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 21-7 v.C 10-0 v.D 21-14 v.B 10-7 v.C 14-13 v.D 7-3
Team B v.A 7-21 v.D 3-10 v.C 0-21 v.A 7-10 v.D 3-21 v.C 0-14
Team C v.D 14-7 v.A 0-10 v.B 21-0 v.D 10-3 v.A 13-14 v.B 14-0
Team D v.C 7-14 v.B 10-3 v.A 14-21 v.C 3-10 v.B 21-3 v.A 3-7

Overall Home Away
Team A (6-0) 83-44 (3-0) 52-21 (3-0) 31-23
Team B (0-6) 20-97 (0-3) 10-63 (0-3) 10-34
Team C (4-2) 72-34 (2-1) 48-21 (2-1) 24-13
Team D (2-4) 58-58 (1-2) 27-20 (1-2) 31-38

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 ((83-44) / 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 21-7 v.C 10-0 v.D 21-14 v.B 10-7 v.C 14-13 v.D 7-3
Team B v.A 7-21 v.D 3-10 v.C 0-21 v.A 7-10 v.D 3-21 v.C 0-14
Team C v.D 14-7 v.A 0-10 v.B 21-0 v.D 10-3 v.A 13-14 v.B 14-0
Team D v.C 7-14 v.B 10-3 v.A 14-21 v.C 3-10 v.B 21-3 v.A 3-7
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 pre-season 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 N-day 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!