Many of you will have already noticed - or been AWARE
of,through what I've said - the DIFFERENCES between these two systems,and
so,this page will be telling you what you already know.
HOWEVER,the more astute of you may have noticed a very
striking SIMILARITY between the two,and that's where I'll start this
discussion.
Remember,firstly,that the P.P.R. is arrived at by calculating
the R.P.F. (Rated Passer Figure or Raw Passer Figure),and the R.A.F. (Rated Average Figure),and
dividing the R.P.F. by the R.A.F. (hence comparing the Passer to his peers).
You might ALSO remember that I had a column showing the R.P.F. in the
All-time top-20's - N.F.L. and P.P.R. page.
The interesting thing of note,is the great SIMILARITY between
the R.P.F. and N.F.L. ratings. If I were to do a top-20 based only on the
R.P.F.,then it would be almost IDENTICAL to the N.F.L. list (just some small
differences here and there).
In fact,based on the P.P.R. all-time top-20,statistical
analysis shows a correlation between these two sets of figures of 0.96!
That's about as close as you can GET to a "perfect" (1) correlation,for figures
that have been arrived at in a totally different way.
In other words,if you were to rank a group of Quarter-backs
using these two different systems,you would probably get the same results.
What THIS all says,is that I have "done good". :-) i.e.
my simple R.P.F. system is making the same assessment of a Passer's
absolute performance as the N.F.L's system.
The FIRST key word in this statement is "simple". The R.P.F.
is simple. The R.P.F. formula is easy to remember. If you have the Passer's
numbers,then you just multiply and divide away,giving you the answer.
The N.F.L's system,on the other hand,is much more
difficult to remember and work with. Take 30 away from this number,and divide
by 20. Take this one away from 9.5,and divide by 5 - or was that 4?? Easy to
get confused,not to mention time-consuming. I managed to get almost identical
results to the N.F.L.,without all those messy calculations and extra numbers
(not to mention that those extra numbers are a source of some of the BIASES
in the N.F.L's system).
The SECOND key word in that statement,is "absolute". The
R.P.F.,as does the N.F.L's system,measures ABSOLUTE performance. The better
your passing figures,the better your rating. This is why few "old-time"
Quarter-backs appear on the N.F.L. all-time top 20 - the STANDARD of play
then,just wasn't what it IS today. The rules were different,they played "both
ways",and didn't spend 8 hours a day,6 days a week playing FOOTBALL. :-)
Is it fair then,to say they aren't as good as current
players,simply because CIRCUMSTANCES were different then?? My answer would be
"of course not!". How can you have an "all-time" list of Quarter-backs without
Slingin' Sammy Baugh on it??
With the exceptions of Otto Graham and Sonny
Jurgensen,none of the players on the N.F.L's list pre-date the sixties! Doesn't
really sound like an "all-time" list TO ME. Is it that all players before
the sixties,except for these 2 players,were HOPELESS?? I don't THINK so.
Certainly,anyone who saw Sammy Baugh play,would probably argue with
that. They didn't nick-name him "Slingin'" for nothing! ;-)
So this is where the R.A.F. comes in,giving us the P.P.R.
This is also where the biases in the P.P.R. come in. ;-)
Biases in the P.P.R.?? SURELY not! Well,yes,there is,after
my lambasting of the biases in the N.F.L's system. ;-) The difference is that
the N.F.L's biases are against a particular STYLE of play - and mine aren't.
The biases in mine come simply from the fact that I have sought to keep the
system as simple as possible. In other words,my results are still not
100% statistically valid,but are MORE so than the N.F.L's.
