Fun Graphs

[Fan from VT]

Graphs 7 and 8 were exploring the other two major parts of offense, Turnovers and Offensive rebounds.

Interestingly, Turnover rate had basically No correlation independently with wins or with overall offense.

Also, Offensive Rebounding had No correlation independently with wins or overall offense either. Also interesting, there was No correlation between Offensive rebounding rate and a team's overall defensive efficiency either, so Defense appears independent of whether a team is good at getting ORebs. (I just noticed an error on graph 8; the legend says "Diff" but it should say "Def" for Defense. Sorry).


More on ORebs, TOs, and their relation of Offensive Efficiency later.

[action781]

Graphs 5+6 were looking at shooting efficiency and trying to correlate those with wins. I used the two more common measures of shooting efficiency, eFG and TS. I found that both were (not surprisingly) fairly strongly related to overall offensive efficiency, but not perfectly. TS was SLIGHTLY more closely correlated, but probably not by a meaningful amount (.74 vs 73).

I am very surprised that TS is not a more accurate indicator (higher r^2 value) for offensive efficiency.  I mean, the formulas (as I understand them) are almost identical, no?  The only difference I think is that TS has a denominator of shot attempts while offensive eff has a denominator of total possessions?  So the only other effector of offensive efficiency I would think is turnovers?

[Celtics18]

Graphs 5+6 were looking at shooting efficiency and trying to correlate those with wins. I used the two more common measures of shooting efficiency, eFG and TS. I found that both were (not surprisingly) fairly strongly related to overall offensive efficiency, but not perfectly. TS was SLIGHTLY more closely correlated, but probably not by a meaningful amount (.74 vs 73).

I am very surprised that TS is not a more accurate indicator (higher r^2 value) for offensive efficiency.  I mean, the formulas (as I understand them) are almost identical, no?  The only difference I think is that TS has a denominator of shot attempts while offensive eff has a denominator of total possessions?  So the only other effector of offensive efficiency I would think is turnovers?

And offensive rebounds.  Although, as Vermont has pointed out apparently there's not a strong correlation between offensive rebounding and turnovers to offensive efficiency when looked at individually, but obviously they can have a rather large impact on offensive efficiency overall.  The Celtics are a pretty good case in point. 

[Fan from VT]

Graphs 5+6 were looking at shooting efficiency and trying to correlate those with wins. I used the two more common measures of shooting efficiency, eFG and TS. I found that both were (not surprisingly) fairly strongly related to overall offensive efficiency, but not perfectly. TS was SLIGHTLY more closely correlated, but probably not by a meaningful amount (.74 vs 73).

I am very surprised that TS is not a more accurate indicator (higher r^2 value) for offensive efficiency.  I mean, the formulas (as I understand them) are almost identical, no?  The only difference I think is that TS has a denominator of shot attempts while offensive eff has a denominator of total possessions?  So the only other effector of offensive efficiency I would think is turnovers?

This gets into the big debate occurring on the front page a few days ago.

Essentially, offensive efficiency is Points Scored Per Possession. A possession only ends when the other team gets the ball: Turnover, Defensive Rebound off a miss, or Inbounding after a make.

So notice that a possession does not end if the shooting team gets an offensive rebound. In that case, it is actually possible to have more Shots than Possessions.

True Shooting only cares about how efficiently shots go in...from 3, from 2, free throws, etc. But it does not take into account Not Shooting (Turnovers) or Shooting More (Offensive rebounds).

So offensive efficiency is basically the balance of Number of Shots you take Per 100 Possessions and Efficiently Making Those Shots Go In.

For example, Celtics were 7th in the league in True Shooting last year but 24th in offense (in fact they are that dot at 53.5% TS by x-axis that is far below the best fit line!). This is because while their shots went in with very good efficiency, Per 100 Possessions they did not get very many shots off due to turnovers (25th place) and Offensive Rebounds (30th place). Other teams, like LAC and Chicago, had elite offensive efficiency despite worse TS% than the C's because they just shot a lot more per 100 possessions, by low turnovers and higher ORebs.


Because Offensive Efficiency depends on Shot Taking Per 100 possessions (not pure shot taking...that depends more on pace; offensive efficiency depends on Relative more shots, so more shots per possession than the opponent) as well as Shot Making Effectiveness (TS%), Total offensive efficiency can be thought to depend on TOs and ORebs (influencing Shot Taking Opportunities) and TS (effective making). But it was not a pure connection. Clearly TS is strongly correlated, but not perfectly as you noted.

