Value of One and Bonehead Plays

[bobf]

First, the Value of One. By that I mean, how many wins per season will a team add by adding just one point to the team's point differential. It turns out to be +2.6 wins. Here is a plot of point differential vs wins for the entire NBA for the past eight seasons. The plot shows it's basically linear. A linear regression comes out to

Season Wins = 41.00 + 2.64 x Point Differential Per Game



The moral is, if you can somehow add say +3 points to your team's point differential, you can take an average team (41-41) and turn them into a (49-33) team.

That leads me to Bonehead Plays. A Bonehead Play is a play that costs your team points, and you did it (the action not the result) on purpose.

Here is my list of top Bonehead Plays. I'm sure you can think of more. The first two are the most critical and easiest to avoid.

1. Fouling a 3 point shooter. Cost ~1.6 points. Quit trying to block the shot, quit running at the shooter out of control. Just get a hand up and contest rationally.

2. Fouling a 2 point jump-shooter. Cost ~0.6. Same idea. Jumping to try to block, or being overly aggressive on a jump shooter not only creates fouls, it takes you out of the play. Get a hand up and complete the play by boxing out and going for the rebound. You can do neither from the air.

3. Poor Shot selection. The difference between a Blazers' great shot and a poor shot is as much as 0.4 points. Here are the approx. value of various Blazer shots. 3 pointers (CJ 1.25, Dame 1.18, Dame "bomb" 1.12). At the rim (Dame 1.21, Turner 1.20, Aminu 1.19, CJ 1.18, Nurk 1.11, Napier 1.11). Mid-range i.e. 5+ feet (CJ 0.99, Napier 0.93, Damian 0.92, Turner 0.92, Nurk 0.84, Aminu 0.79). Stop choosing to take a sub-par shots with lots of shot clock.

4. High risk low reward passes. A turnover costs you about 1.2 points. Examples. (1) Dame fires a long pass to CJ which is nearly stolen. CJ catches the pass only to find that the defense was fully back, and he's going one on three. What was the point of that pass? (2) Nurk makes a risky pass to Aminu in the paint. The pass barely gets there. Chief finds himself amidst three defenders.

5. Reckless fouling in general. The cost of putting opponents in the penalty is hard to estimate. But we all know it's terrible (last game 3rd quarter vs Warriors it almost cost us the game). You get 4 free fouls per quarter. "Use" them sparingly playing aggressive defense, causing turnovers or stripping a player at the rim. Not on jump shooters. Not carelessly.

6. Passing up an open 3 pointer because it doesn't feel right. Take the damn shot. Even a mediocre 3-point shooter can hit 33% of his open 3's. That is actually a very good shot. Passing it up often leads to either a travel, stepping out of bounds, or a 3 second call on your big man who thought you were going to shoot and stayed in the paint to grab the rebound.

In my estimation, teams easily give up 5+ points per game on Bonehead Plays.

That's 13 games per year.

 

[Boob-No-More]

First, the Value of One. By that I mean, how many wins per season will a team add by adding just one point to the team's point differential. It turns out to be +2.6 wins. Here is a plot of point differential vs wins for the entire NBA for the past eight seasons. The plot shows it's basically linear. A linear regression comes out to

Season Wins = 41.00 + 2.64 x Point Differential Per Game

View attachment 19339

The moral is, if you can somehow add say +3 points to your team's point differential, you can take an average team (41-41) and turn them into a (49-33) team.

That leads me to Bonehead Plays. A Bonehead Play is a play that costs your team points, and you did it (the action not the result) on purpose.

Here is my list of top Bonehead Plays. I'm sure you can think of more. The first two are the most critical and easiest to avoid.

1. Fouling a 3 point shooter. Cost ~1.6 points. Quit trying to block the shot, quit running at the shooter out of control. Just get a hand up and contest rationally.

2. Fouling a 2 point jump-shooter. Cost ~0.6. Same idea. Jumping to try to block, or being overly aggressive on a jump shooter not only creates fouls, it takes you out of the play. Get a hand up and complete the play by boxing out and going for the rebound. You can do neither from the air.

