Power Ratings
by Parrish Heppenstall
Power Ratings are a deadly weapon in any handicapper's arsenal.
No other method allows us to judge as accurately and objectively
the relative strengths of two sports teams. Unlike 'angle'
handicapping systems, Power Ratings (hereafter referred to as
PR's) tell us exactly how many points (or runs) a team should
beat an opponent by. Unlike fundamental handicapping, Power
Ratings are purely objective. No emotion or bias is involved.
If Power Ratings are such an exceptional handicapping tool, why
isn't everybody using them? Well every handicapper worth his or
her salt IS using them. Those who aren't often use excuses such
as 'it's too hard', 'it takes to long', 'I'm not good at math',
etc. If you fall in this category stop reading now. PR's will
take some effort to implement successfully. However if you're
willing to spend the time, this article will help show you how
to calculate Power Rating's sharper than a razor's edge.
Well, let's jump into it. Imagine we have a league of four
teams: A, B, C and D. After 6 games here's how they stand.
Table 1
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
Team A v.B 217 v.C 100 v.D 2114 v.B 107 v.C 1413 v.D 73
Team B v.A 721 v.D 310 v.C 021 v.A 710 v.D 321 v.C 014
Team C v.D 147 v.A 010 v.B 210 v.D 103 v.A 1314 v.B 140
Team D v.C 714 v.B 103 v.A 1421 v.C 310 v.B 213 v.A 37
Overall Home Away
Team A (60) 8344 (30) 5221 (30) 3123
Team B (06) 2097 (03) 1063 (03) 1034
Team C (42) 7234 (21) 4821 (21) 2413
Team D (24) 5858 (12) 2720 (12) 3138
The first score listed is the top team's. Bold scores represent
home games for the top team. The summary shows team record in
parenthesis, points scored and points against for home, away and
overall locations. This is all we will need to calculate POWER
Power Ratings.
Before continuing, let my explain my reasoning for using only
final scores to calculate PR's. While some handicappers use all
sorts of funky statistics in their calculations, what are we
trying to predict? First downs? Fumbles? Points per yard? No, we
want to know the outcome of the game. What basic statistic
better represents this than the final score? If there is a
stronger indicator, I don't know of it. However, it is possible
to modify the final score with these and other statistics to
remove the effects of luck and other variables. I tread
carefully here for one reason; it brings subjectivity back into
the picture. How many points should we add/subtract for a
fumble, blowout or other variable? While not impossible to do
correctly it falls beyond the scope of this article.
EZ Power Ratings
The least painful Power Rating calculation is what I like to
call EZ PR's. It is just the points scored minus points against
divided by number of games played:
(PF  PA) / Games
Using the above formula and overall results only, Team A has an
EZ PR of 6.5 ((8344) / 6). Now to make power ratings easier to
work with it, is advisable to add an arbitrary number to the
result. This will remove negative PR's and generally make our
life easier. I always add 100. Continuing for each team we have:
Table 2
Overall Home Away
Team A 106.5 110.3 102.6
Team B 87.2 82.3 92.0
Team C 106.3 109.0 103.7
Team D 100.0 102.3 97.7
What do these numbers represent? That's easy, and it's the same
for all power ratings created throughout his article. If Team A
were playing Team D at home take the Team A's home PR and
subtract Team D's away PR. The result is how many points Team A
should win or lose by. In this case it would be 110.3  97.7 =
12.6. Team A should win by 12 or 13 points. Obviously a negative
result means the team should lose by that amount.
You may have noticed how I use the location PR not the overall
PR to predict scores. The reason should be obvious. Take a look
at the results in table 2. If we just used overall PR's, we
could be off by as much as 4 points per team. I don't know about
you, but Power Ratings accurate to only ±8 points a game are
worthless to me. Later we will find use for overall PR's as
early season indicators and trend locators.
