because his Charlie shot is only worth 3 points instead of 4.  So for the Minor PF shooter, he needs to shoot a A-C in 0.80 seconds or less to make shooting an A-C more advantageous than an A-A.  Although the Minor shooter may be cutting it close, shooting an A-C in 0.10 or even 0.20 seconds faster than an A-A is actually an achievable task for many shooters.  So remember, if you can shoot fast enough to make up the time added for your lost point/s, then you will actually be benefiting from speeding up and taking some Charlie's because doing so will improve your HF overall.  The opportune time to do this is when the value of seconds/point is very low, (which is on high HF stages).

Example 2: Shooting a Low Hit Factor Stage

A stage is denoted a "Low Hit Factor" if there are few points available and/or the shooter must take significant time to complete the stage.  A Low HF is usually something around a HF of 4.0-5.0.  So for the sake of this example, let's say that the stage has 10 targets or 100 available points (10 targets X 10 points per target = 100 points) which shooterX can shoot in 20.00 seconds; 100 points/20 seconds = 5 HF.  In this case, we can deduce that a point is worth exactly 0.20 second (20s/100p = 0.2s/p).  So if the stage has a low HF, then shooting points down has a higher time penalty which the shooter must balance with increased speed.  If the shooter can shoot an A-A in 1.00 seconds and can shoot an A-C in anything faster than 0.80 seconds, then he is actually going to improve his overall HF by shooting A-C's (assuming the shooter is shooting Major PF).  If the shooter in the same example were to be shooting Minor PF, then his value of shooting a Charlie would be doubled from 0.20s to 0.40s because his Charlie shot is only worth 3 points instead of 4.  So for the Minor PF shooter, he needs to shoot an A-C in 0.60 seconds or less to make shoot an A-C more advantageous than an A-A.  As you can see the Major PF shooter is still liable to  be able to at least break even or maybe pick up some small fractions of time when shooting Charlies so long as he is moving quickly, but the Minor PF shooter most likely will not.  What this means is that Major PF shooters can afford to take some Charlie's on low HF stages so long as they are moving quick enough to account for them, whereas Minor PF shooters really cannot afford to do so.  This is the prime advantage of shooting Major PF in USPSA.

Example 3: For Example Only - A Hit Factor of 1

In this example, we have a stage with a HF of 1.0 (it is extremely unlikely that you will see a stage like this, but it helps hammer home the point of mathematical balance).  This would be a stage where there are 10 available points, but it takes the shooter 10 seconds to finish the stage.  In this case, a single point is actually worth an entire second of time (10s/10p = 1p/s), and therefore, unless the shooter can shoot an A-C more than 1.00 seconds faster than an A-A, then shooting the A-A would be more beneficial to the shooter's score.  Remember, in USPSA the stage's HF denotes what level of accuracy and what level of speed is needed to maximize score.  BUT, remember also that each shooter's HF on a given stage will always be different and each shooter needs to calculate a stage's HF for himself/herself in order to denote the value of shooting a Charlie so that they can weigh the cost/benefit analysis of doing so.

On the average, we can deduce that shooting a point down for Major PF shooters is usually worth about an additional 0.15 seconds and therefore, unlike in IDPA, it actually makes sense to forgo some level of accuracy in favor of speed when shooting Major.  However, when shooting Minor, we can deduce that a point on average, is worth around 0.33 seconds.  This, like in IDPA, means that it is most likely more advantageous to shoot all A's unless the stage has an extremely high HF where a shooter would be able to make up (the approximately) 0.20 seconds he loses per point.  Either way, remember that only you can control what your HF is per stage.  So based on your shooting ability, you might not be able to achieve high HF's and that simply means that you have to pay more attention to collecting all your points as they are worth more for you.  So can you "miss" fast enough to win....well, no, but you can certainly shoot some Charlie's and still win, and if doing so allows you to free up some speed you otherwise don't use, doing so might even help you improve your score.