3. Poor Shot selection. The difference between a Blazers' great shot and a poor shot is as much as 0.4 points. Here are the approx. value of various Blazer shots. 3 pointers (CJ 1.25, Dame 1.18, Dame "bomb" 1.12). At the rim (Dame 1.21, Turner 1.20, Aminu 1.19, CJ 1.18, Nurk 1.11, Napier 1.11). Mid-range i.e. 5+ feet (CJ 0.99, Napier 0.93, Damian 0.92, Turner 0.92, Nurk 0.84, Aminu 0.79). Stop choosing to take a sub-par shots with lots of shot clock.

4. High risk low reward passes. A turnover costs you about 1.2 points. Examples. (1) Dame fires a long pass to CJ which is nearly stolen. CJ catches the pass only to find that the defense was fully back, and he's going one on three. What was the point of that pass? (2) Nurk makes a risky pass to Aminu in the paint. The pass barely gets there. Chief finds himself amidst three defenders.

5. Reckless fouling in general. The cost of putting opponents in the penalty is hard to estimate. But we all know it's terrible (last game 3rd quarter vs Warriors it almost cost us the game). You get 4 free fouls per quarter. "Use" them sparingly playing aggressive defense, causing turnovers or stripping a player at the rim. Not on jump shooters. Not carelessly.

6. Passing up an open 3 pointer because it doesn't feel right. Take the damn shot. Even a mediocre 3-point shooter can hit 33% of his open 3's. That is actually a very good shot. Passing it up often leads to either a travel, stepping out of bounds, or a 3 second call on your big man who thought you were going to shoot and stayed in the paint to grab the rebound.

In my estimation, teams easily give up 5+ points per game on Bonehead Plays.

That's 13 games per year.

So, correlation or causation: more minutes for Collins, fewer minutes for Aminu = fewer boneheaded plays = more wins?

Might also explain why Stotts prefers Ed Davis over Nurk in the 4th quarter of close games.

BNM

 

[bobf]

I think it's clear that increasing point differential causes more wins. I was surprised about the degree. My point was not for Stotts to play the players who make fewer boneheaded plays. Nurk & Aminu are two of my favorite players and their positives outweigh their boneheadedness. My point is pick the low hanging fruit - coach should teach players which things are boneheaded and why, and insist that players reduce those decisions.

 

[Pinwheel1]

Totally agree with this theory. Recently we have cut down on bonehead plays and it has made a difference. Like you say most games are decided by such a small amount, a few less mistakes become huge.

 

[bobf]

Totally agree with this theory. Recently we have cut down on bonehead plays and it has made a difference. Like you say most games are decided by such a small amount, a few less mistakes become huge.

Yes, the Warriors game was a prime example. Blazers committed very few boneheaded plays. Warriors had a ton of them. I think they fouled the 3-pointer shooter three times. Those were not just accidents. They were either trying to block the shot or hyper-aggressively running at the shooter. I see that over and over in the NBA. Same thing with 2 point shooters. What is the point of turning a 40% shot into an 80% shot with a possible and one. A mid-range two is rarely a great shot. You got them to take a marginal shot. Don't foul them for god's sake.

 

[Wizard Mentor]

First, the Value of One. By that I mean, how many wins per season will a team add by adding just one point to the team's point differential. It turns out to be +2.6 wins. Here is a plot of point differential vs wins for the entire NBA for the past eight seasons. The plot shows it's basically linear. A linear regression comes out to

Season Wins = 41.00 + 2.64 x Point Differential Per Game

View attachment 19339

The moral is, if you can somehow add say +3 points to your team's point differential, you can take an average team (41-41) and turn them into a (49-33) team.

That leads me to Bonehead Plays. A Bonehead Play is a play that costs your team points, and you did it (the action not the result) on purpose.

Here is my list of top Bonehead Plays. I'm sure you can think of more. The first two are the most critical and easiest to avoid.

1. Fouling a 3 point shooter. Cost ~1.6 points. Quit trying to block the shot, quit running at the shooter out of control. Just get a hand up and contest rationally.

2. Fouling a 2 point jump-shooter. Cost ~0.6. Same idea. Jumping to try to block, or being overly aggressive on a jump shooter not only creates fouls, it takes you out of the play. Get a hand up and complete the play by boxing out and going for the rebound. You can do neither from the air.