POWER Power Ratings
EZ Power Ratings have a major flaw. They fail to take into
consideration strength of opposition. A team which beats up on
cellar dwellers is a far cry from a team which can do it to the
upper echelon. How do we account for this in our calculations?
Easily. We average the PR's of a team's opponents and plug it
into this formula:
Adjusted PR = Original PR + (Average PR  100)
For example using Team C's overall PR we first need to calculate
the average PR of their opponents. Go back to table 1 and list
their opponents PR's. We have 100.0, 106.5, 87.2, 100.0, 106.5
and 87.2. The average is 97.9 (587.4 / 6). Using the above
formula Team C's adjusted PR is 106.3 + (97.9  100) = 106.3 +
(2.1) = 106.3  2.1 = 104.2. As we can see Team C's overall
Power Rating has dropped roughly 2 points. Continuing for the
remaining teams we end up with Table 3.
Table 3
Adjusted Overall
Team A 104.3
Team B 91.5
Team C 104.2
Team D 100.0
Calculating the adjusted home/away PR is done basically the same
with a slight twist. To calculate Team A's adjusted home PR we
average their opponent's away PR's. We then plug that result and
Team A's home PR (as the original PR) into the above formula.
When we do, we get the following results:
Table 4
Adjusted Home Adjusted Away
Team A 108.1 100.5
Team B 89.6 99.9
Team C 106.4 102.0
Team D 101.7 98.6
While this is better than EZ PR's, we are not done yet. Why stop
after one adjustment? Why not continue until...until we see what
happens. That is exactly what we will do. For the sake of
brevity we will concern ourselves with only the overall PR's. I
leave home/away PR's as an exercise for the reader. The formula
we will use is:
Adjusted PR = Adjusted PR + (Average PR  Last Averaged PR)
where Average PR is the average of the current opponent adjusted
PR's and Last Averaged PR is the Average PR used in the previous
calculation. The original Adjusted PR is the value listed in
Table 3.
Table 5
Raw PR (EZ) Adjusted 1 Pass 2 Pass 3 Pass 4
Team A 106.5 (100) 104.3 (97.8) 105.1 (98.6) 104.8 (98.3) 104.9
(98.4)
Team B 87.2 (100) 91.5 (104.3) 90.0 (102.8) 90.5 (103.3) 90.4
(103.2)
Team C 106.3 (100) 104.2 (97.9) 104.9 (98.6) 104.7 (98.4) 104.7
(98.4)
Team D 100.0 (100) 100.0 (100) 100.0 (100) 100.0 (100) 100.0
(100)
The value listed in parenthesis is the averaged opponent PR's
for the row. This value is used twice. First for the Average PR
and then again on the next pass as the Last Averaged PR. The
results are interesting. In all cases (except D, which lies on
the league average) The Adjusted PR's occilate and eventually
stabilize. This is exactly what should happen. The stabilized
result are our final POWER Power Ratings.
Front Loaded Power Ratings
While our POWER Power Ratings are good, they can be made even
better. One problem is they fail to reflect recent performance.
All games are weighted equally be it two months or two weeks
ago. There are many ways to solve this problem. The first is by
using only the last N (3,5,10, etc.) games or date cutoff to
calculate the overall, home and away PR's. Just throw out all
games occurring before your cutoff and calculate the PR's
normally. The problem with this is if your team has just
finished an extended homestand or road trip. This will cause
your home/away PR's will either be old (if using last N games)
or inaccurate due to limited games (if using date cutoff).
A better technique would be to calculate all PR's for the full
season and a N game overall PR. Then use the increase/decrease
in the N day overall against the season long overall to tell you
how much to increase the home/away PR's. For example, if your
results show:
Table 6
Team A
Overall 106.0
Home 110.0
Away 102.0
N Day Overall 109.0
that Team A has an increase of 3 points in their last N games
either add or average these points to the home/away PR's for the
current game.
The best solution is to front load your power rating
calculation. Front loading is a process by which most recent
games are weighted more heavily in the power rating
calculations. To see how this could be implemented let us go
back to table 1 and add weights.