To get a TRUE number to rate all these guys,it is neccessary
to do a bunch more than what we do to get the P.P.R. One thing that has been
ignored,to keep it simple,is variance. In statistical terms,these results
haven't been normalized. This would be very time-consuming,and beyond most
people,so I left it out. An important aim for me was to keep this SIMPLE. My
goal wasn't just to produce more representative results than the N.F.L.,but
also to have a SIMPLER system than the N.F.L. The more people UNDERSTAND how
it works,the BETTER,right?? :-) No good having a formula that only "rocket
scientists" understand. ;-)
Also in the name of keeping it simple,only RAW numbers are
used in the formula. In other words,the results are biased towards years
with a greater number of ATTEMPTS in them. To get a truly representative
number,you'd have to take out these biases,but that would make it all more
complicated,and it's not REALLY going to make THAT big of a difference. Even
with these small biases in it,I have made huge leaps towards getting more
representative results,so I'm happy to leave it there,with an easily
understood formula. :-) If some Statisticians want to take it further,and
REMOVE these biases,that would be good,but it is something beyond the Man in the
street,and is not desire-able in the "for general consumption" model. :-)
Lastly,because the P.P.R. uses ACTUAL numbers for comparison
puposes - not an arbitrary standard - it is NOT N.F.L. or era-specific. Not
only can you compare Passers from different eras,but different LEAGUES.
For example,it is possible to include the C.F.L. years
for people like Warren Moon and Doug Flutie,or the U.S.F.L. years of
Steve Young. In fact,you can even include COLLEGE years! :-) Imagine
being able to calculate a career-rating for Joe Montana that included his
NOTRE DAME years,and not JUST his N.F.L. years. :-) With the P.P.R.,you can
include any era of any league that you have total numbers for.
Now that we've dealt with the mathematical differences, what
about the actual results? As we've seen in the
All-time top-20's - N.F.L. and P.P.R., there
are significant differences between the two systems when rating careers (as a
result of the P.P.R. system taking historical-context into account), so
little comment is needed there, but what about when we use the two systems
for single-season ratings? This takes away the evolutionary aspect of the
game (since we are no longer comparing different players from different eras),
and there might not be much difference.
As it turns out, we DO see players having a
significantly different ranking in one system to the other at times, and
it is often related to interception percentage.
If we look at all qualified Passers 2000,
we see Trent Green at 2nd in both systems, whereas Kurt Warner is 3rd in the
N.F.L. system, but only 9th in the P.P.R. system. If we compare those two, we
see Warner is about 10% better in completion percentage, Green is about 10%
better in touchdown percentage, but Warner is 2.5 times WORSE than Green in
interception percentage (in fact, Warner's interception percentage is 3rd worst
on the list).
The reason for this difference is that the N.F.L.
system is based on a linear-relationship, whereas the P.P.R. system
accurately reflects the exponentially-increasing difficulty.
Consider a Passer who had 30 intercepts in a year.
Obviously some coaching, some practice, and some experience could see that
fairly easily reduced to 25 the next year (all else being equal). Now
consider a Passer who only had 5 intercepts in a year. Probably no amount
of coaching or practice can get that down to zero the next year - you would
have to become "perfect".
If we assume that the latter Passer DID get down to zero
the next year, then in this example we have the N.F.L. system, being based
on linear eqautions, treating the two as having the same improvement - both
decreased their interceptions by the same amount - but the P.P.R. system
reflects the much more difficult achievement of the latter Passer.
A Passer who reduced his interceptions from 2% to 1%
- all else remaining equal - would double his P.P.R., whereas a Passer who
reduced his interceptions from 5% to 4% would only increase his P.P.R. by
20%. The N.F.L. system would increase both ratings by a relatively
equal amount.
The same is true of other categories, but seems to be more
notice-able with intercepts. I haven't done any statistical analysis, but I
am guessing that the variation in intercept percentages is much larger than
in other categories. i.e. there is more difference bewteen the best and worst.
So,in short,the R.P.F.,being a measure of ABSOLUTE
performance,gives VERY similar numbers to the N.F.L's;dividing the R.P.F.
by the R.A.F. - giving us the P.P.R. - en-ables us to compare across eras,as
well as across leagues,unlike the N.F.L's;and the only biases present in the
P.P.R. are ones tht have been CHOSEN to be sacrificed,so as to keep the system
SIMPLE. None of the biases are against a particular style of play,unlike the
N.F.L's system,and the N.F.L's system could HARDLY be called "simple". The
P.P.R. system also accurately reflects that increases in difficulty are
exponential, not linear.