3. Poor Shot selection. The difference between a Blazers' great shot and a poor shot is as much as 0.4 points. Here are the approx. value of various Blazer shots. 3 pointers (CJ 1.25, Dame 1.18, Dame "bomb" 1.12). At the rim (Dame 1.21, Turner 1.20, Aminu 1.19, CJ 1.18, Nurk 1.11, Napier 1.11). Mid-range i.e. 5+ feet (CJ 0.99, Napier 0.93, Damian 0.92, Turner 0.92, Nurk 0.84, Aminu 0.79). Stop choosing to take a sub-par shots with lots of shot clock.

4. High risk low reward passes. A turnover costs you about 1.2 points. Examples. (1) Dame fires a long pass to CJ which is nearly stolen. CJ catches the pass only to find that the defense was fully back, and he's going one on three. What was the point of that pass? (2) Nurk makes a risky pass to Aminu in the paint. The pass barely gets there. Chief finds himself amidst three defenders.

5. Reckless fouling in general. The cost of putting opponents in the penalty is hard to estimate. But we all know it's terrible (last game 3rd quarter vs Warriors it almost cost us the game). You get 4 free fouls per quarter. "Use" them sparingly playing aggressive defense, causing turnovers or stripping a player at the rim. Not on jump shooters. Not carelessly.

6. Passing up an open 3 pointer because it doesn't feel right. Take the damn shot. Even a mediocre 3-point shooter can hit 33% of his open 3's. That is actually a very good shot. Passing it up often leads to either a travel, stepping out of bounds, or a 3 second call on your big man who thought you were going to shoot and stayed in the paint to grab the rebound.

In my estimation, teams easily give up 5+ points per game on Bonehead Plays.

That's 13 games per year.

Love the analysis. So, take these comments with a grain of salt.

Ideally, your "Bone-Headed" play list at some point should be accompanied by an "Exceptional" play list which adds extra points per game.

Some of the players who make bone-headed plays also make exceptional plays (e.g. Russ).

Nate Mcmillan was a coached who hated turnovers, but sometimes this emphasis leads to less aggression and less efficiency. That's one of the reasons Sarge has lost credibility with the s2 community.

Drexler once said that turnovers are an overrated stats because if you're not making turnovers, you're not trying to do anything.

So, yes, the goal is to "allow errors of commission, but not those of omission" (John Wooden).

In the recent years, Aminu has been our biggest "bonehead" on the offensive end of the court, and I have noticed a lot Aminu fast break turnovers this year. Perhaps thats
one of the reasons we are playing better.

Your list does not include defensive plays, where Biebs would dominate the boneheaded play category (regardless of how many swish3s he makes).

 

[BBert]

Totally agree with this theory. Recently we have cut down on bonehead plays and it has made a difference. Like you say most games are decided by such a small amount, a few less mistakes become huge.

I don't know what the stats say, but earlier in the season there were games where the Blazers just gave the ball away on BONEHEAD turnovers like a grandma giving away candy on Halloween. Sometimes in bunches. Turnovers = Losses. I think Stotts feels the same way. Hence, Ed and Zach have been playing 4th quarters.

 

[bobf]

Love the analysis. So, take these comments with a grain of salt.

Ideally, your "Bone-Headed" play list at some point should be accompanied by an "Exceptional" play list which adds extra points per game.

Some of the players who make bone-headed plays also make exceptional plays (e.g. Russ).

Nate Mcmillan was a coached who hated turnovers, but sometimes this emphasis leads to less aggression and less efficiency. That's one of the reasons Sarge has lost credibility with the s2 community.

Drexler once said that turnovers are an overrated stats because if you're not making turnovers, you're not trying to do anything.

So, yes, the goal is to "allow errors of commission, but not those of omission" (John Wooden).

In the recent years, Aminu has been our biggest "bonehead" on the offensive end of the court, and I have noticed a lot Aminu fast break turnovers this year. Perhaps thats
one of the reasons we are playing better.

Your list does not include defensive plays, where Biebs would dominate the boneheaded play category (regardless of how many swish3s he makes).

My idea of Bonehead plays is that every team gives away lots of points by easily correctable decisions. I really can't think of a way to just "decide" to make exceptional plays. Maybe there is, but I can't think of any.

Yeah, I don't advocate going into a shell to avoid making mistakes. There is a trade-off between risk & reward and I don't fault players trying to make plays. Sometimes you even have to go with "negative EV" plays in order for players to learn. Like posting up Nurk or Zach is probably bad for or offense right now. But how are they gonna learn?