But look at the last graph.



This graph represents a teams Actual Offensive Efficiency relative to their "score" in TOs, ORebs, and TS%. It has a great association. The tricky part was figuring out the relative "value" of TOs vs ORebs vs TS in figuring out how they impacted Offensive Efficiency. Being not a mathematician, I used trial and error, basically, and found that this formula very accurately predicts offensive efficiency:

[(0.55 x OffRebRate) - (1.2 x TORatio) + (2.3 x TS%)]/1.059

The 1.059 is just a correction factor for if you want to use the above formula to try and actually predict an offensive efficiency; using it or not doesn't change the correlation trend.

Basically this implies that all are significantly important in offensive efficiency. TS% is about twice as important as turnovers, and turnovers are twice as important as OffRebs, and TS% is about 4 times as important as OffRebs for a teams offensive efficiency.

The front page debate was that considering the C's were worst in history of league last year at Orebs, but still 7th in TS, which one would you try to change to improve their 24th best offense? Any change in TS% will have a greater relative change in Offensive Efficiency, but I was personally arguing that it would be easier to improve from worst all time to low-average than to improve, say, from 7th in TS to even 4th.

[Fan from VT]

And offensive rebounds.  Although, as Vermont has pointed out apparently there's not a strong correlation between offensive rebounding and turnovers to offensive efficiency when looked at individually, but obviously they can have a rather large impact on offensive efficiency overall.  The Celtics are a pretty good case in point.

Yeah, not independently, but together, with TS, and weighted appropriately there was a very tight association, as evidenced by the last graph

[Celtics18]

Another important factor in offensive efficiency that you haven't mentioned is getting to the line.  I realize that free throw makes are tied in with true shooting percentage, but the Celtics were among the leagues worst teams in free throws made per game last year.  Still, being seventh in true shooting percentage means that the team was very efficient at hitting the shots that they got from the floor.  Getting to the line more would presumably up their true shooting percentage, as well as their offensive efficiency.

I'm guessing, though, that if you turned the numbers into a graph, that free throws made per game (or per possession) would show no more correlation to offensive efficiency as an individual statistic than turnovers or offensive rebounds. 

[Fan from VT]

Graphs 9, 10, 11.





So remember there were graphs that showed that a team's Efficiency Differential (OffEff-DefEff) very strongly (>.91) correlated with actual wins. But I wanted to see if certain factors were more important than other ones in correlating to wins. Graphs 9 and 10 essentially show a moderately good connection between being better in either offensive efficiency or defensive efficiency and winning. Not surprising; if you are better at 50% of the game, you tend to win more. And, not surprisingly, each one independently was not as good as the overall differential between the two for predicting wins.

An improvement in Offensive Efficiency was somewhat more strongly related to an improvement in wins; whether this means being better at offense is modestly more important than defense, I don't know.

Graph 11 was exploring Pace.



I think we are all finished with the idea that Lots of Points Per Game = Good Offense. However, I'm not as certain that we are as finished with the idea that Lots of Points Per Game Allowed = Bad Defense, but we should be just as finished with that as the former previous truism. No matter how fast or slow a team plays, because a possession ends in the same measurable discrete ways, it is your offensive and defensive efficiencies that matter.

However, I wanted to explore Pace.
-Do bad teams play faster to be more entertaining?
-Do bad defensive teams play faster to try to cover up their defense?

Basically, not too surprisingly, there was essentially Zero correlation with a team's pace and Offensive efficiency, Defensive efficiency, Wins, etc.

I assume then that it's completely stylistic and team/athlete dependent for the coach to try to determine if their personnel will maximize their Offensive-Defensive efficiency differential by playing fast or slow.

[Fan from VT]

Another important factor in offensive efficiency that you haven't mentioned is getting to the line.  I realize that free throw makes are tied in with true shooting percentage, but the Celtics were among the leagues worst teams in free throws made per game last year.  Still, being seventh in true shooting percentage means that the team was very efficient at hitting the shots that they got from the floor.  Getting to the line more would presumably up their true shooting percentage, as well as their offensive efficiency.

I'm guessing, though, that if you turned the numbers into a graph, that free throws made per game (or per possession) would show no more correlation to offensive efficiency as an individual statistic than turnovers or offensive rebounds.

I did not look at that independently.

My instinct is that it is fully accounted for in TS.

