After a
"Resistance Break", here we're again. We were working on
TDR and
TOR formulas recently. We've some doubts about both formulas. They have some imperfections. For example, in some cases points created by an assist valued a little bit more than it deserves or offensive rebounds allowed are penalized a little bit harsh for some teams. Yet, main problem occurred in comparisons. We were evaluating every team for same standards. However, every team faces different teams during their EL run. So, they should be evaluated by considering their opponents.
Another problem was fitting the
TDR and
TOR values to normal distribution curve. It wasn't a bad assumption since like most of the things in the world, majority of stats in basketball fits perfectly to normal distribution curve. Yet, after several detailed researches on performances from 2000-01 to 2012-13 seasons, it became more clear that every season's distribution differs from each other. So, I decided to evaluate every season with its own performance curve. I should admit that, using normal distribution curve much more simple since it can be easily calculated by
Mr. Excel. On the other hand,creating a new distribution for respecting season is whole another thing.Yet, it's a burden we have to endure. It will make everything more smoother and accurate. It will eliminate one of the biggest assumptions in the formula which will lead better results. Besides, comparing to fight we put up against tear gases and lovely police kicks lately , it's nothing. :)
Let me start with
Team Performance Ranking aka
TDR. First of all, I should mention about concepts of
play and
PSP. We've mentioned about play at
this post and about PSP at
this post. Basically, a play shows an offense which resets shot clock and ends with beginning of another shot clock. As for PSP
(Projected Score per Play),it shows a team's projected score per play as the name suggests. We calculated everything about offense like field goal percentages, field goal tendencies, foul receiving rates, free throw percentages,offensive rebound rates, probability of scoring second chance points, turnover rates and everything to determine PSP. So, basically PSP shows the efficiency of a play.
I should also mention about a new stat; efficient number of play (
ePl). It's not a whole new stat actually, it's just modified version of play. In ePl, wasted offenses like which ended with turnover or failed field goal attempts are not included. Let me put it this way, quality of an offense can be measured with how many efficient play a team succeed and efficiency of those plays.
In defensive side of the game, quality of defense can be measured with how many efficient plays a team allowes to his opponents and at which level the team keeps its opponents' PSP, as expected. If a team allows low number of efficient play and keeps its opponents' PSP as low as possible, it would be fair to say that the team is defensively sufficient. Yet, it's still not enough. Because we have to analyze its opponents regular offensive performances. Because concept of defence is also about how a team discomforts its opponent. Defending a poor offensive team and defending a great offensive team should not be rewarded equally. It would make comparison of teams more accurate.
Last but not least, I changed one more thing in traditional defensive efficiency measurement system. Points allowed per 100 possession is commonly used while evaluating defensive performances for both European and NBA teams. It was a revolutionary approach,I agree. Yet, something was bugging me since the first day I've encountered this stat. It was evaluating every performance for 100 possession. I've always think there is something wrong with it. Because, a team's performance at a number of possession doesn't necessarily continue while number of possession rises. I mean that number of play could be the most efficient number of play for a team and if the team increases its number of play their efficiency would decrease and points per possession would decrease as well. No one can guarantee that a team which scores
70 points in
70 possession would score
100 points in
100 possession. Maybe it will be
90 points or maybe
110 points, you just can cannot be sure. So,at this new
TDR, I've dedicated myself to solve this problem and glad to say that I've managed it.
Now, that's how this new formula works. First we've calculated the every team's season PSP and ePl numbers. Then, according team's schedules we've determined respecting opponents' performances for every team. That yielded a base to compare. After that, we calculated how these opponents performed against the team. That was the second component for the comparison. ePL was our
'x variable'. Than we've created a
' function y ' which is formed by multiplying
variable x and
'constant a (PSP)' -which is actually not a pure constant since it also includes 'variable x' in it, yet for the sake of simplicity I'm calling it just 'constant a'-. Then we created a
x-y graph. The graph below is an example for a performance function.
As you can see, this fabrication team's
- let's call it Team F- opponents showed better offensive performance in its EL run than they showed against the
Team F. So,
Team F is probably get a high place at defensive ranking list. The axis of the graph shows the number of efficient plays
Team F allowed. It's obvious that dynamics of the defensive competence changes while ePl increases. Now, we have to find its defensive efficiency with numbers for a comparison. I've preferred using areal difference,in other saying taking the integral, to calculate it.Every game starts with "0" play
-obviously-, then
0 will be the lower bound of the integral.
Team F allowed
16 ePL for its opponents so it will be the upper bound. That would do the trick. You see, since I've chose
Team F's ePl as upper bound of integral, I wouldn't need any iteration while comparing teams. Calculating every performance for 100 possession or anything like that would not be needed. Because, every team plays at different level of pace,so they should be rewarded or penalized at that very pace, not at an imaginary pace level. After calculating that, distribution of the whole sample should be found.
First we need to find how sample data
-which consists of defensive performances of every team- is distributed. Then, we should form the probability density function and find the value every team take from cumulative probability function by calculating area under the probability density function. Let me put it that way, what we do here is fitting the defensive performance values between numbers from
0 to
1. It would both make it easier to compare and help using
TDR values in other computations. Because, by using cumulative probability function values, we can evaluate every performance in
0-1 base.
A final note, we add a phase multiplier to make it smoother. Phase multiplier made a small increments by considering how far teams' went last season.
To sum up what I did step-by-step;
- Calculation of PSP and ePl for each team
- Creating a function y (offensive efficiency function) by using teams' PSP and ePl for each team
- Calculating opponents' normal function y values with help of teams' schedule
- Creating opponent's function y -which shows the opponent's performance against team- by using PSP and ePl which are only performed against respecting team
- Integrate both function y with respect to x between 0 and ePl(team allowed) to calculate areal difference
- Fitting all defensive performances to season's distribution curve
- Finding the shares they took from cumulative probability function
- And finally,multiplying these values with phase multipliers.
Now, let's look at the defensive performances of season 2012-13;
No one surprised at #1 I guess. Pascual makes it almost every year. A Greek domination for #2 and #3. Olympiacos was a good defensive team in 2011-12. After Ivkovic left the club, Bartzokas
- admittedly I have some doubts about him at first - made a great job and also carried Olympiacos to a level further, I believe. No matter what people say, after group phase Olympiacos was in my "Most Likely Succeed" list. As for Panathinaikos, I had to say their defensive performance this year surprised me a little. Yes, I know they have a great commander who had won the defensive player of the year countless time and also they have some great defenders like Lasme but also Panathinaikos has Ukic and Gist in its roster. I had a chance to follow them more closely since they've also played in Turkey, and I just can't believe that a team can be one of the best defensive teams with them playing over 20 minutes. I mean come on, we even made up a word from
Gist's name. Let me give an example;
(Let's say Player X made an unnecessary move to block the shot or steal the ball, and as a result he lost his place for nothing and his team allowed an easy basket because of him)
+Dude, did you see what Player X did?
-Yeah, he Gisted very bad.
There is a common say you know;
"You can cut the budgets of Greek basketball teams, you can take their players and coaches,yet they will succeed anyway". If there is not, there should be.
Also, I want to talk about one of my disappointments; Messina. Don't get me wrong neither CSKA nor Messina was unsuccessful,I think. Yet, I was expecting better defensive team from him. Messina has a great reputation at defensive side of the game. After his NBA adventure, it seems to me that he changed his style a little bit. #7 not bad, but comparing to expectations, it's disappointing.
Teams at bottom at the list don't surprise me and I doubt that anyone will surprise.
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