As for Meyers Leonard, does he make a lot of bonehead defensive plays? I'm probably not enough of a basketball wiz to notice those. What I see with him is a player who just cannot defend at the rim. He just can't time it no matter how hard he tries. In contrast, Nurk intimidates the hell out of guards at the rim because he times his contest perfectly and goes to the exact correct spot in the air, second nature.

 

[bobf]

I don't know what the stats say, but earlier in the season there were games where the Blazers just gave the ball away on BONEHEAD turnovers like a grandma giving away candy on Halloween. Sometimes in bunches. Turnovers = Losses. I think Stotts feels the same way. Hence, Ed and Zach have been playing 4th quarters.

I think so. Against Warriors I counted two or three bonehead plays and they were of the more minor variety. That's exceptionally low. Early in the season I could count typically 10 and sometimes 15 per game. That's one reason we are winning. The other big reason I think is we figured out (partially) how to deal with teams who decide to shut down Dame & CJ at all costs.

 

[SportsAndWhine]

I have seen some very interesting differences between games 1-54 and games 55-66, but they are of a nature so sensitive to my jinx meter that I'm afraid of even mentioning them for fear of breaking the spell. Sufficed to say, as much as we've been improving on our boneheaded plays, the most recent staff hire by Paul Allen appears to be paying off handsomely.

Running the math on the points gained through this aspect alone (+4.3 points), our win percentage between games 55-82 would be .730, which would get us to 49 or maybe even 50 wins. It's interesting to me how this agrees so much with all the automated winbot predictions like fivethirtyeight's.

 

[bobf]

So, correlation or causation: more minutes for Collins, fewer minutes for Aminu = fewer boneheaded plays = more wins?

Might also explain why Stotts prefers Ed Davis over Nurk in the 4th quarter of close games.

BNM

Your "correlation or causation" comment got me thinking more. It's a totally a valid point. Increasing point differential by 1 point certainly causes more wins. But not necessarily +2.64 wins as my graph shows. Because winning also causes point differential. Like if a team is up by 5 points with 30 seconds left, you get intentional fouls which inflates point differential. Not sure how to separate the two.

 

[Wizard Mentor]

My idea of Bonehead plays is that every team gives away lots of points by easily correctable decisions. I really can't think of a way to just "decide" to make exceptional plays. Maybe there is, but I can't think of any.

Yeah, I don't advocate going into a shell to avoid making mistakes. There is a trade-off between risk & reward and I don't fault players trying to make plays. Sometimes you even have to go with "negative EV" plays in order for players to learn. Like posting up Nurk or Zach is probably bad for or offense right now. But how are they gonna learn?

As for Meyers Leonard, does he make a lot of bonehead defensive plays? I'm probably not enough of a basketball wiz to notice those. What I see with him is a player who just cannot defend at the rim. He just can't time it no matter how hard he tries. In contrast, Nurk intimidates the hell out of guards at the rim because he times his contest perfectly and goes to the exact correct spot in the air, second nature.

Good post. Your "Bonehead plays" drive coaches and fans to distraction.

I mostly ball-watch, but from the complaints here on s2, Bieb's out of position all the time. One person out of position can ruin an entire defense, which is (one of the
reasons) why he doesn't play.

 

[riverman]

Turnovers via pass are often a fine line between a great pass and a turnover...like a tennis serve there's a fraction of an inch between an ace serve and a net serve but you don't start serving softballs just so you can get a serve in...you continue to bring the heat...passing a basketball in traffic is very similar...getting stripped is a bonehead turnover though or throwing it in the stands also moving picks and 3 second violations...bonehead turnovers

 

[Wizard Mentor]

First, the Value of One. By that I mean, how many wins per season will a team add by adding just one point to the team's point differential. It turns out to be +2.6 wins. Here is a plot of point differential vs wins for the entire NBA for the past eight seasons. The plot shows it's basically linear. A linear regression comes out to

Season Wins = 41.00 + 2.64 x Point Differential Per Game

View attachment 19339

The moral is, if you can somehow add say +3 points to your team's point differential, you can take an average team (41-41) and turn them into a (49-33) team.

That leads me to Bonehead Plays. A Bonehead Play is a play that costs your team points, and you did it (the action not the result) on purpose.

Here is my list of top Bonehead Plays. I'm sure you can think of more. The first two are the most critical and easiest to avoid.

1. Fouling a 3 point shooter. Cost ~1.6 points. Quit trying to block the shot, quit running at the shooter out of control. Just get a hand up and contest rationally.