A possession ends by turnover, missed shot - Dreb, or made shot. So a free throw ends the possession by either a make or a D-Reb, and the number of free throws a team shoots and their rate at hitting them is already accounted for in TS; changing number or percentage of FT's would change TS, so I'm not sure they need to be added in separately; if anything, with a >.99 correlation already, it may get worse if i try to add more stats.

[action781]

Graphs 5+6 were looking at shooting efficiency and trying to correlate those with wins. I used the two more common measures of shooting efficiency, eFG and TS. I found that both were (not surprisingly) fairly strongly related to overall offensive efficiency, but not perfectly. TS was SLIGHTLY more closely correlated, but probably not by a meaningful amount (.74 vs 73).

I am very surprised that TS is not a more accurate indicator (higher r^2 value) for offensive efficiency.  I mean, the formulas (as I understand them) are almost identical, no?  The only difference I think is that TS has a denominator of shot attempts while offensive eff has a denominator of total possessions?  So the only other effector of offensive efficiency I would think is turnovers?

This gets into the big debate occurring on the front page a few days ago.

Essentially, offensive efficiency is Points Scored Per Possession. A possession only ends when the other team gets the ball: Turnover, Defensive Rebound off a miss, or Inbounding after a make.

So notice that a possession does not end if the shooting team gets an offensive rebound. In that case, it is actually possible to have more Shots than Possessions.

True Shooting only cares about how efficiently shots go in...from 3, from 2, free throws, etc. But it does not take into account Not Shooting (Turnovers) or Shooting More (Offensive rebounds).

So offensive efficiency is basically the balance of Number of Shots you take Per 100 Possessions and Efficiently Making Those Shots Go In.

For example, Celtics were 7th in the league in True Shooting last year but 24th in offense (in fact they are that dot at 53.5% TS by x-axis that is far below the best fit line!). This is because while their shots went in with very good efficiency, Per 100 Possessions they did not get very many shots off due to turnovers (25th place) and Offensive Rebounds (30th place). Other teams, like LAC and Chicago, had elite offensive efficiency despite worse TS% than the C's because they just shot a lot more per 100 possessions, by low turnovers and higher ORebs.


Because Offensive Efficiency depends on Shot Taking Per 100 possessions (not pure shot taking...that depends more on pace; offensive efficiency depends on Relative more shots, so more shots per possession than the opponent) as well as Shot Making Effectiveness (TS%), Total offensive efficiency can be thought to depend on TOs and ORebs (influencing Shot Taking Opportunities) and TS (effective making). But it was not a pure connection. Clearly TS is strongly correlated, but not perfectly as you noted.

But look at the last graph.



This graph represents a teams Actual Offensive Efficiency relative to their "score" in TOs, ORebs, and TS%. It has a great association. The tricky part was figuring out the relative "value" of TOs vs ORebs vs TS in figuring out how they impacted Offensive Efficiency. Being not a mathematician, I used trial and error, basically, and found that this formula very accurately predicts offensive efficiency:

[(0.55 x OffRebRate) - (1.2 x TORatio) + (2.3 x TS%)]/1.059

The 1.059 is just a correction factor for if you want to use the above formula to try and actually predict an offensive efficiency; using it or not doesn't change the correlation trend.

Basically this implies that all are significantly important in offensive efficiency. TS% is about twice as important as turnovers, and turnovers are twice as important as OffRebs, and TS% is about 4 times as important as OffRebs for a teams offensive efficiency.

The front page debate was that considering the C's were worst in history of league last year at Orebs, but still 7th in TS, which one would you try to change to improve their 24th best offense? Any change in TS% will have a greater relative change in Offensive Efficiency, but I was personally arguing that it would be easier to improve from worst all time to low-average than to improve, say, from 7th in TS to even 4th.

Very nice work.

So your "weighted sum" is obtained by the [(0.55 x OffRebRate) - (1.2 x TORatio) + (2.3 x TS%)]/1.059 formula?

So, you say those weights are by trial and error?  Have you thought about weighing them based on what % of possessions have an O-Reb (tricky with multiple o-boards in some possessions), what % of possessions end in turnover, and weighing TS by the remaining %?

And this really shows you how horrific of an offensive team Charlotte was last year - geesh!

[Fan from VT]

Very nice work.

So your "weighted sum" is obtained by the [(0.55 x OffRebRate) - (1.2 x TORatio) + (2.3 x TS%)]/1.059 formula?

