Game Rating Explanation

Congratulations to Florida, UConn, Arizona, and Butler for winning their games and advancing to the Elite 8. I have to say that I was quite saddened when Duke got beaten so badly. But I guess that's what happens when Derrick Williams goes 5-6 from behind the arc and leads the Wildcats on an amazing scoring run to start the second half. So, as sad as I am to see the Blue Devils eliminated (I had them losing in the finals in my bracket), it is good to see a fellow Pac-10 team performing so dominantly in a tough game. This should lead to a good conference season next year in the Pac-12 if all players decide to stay.


Anyways, onto the stats. In this post I will be describing my current method through quick examples and formula discussion. The first thing I started thinking about was the ability that teams can play to. Using the offensive and defensive ratings of the teams in each game, I was able to find a normal distribution curve that would approximately model the "average" playing strength of each team. 


Continue reading after the jump





Offensive Rating(ORtg) = 100 * Pts / (FGA + 0.4 * FTA - 1.07 * (ORB / (ORB + DRB)) * (FGA - FGM) + TO)


This formula is derived from looking at how efficient you are with each possession. A possession can end with a field goal, free throws, or a turnover. The weights on FTA and rebounds are taken from statistical studies and are the accepted weights. When looking at the ORtg, a score of over 100 is generally seen as good while a score below 100 is a poor offensive performance.


Defensive Rating(DRtg) = Points Allowed per 100 possessions


Possessions(POS) = FGA - (ORB / (ORB + DRB)) * (FGA - FGM) * 1.07 + TO + 0.4 * FTA


Using the POS formula will give you an approximation of how many possessions one team had during the game. Once POS and points allowed are known, you can calculate DRtg as PA / POS * 100. Unlike with ORtg, where 100+ is good and 100- is bad, under 100 is a good defensive performance and over 100 is a weak performance. With the judgement being opposite with ORtg and DRtg, this posed a problem when trying to find an overall game rating(GRtg). 


Say a team had a 120 ORtg and a 80 DRtg. This would mean that a team played well on both sides of the ball. So, to find the GRtg for this team you would average the values. This would give the team a GRtg of 100 which is average. Now, a second team has a 70 ORtg and a 130 DRtg. Team B would lose this game (unless their opposition was EXTREMELY bad) but their overall GRtg would again average to 100. As you can see in this example, these two hypothetical teams performed opposite of each other but in the end their GRtg was equal. In order to change this effect, I reworked the DRtg formula so that 100+ would be a good rating while 100- would be bad. The new DRtg formula is as follows:


DRtg = 200 - (PA / POS * 100)


What this does is it keeps the median at 100 but it flips the slope so that my needs would be reflected in the trend line.


Now that we know how to calculate ORtg and DRtg we can start looking at how GRtg was calculated. Teams usually seem to have a better defensive performance at home due to the crowd distracting the opponents. This needs to be taken into effect in order to equalize the ORtg and DRtg of the teams based on where they play. Games played at neutral locations will not have an offensive or defensive modifier due to the neutrality of the crowd. For home games, ORtg is increased by 1.4% while DRtg is decreased by 1.4%. For away games, ORtg is decreased and DRtg is increased. Once these modifiers have been applied, we can then average our ORtg and DRtg in order to find the GRtg. So, this is what the GRtg formula would look like for a home game:


GRtg = (1.014 * ORtg + 0.986 * DRtg) / 2


Well, this should get you guys started in understanding my process for determining average team strength. Tomorrow I will do a post getting into the distribution of these points and how basic win probability can tie in. As of right now I am thinking that this will be a three part series with the third part serving as an overview of everything previously covered and then going into my hypothetical theory about where I am going. As soon as this series is completed I will start posting some data for you guys to look over.


Thanks for reading and keep on checking back for the next part.
-Dan