2. Fouling a 2 point jump-shooter. Cost ~0.6. Same idea. Jumping to try to block, or being overly aggressive on a jump shooter not only creates fouls, it takes you out of the play. Get a hand up and complete the play by boxing out and going for the rebound. You can do neither from the air.

3. Poor Shot selection. The difference between a Blazers' great shot and a poor shot is as much as 0.4 points. Here are the approx. value of various Blazer shots. 3 pointers (CJ 1.25, Dame 1.18, Dame "bomb" 1.12). At the rim (Dame 1.21, Turner 1.20, Aminu 1.19, CJ 1.18, Nurk 1.11, Napier 1.11). Mid-range i.e. 5+ feet (CJ 0.99, Napier 0.93, Damian 0.92, Turner 0.92, Nurk 0.84, Aminu 0.79). Stop choosing to take a sub-par shots with lots of shot clock.

4. High risk low reward passes. A turnover costs you about 1.2 points. Examples. (1) Dame fires a long pass to CJ which is nearly stolen. CJ catches the pass only to find that the defense was fully back, and he's going one on three. What was the point of that pass? (2) Nurk makes a risky pass to Aminu in the paint. The pass barely gets there. Chief finds himself amidst three defenders.

5. Reckless fouling in general. The cost of putting opponents in the penalty is hard to estimate. But we all know it's terrible (last game 3rd quarter vs Warriors it almost cost us the game). You get 4 free fouls per quarter. "Use" them sparingly playing aggressive defense, causing turnovers or stripping a player at the rim. Not on jump shooters. Not carelessly.

6. Passing up an open 3 pointer because it doesn't feel right. Take the damn shot. Even a mediocre 3-point shooter can hit 33% of his open 3's. That is actually a very good shot. Passing it up often leads to either a travel, stepping out of bounds, or a 3 second call on your big man who thought you were going to shoot and stayed in the paint to grab the rebound.

In my estimation, teams easily give up 5+ points per game on Bonehead Plays.

That's 13 games per year.

I'm planning on using your graph for a homework assignment. Is that OK? Did you make the graph? What is the data that you're using?

 

[bobf]

I'm planning on using your graph for a homework assignment. Is that OK? Did you make the graph? What is the data that you're using?

Sure you can use it. Yes, I created the graph in Excel using W/L and +/- data from here:
https://stats.nba.com/teams/traditional

 

[bobf]

I tried another approach to get the "value of one point". My previous method had a defect that winning inflates point-differential due to intentional fouling at the end of the game. My new method probably has some flaws too, but much less I think.

I got box scores from last year and this year. I took the cumulative scores to obtain point differential at the end of each of the first three quarters and then correlate that with win or loss:

If the score is even... what % did a team win.
If a team is up +1... what % did that team win.
If a team is up +2... what % did that team win.
etc.
I did that for end of Q1, end of Q2, end of Q3 and graphed the results.



If you follow the graphs, one point is worth about:
2+% at end of 1st quarter or +1.7 wins per season.
3% at end of 2nd quarter or +2.5 wins per season
4% to 5% at end of 3rd quarter in fairly close games or +3 to +4 games (that's a lot for just one point!)
4th quarter is likely even more!

What I'm trying to show is that one point is worth a lot more than we imagine over the course of a season. Bonehead plays are both costly and easily avoided.

I'm seeing that the Blazers are committing far less bonehead plays than earlier in the season. Watch how careful Blazers are to not foul jump shooters. Dame has been fouled on 3's so many times in the past few games. Blazers have avoided that and even rarely foul 2 point jump shooters.

Against the Clippers we played great overall. Clippers made way more Bonehead plays. Nevertheless we still commited too many. Examples from Clippers game:
- Shabazz fancy globetrotters pass, turn-over, fast-break. 2 points lost (-1 us, +1 them).
- Shabazz passed on wide open three, drove, 3 seconds on Nurk. Shabazz's fault. 1 point lost.
- Aminu gets ORB and forces up a low % inside shot instead of kicking it back out like Harkless did.
- Turner, taking long mid-range shot with lots of shot clock.
- Nurk, also taking long mid-range shots. He made them, but they are sub-par shots.

 

[PtldPlatypus]

I tried another approach to get the "value of one point". My previous method had a defect that winning inflates point-differential due to intentional fouling at the end of the game. My new method probably has some flaws too, but much less I think.