So, you say those weights are by trial and error?  Have you thought about weighing them based on what % of possessions have an O-Reb (tricky with multiple o-boards in some possessions), what % of possessions end in turnover, and weighing TS by the remaining %?

And this really shows you how horrific of an offensive team Charlotte was last year - geesh!

Quick comment: I had a typo. 1.059 was the correction factor for '10-'11. For '11-'12 it was 1.050.

Thanks. I did not approach the weighting system with any kind of organized approach, really. I could check it out. It would essentially change the coefficients to TO/100 x TO, OReb/100 x OReb, and [1-(TO/100+Oreb/100)] for TS%.

Basically, I just summed them all together, and found there wasn't a great association. But then I tweaked their relative value by adding coefficients one at a time and changing them until I found their "peak" R^2 value. Then I moved on to the next one. Not sure how tighter I can get!

Just checked, and it's not close. .51 R^2 or so.


Also, I want to be clear that the last graph shows the "weighted sum" on the x axis that i used as I was exploring how tightly TO, TS, and OReb could be correlated with OffEff. So the formula there is just (0.55 x OffRebRate) - (1.2 x TORatio) + (2.3 x TS%).

I then wanted to be able to adjust a team's Orebs, TOs, or TS and predict how this would change their OffEff, so I went back, compared the "weighted sum" to teams' actual OffEffs and found that the "weighted sum" was a 1.050 overestimate of OffEff. So by dividing by 1.05 you keep the same R^2 association, but now you can actually use it to estimate a real team's Off Eff.

For example, Boston last year had an OffEff of 98.9 last season, with ORR 19.7, TO 25.7, and TS 53.3. By the leaguewide formula I found, using their ORR, TO, and TS would estimate them to have an OffEff of 98.1. So close. Now you could say you wanted them to have an OffEff of 12th, like their championship season I believe. OffEff of 103 would get you there.

So how do the C's get there? Well if they just increased their TS to 55.7 they'd be right there. Of course that would mean they were 3rd in the league in TS, up from 7th this past year. Hard to do, but not impossible.

Or they could cut down their TOs. Reducing their TO ratio from 25.7 to 21.5 would do it. Of course that would be second best in the league, and their 25th ranking is the best they've done in the KG era.

Or they could increase ORebs. Just changing to 28.8 would do it, but that would be 9th place last year. Likely an unreasonable jump.

However, just going from Putrid to 18th(26.7) in ORebs by itself would increase their OffEff to 101.8 (17th) and represent several more wins than last season's 24th mark in OffEff.

So probably, if the C's want to be a better offensive team, they need to make modest gains across the board. Say they go from Putrid to 18th or so in ORebs, then stay the same in TOs. Then a smaller bump in TS just to 54% (5th in the league instead of 7th) gets them to be a top 12 offense at 103 OffEff. If they do that while still being 2nd or so in Defense, that's a truly improved team.

[LEHGOCELTICS]

Wow this is incredible. How long did this take?

[Fan from VT]

Wow this is incredible. How long did this take?

Honestly? 2 hours a day from Friday over the weekend. Generally while watching football or something else.

[mmmmm]

Improved Graph 1.

-Now shows Point Diff as a league rank, showing the decreasing trend.

-Also added rank in Wins, showing the decreasing place in the standings each season.

-Note: Difficult to see both Point Diff and Wins, as the C's league rank in these two categories (not surprisingly, they are tightly correlated) were identical for most seasons.

Great job on all of this!

I'll try to toss in a few comments on the others, but the only graph I don't really like is ... this one.

The reason is, the relative rankings aren't really comparable across categories.   For example, last year, in real terms, when you pace adjust and account for number of opponent misses, the difference between being first and last in Defensive Rebounding Rate was just a couple of rebounds per game - which is almost in the game-to-game noise.   Not meaningless, but far less dramatic that appears by simply looking at the rankings of '1st' vs '30th'.   So while the chart may show a dramatic fall in the rankings from year to year in a category, it may not mean as much in real terms for one category as it does in another category.

Still, it is interesting to look at the rankings anyway.   So this is a pretty minor quibble.

[mmmmm]

Graph 11 was exploring Pace.



I think we are all finished with the idea that Lots of Points Per Game = Good Offense. However, I'm not as certain that we are as finished with the idea that Lots of Points Per Game Allowed = Bad Defense, but we should be just as finished with that as the former previous truism. No matter how fast or slow a team plays, because a possession ends in the same measurable discrete ways, it is your offensive and defensive efficiencies that matter.

