Performance factor is a rough way of measuring how well you run over different
distances. For any distance a PF of 1000 aproximately corresponds to a
 world record. A PF of 600 is closer to High School performances<P>
Estimated VO2max is another method, which estimates your maximum possible
usage of oxygen.  This also corresponds to performance. <P>
Another calculation is the Purdy Point system which uses world record charts
from 1960 (a current world record is about 1100 purdy points)
This seems to be much more accurate for all distances. A good Windows
based program to calculate Purdy points is RUNNER (see rec.running FAQ)
 
Normalized inverted pace (used in my plots) is simply pace inverted and scaled
to the PF of your first listed race.  For the same exact distance NIP is the
same as PF.  ex. 1st race pf=671,*pace = 3444.5, NIP = 3444.5/pace<P>
<PRE>
  As an example my PR's are:   PF  VO2max          Purdy Points  Pace   NIP
      1 mile    5:08  1966    671   57.7 kg/ml/min      568      5:08   671
      5 mile   30:14  1978    637   55.16   "           558      6:03   569
   26.2 mile 3:14:00  1978    583   48.93   "           464      7:24   465
</PRE> 
 All three calculations say my 5:08 mile is my "best performance". Personally
I didn't even care too much about running when I did a 5:08, didn't train much
and think the other two performances were better. Actually, I should
have broken 3 hrs but I hit the "famous" wall. (and never ran anything longer 
than 15 miles)<P>

In the rec.running FAQ is listed multiplying factors to get "estimated"
times for different distances. This is broken down by 3 types of runners
long distance, distance and middle distance (less than 1500m).
 This implies that
one might never achieve the same PF at widely varying distances.
Someday I might include these multiplying factors in this web page.<P>

A 568 Purdy point gives a 57.8 400m. However, using PF or est. VO2max
the same 5:08 miles predicts a 69 sec 1/4 mile. (see the PF calc section)
Using the PF & VO2max for time predictions gets worse at the ends of the 
distance scales. <P>


Here are the details for both formulas.    <P>
<PRE>
	formula for performance factor

	  pf = (3337/pace)*(kilom^.0689)

	where pace is in minutes per mile
        kilom is total number of kilometers run.

      An attempt at an explanation of the formula:
	   The equation   (3337/pace)
	   for the same distance
	   goes down asymptotically toward 0 as pace increases.

v            The equation   (dist^.0689)
            increases exponentially (with a decreasing rate)
            as distance increases for the same pace.

       Multiplying the two functions gives the performance curve that
         varies with pace and distance.

******************************************************************
	Calculations for estimated vo2max
	       (from Matt Mahoney's program)
		  
	v = 1609.3/pace; /* calc meters/mile*/
	/* VO2 and percent_max based on "Jack Daniels, Conditioning for
	   Distance Running - The Scientific Aspects", Wiley & Sons, 1978 */
	vo2 = -4.60 + 0.182258*v + 0.000104*v*v;
	percent_max = 0.8 + 0.1894393*exp(-0.012778*minutes)
	    + 0.2989558*exp(-0.1932605*minutes);
	vo2max = vo2/percent_max;
       

	minutes is total minutes run.
	exp(-0.012778*minutes)
           means e raised to the power of (-.012778 times minutes)
	percent of VO2max = percent_max*100

</PRE>