I got box scores from last year and this year. I took the cumulative scores to obtain point differential at the end of each of the first three quarters and then correlate that with win or loss:

If the score is even... what % did a team win.
If a team is up +1... what % did that team win.
If a team is up +2... what % did that team win.
etc.
I did that for end of Q1, end of Q2, end of Q3 and graphed the results.

View attachment 19585

If you follow the graphs, one point is worth about:
2+% at end of 1st quarter or +1.7 wins per season.
3% at end of 2nd quarter or +2.5 wins per season
4% to 5% at end of 3rd quarter in fairly close games or +3 to +4 games (that's a lot for just one point!)
4th quarter is likely even more!

What I'm trying to show is that one point is a lot worth more than we imagine over the course of a season. Bonehead plays are both costly and easily avoided.

I'm seeing that the Blazers are committing far less bonehead plays than earlier in the season. Watch how careful Blazers are to not foul jump shooters. Dame has been fouled on 3's so many times in the past few games. Blazers have avoided that and even rarely foul 2 point jump shooters.

Against the Clippers we played great overall. Clippers made way more Bonehead plays. Nevertheless we still commited too many. Examples from Clippers game:
- Shabazz fancy globetrotters pass, turn-over, fast-break. 2 points lost (-1 us, +1 them).
- Shabazz passed on wide open three, drove, 3 seconds on Nurk. Shabazz's fault. 1 point lost.
- Aminu gets ORB and forces up a low % inside shot instead of kicking it back out like Harkless did.
- Turner, taking long mid-range shot with lots of shot clock.
- Nurk, also taking long mid-range shots. He made them, but they are sub-par shots.

You gotta send some of this stuff to @Dan Marang . he'd eat it up.

 

[bobf]

You gotta send some of this stuff to @Dan Marang . he'd eat it up.

I sent Dan a link to this thread in case he's interested.

 

[tester551]

I tried another approach to get the "value of one point". My previous method had a defect that winning inflates point-differential due to intentional fouling at the end of the game. My new method probably has some flaws too, but much less I think.

I got box scores from last year and this year. I took the cumulative scores to obtain point differential at the end of each of the first three quarters and then correlate that with win or loss:

If the score is even... what % did a team win.
If a team is up +1... what % did that team win.
If a team is up +2... what % did that team win.
etc.
I did that for end of Q1, end of Q2, end of Q3 and graphed the results.

View attachment 19585

If you follow the graphs, one point is worth about:
2+% at end of 1st quarter or +1.7 wins per season.
3% at end of 2nd quarter or +2.5 wins per season
4% to 5% at end of 3rd quarter in fairly close games or +3 to +4 games (that's a lot for just one point!)
4th quarter is likely even more!

What I'm trying to show is that one point is worth a lot more than we imagine over the course of a season. Bonehead plays are both costly and easily avoided.

I'm seeing that the Blazers are committing far less bonehead plays than earlier in the season. Watch how careful Blazers are to not foul jump shooters. Dame has been fouled on 3's so many times in the past few games. Blazers have avoided that and even rarely foul 2 point jump shooters.

Against the Clippers we played great overall. Clippers made way more Bonehead plays. Nevertheless we still commited too many. Examples from Clippers game:
- Shabazz fancy globetrotters pass, turn-over, fast-break. 2 points lost (-1 us, +1 them).
- Shabazz passed on wide open three, drove, 3 seconds on Nurk. Shabazz's fault. 1 point lost.
- Aminu gets ORB and forces up a low % inside shot instead of kicking it back out like Harkless did.
- Turner, taking long mid-range shot with lots of shot clock.
- Nurk, also taking long mid-range shots. He made them, but they are sub-par shots.

You forgot to include the chart for the 4q.

I'd imagine that when you have a lead at the end of the 4q, your winning percentage is damn near perfect...

 

[bobf]

You forgot to include the chart for the 4q.

I'd imagine that when you have a lead at the end of the 4q, your winning percentage is damn near perfect...

Yeah, I suspect you are correct!

 

[Dan Marang]

This is good stuff! I'm going to reach out to some folks I know and see if I can pull some of the actual data from a few things @bobf had to estimate and see if we can't tighten this up. There's some really good things to be taken from this- especially if you can pair it with actual PBP data.

Nice work man!