However, I wanted to explore Pace.
-Do bad teams play faster to be more entertaining?
-Do bad defensive teams play faster to try to cover up their defense?

Basically, not too surprisingly, there was essentially Zero correlation with a team's pace and Offensive efficiency, Defensive efficiency, Wins, etc.

I assume then that it's completely stylistic and team/athlete dependent for the coach to try to determine if their personnel will maximize their Offensive-Defensive efficiency differential by playing fast or slow.

Yes, I made a comment to this extent a week or two ago when some article linked on the front page was confusing our 'pace' with 'fast break'.   A fast break offense - which means scoring quickly on a possession - is good.  But that's not the same thing as pace.   You arguably want a slow pace on defense - force the opponent to use up a lot of clock - while playing a fast pace on offense.

I posted some results last year looking at pace versus playoff depth and found that, at least for Celtics teams over the last 30 years or so, we only rarely got as far as the ECF with a team that played at a high pace.  Most of our teams that made it deep in the playoffs were very slow paced teams.

I haven't done a league-wide study, but I suspect that is true in general.  I think the pace of play tends to slow down dramatically in the playoffs, with the more even talent and better defenses.

In other words, while pace has no strong correlation with regular season wins, I suspect it has a stronger correlation with playoff success.

Admittedly, though, that suspicion needs to be tested by looking at the data.

[Fan from VT]

Improved Graph 1.

-Now shows Point Diff as a league rank, showing the decreasing trend.

-Also added rank in Wins, showing the decreasing place in the standings each season.

-Note: Difficult to see both Point Diff and Wins, as the C's league rank in these two categories (not surprisingly, they are tightly correlated) were identical for most seasons.

Great job on all of this!

I'll try to toss in a few comments on the others, but the only graph I don't really like is ... this one.

The reason is, the relative rankings aren't really comparable across categories.   For example, last year, in real terms, when you pace adjust and account for number of opponent misses, the difference between being first and last in Defensive Rebounding Rate was just a couple of rebounds per game - which is almost in the game-to-game noise.   Not meaningless, but far less dramatic that appears by simply looking at the rankings of '1st' vs '30th'.   So while the chart may show a dramatic fall in the rankings from year to year in a category, it may not mean as much in real terms for one category as it does in another category.

Still, it is interesting to look at the rankings anyway.   So this is a pretty minor quibble.

Thanks for the comment mmmmmmmmmm.

I like this one, for a couple reasons with a couple caveats.

1. It is useful for looking at trends. I think that 82 games is enough that a small difference may still be significant and not just noise, and over a few seasons ends up showing trends. Trends then provide good fodder for self reflection and debate:
-Why are the trends happening? Is it decline/improvement of current players, changes in coaching, or poor/good roster changes year to year?
-How could you change the trends?
-Do you need to change the trends?
-Do the particular trends serve as a harbinger for change in other trends?
(For example on the celtics, everything has dropped off except defense. Is this because defense is totally unrelated to other things, or does it indicate slipping athleticism that will inevitably catch up to defense as well, or does it indicate that due to declining abilities the C's have had to intentionally sacrifice some areas to maintain a particular area of emphasis?)

2. The Caveat: you are right that a relative change in value does not necessarily reflect how much that impacted your team. But it shows where to look. From the other data, it does appear that TS% is about 4 times as impactful on your offense compared to ORebs, and twice as impactful compared to Turnovers. So knowing that, you can decide what/how you want to improve your team.

Edit: 3. The other thing about ranks is that for whatever reason, be it reffing, rule emphasis, etc., absolute benchmarks seem to change year to year.

For example, Last season the C's were 24th in the league in offensive efficiency, at 98.9. So you'd ask, "why can't they get back to the year before?" Well the year before they were at 104; had they duplicated that they would have ended up 7th best last season in offensive efficiency. But they were not that good in 2011, as that 104 mark was only 17th in the league!

So which is more "accurate" an expectation? That last year's C's should have been "as good as" the year before, at 104, good for 7th in the league? Or that last year's team should have been "as good as" the year before in terms of maintaining 17th place in offense.

Due to the year to year changes across the league, when looking at a team's change from year to year I think it is helpful to look at rankings to see how a team has improved or regressed.

After all, if their offensive efficiency had been 101.7 last year, it would have been "down" from 104 the year before, but it would still have been 17th place just like the year before because ALL offenses fell off last year.