Table 1
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
Team A v.B 217 v.C 100 v.D 2114 v.B 107 v.C 1413 v.D 73
Team B v.A 721 v.D 310 v.C 021 v.A 710 v.D 321 v.C 014
Team C v.D 147 v.A 010 v.B 210 v.D 103 v.A 1314 v.B 140
Team D v.C 714 v.B 103 v.A 1421 v.C 310 v.B 213 v.A 37
Weight 1 2 3 4 5 6
The easiest weighting system is incremental. Each subsequent
game is worth one more than the previous. The Power Rating
calculations must then be modified so that this weight is taken
into considerations. Just multiply all scores by the weight and
divide all averages by the total of all the weights. Obviously
we are entering an area where the home computer begins earning
it's price tag.
There are other front loading schemes. Double and triple
incremental, logarithmic and user defined to name a few. Again,
a computer is a necessity when we begin getting this involved.
You now have the ability to calculate razor sharp power ratings.
In the following sections, I will describe how to put them to
practical use.
Pro & College Football
Due to the limited number of games played in a season it is very
important to get accurate power ratings as quickly as possible.
Also distinct power rating for home and away are a must. Trend
tracking is also extremely important. To sum it up, your PR
calculations must be very responsive or they'll be old news
before you can use them. Here's what I do.
Begin the season by modifying last year's team power ratings
based on draft choices, graduation, coaching changes, etc.
Average early season game PR's with this result.
Use the last 2 preseason games as part of the Power Rating
calculation.
Use a heavily front loaded PR calculation. Be very careful
home/away PR's reflect recent overall trends.
Pro Basketball
Due to the large number of games in a season you need not go to
any great lengths to get accurate early season PR's. After about
10 games you should have solid numbers. However Pro Hoops is
extremely streaky. I recommend keeping two PR's. One slightly
front loaded PR for the entire season and one heavily front
loaded (or N day) relying on about the last 10 days. Using one
or a combination of both I am able to catch line errors and most
streaks.
College Basketball
Use the same method as football.
Pro Baseball
Similar to Pro Basketball insofar as the number of games and
streakiness are concerned, baseball is very different as far as
how to use the basic PR's. We all know pitchers are very
important to the outcome of any game. Therefore I recommend
keeping PR's for all teams and pitchers. Then using some
weighting scheme (I use 65% pitcher), combine the team and
pitchers PR's. When you are done you will get an expected run
differential.
This won't do you much good since most baseball games are odds
based. However I will reveal a formula you can use to estimate
run differential based on games odds.
Take the 5 cent line and drop the hundred column and then
reverse the sign. Call this variable 'X'
Plug it into this formula: RunDiff = 0.30 + (0.025 * X) +
(0.0001 * X * X)
This will produce the following run differentials.
Home Odds 170 130 100 130 170
X 70 30 0 30 70
Run Differential 1.94 0.54 0.30 0.96 1.56
As expected the high favorites result in high positive run
differentials, while big underdogs result in large negative run
differentials.
To make a play on a game, compare the expected run differential
against the PR differential. If the variance is large enough
(~1.0 or more runs) take the appropriate team.
Happy Hunting
Using these Power Rating calculations should greatly improve
your handicapping. Even without a computer the EZ PR's should
give you a sizable edge over the uninformed bettor. With a
computer you can calculate power ratings better than even Las
Vegas. However considerable programming skills are needed to
reach this advanced level.
If you like these ideas, but have neither the time nor ability
to execute them, you can always purchase one of my SURE BET
Sports Handicapping software programs. All calculate extremely
accurate season long and Nday split location Power Ratings. Not
to mention providing the user with a host of other invaluable
handicapping tools and information. If you're interested, check
out our full page on the following pages.
No more excuses! POWER Power Ratings are within reach. Apply the
techniques taught in this article and you WILL become a
consistent winner. Good luck!
