APBRmetrics

[mathom]

In looking over some player stats, I began wondering about the value of 2p and 3p shots or if anyone has studied the affect of 3p/2p FGs on FTs. It seems to me as though players are moving more and more toward the 3pt line and many players (and coaches) might be doing themselves a disservice because it lowers the number of opportunities they have to get to the line. I don't doubt there are some players that are costing themselves efficiency in this way even though their 3pFG% may be quite respectable. It seems also that getting to the free throw line is indirectly more valuable as well, by putting players in foul trouble - not unlike the value of pitches taken per at bat in baseball. In a simplistic comparison, the efficiency of a 3p shot would be 3pFG% *1.5 vs 2pFG%. But it seems to me a better comparison then is 3pFG%*1.5*P1 vs 2pFG%*P2, where P1/P2 is some constant that measures a player's ability to get to the line when taking a FG of whatever type. To determine P1/P2, I think some research will need to be done regarding the rate at which players are fouled on 3p shots first. Once you have that piece of knowledge, you could use the ratio of (FTA-FTA from fouls on 3pers)/2pFGA, and determine the efficiency of each type.

However, I think a better method than FTA/2pFGA would be to introduce another constant, one that is universal and relates the number of FTs to the length of time a player possesses the ball. I would say the large majority of non-shooting fouls that result in FTs are done against the player holding the ball. While you could probably argue that some players do have an ability to draw non shooting fouls more than others, I dont think the variance will be that large, and that using a league wide constant and applying it to all players (or at the least, players of the same position) would give a very good approximation. In order to determine that sort of constant however, some data collection would need to be done on non shooting fouls that resulted in FTs.

I have a feeling that if someone were to go through all of the work and calculations, it would turn out that 2pFGs are actually more efficient than 3pFGs in many cases, and that a lot of players would be better served driving to the basket than taking 3pFGs, even when on the surface it appears their 1.5*3pFG% is higher than their 2pFG%. (And it might help explain why the championship teams always seem to be teams that have a quality bigman and get to the line).

One last parting thought: should technical free throws be subtracted from a player's PPG average when considering efficiency? If a player takes 1 tech FT every other game, and sinks say 85%, it would increase their PPG avg by more than .4 a game, which depending on the number of possessions the player uses otherwise could swing their efficiency substantially. I tend to think maybe we should, but I can see an argument being made both ways.

[WizardsKev]

Here's a pretty straighforward graph of where points have come from in the NBA since 73-74. Each category is expressed as a percentage of total points. Note that the percentage of pts from 2pt fgs has declined, has gone up from 3pt fgs, and remained relatively constant from FT. Pts from the FT line may be declining a little since 2000, but it's not a big move.



_________________
If you can't explain it simply, you don't understand it well enough.

-- Albert Einstein

[mathom]

Actually, I'd say this graph is rather deceptive

Even though it looks like FT have remained stable, FTA and FTA/FGA have both decreased rather significantly since 1980 (by about 15% and 10% respectively).

http://www.geocities.com/torch772/ssnbastats.htm

If you click the historical shooting tab at the bottom, it has some stats on shooting over the years.

[WizardsKev]

I don't think it's deceptive at all.

It's a measure of where pts are coming from -- as a percentage of total points. FTA/FGA may be down (I haven't looked at that measure specifically), but pts from FT has remained pretty stable through the years, as has FT%.
_________________
If you can't explain it simply, you don't understand it well enough.

-- Albert Einstein

[mathom]

Right, but that doesn't really tell me much.. if FTA/FGA is going down, but my efficiency is also going down and I score less points, then my FTA/PPG can be relatively stable, and it masks what's really going on.

[WizardsKev]

[gabefarkas]

[WizardsKev]

[gabefarkas]

right now your 3 lines represent:

Points from 2FGA
Points from 3FGA
Points from FTA

i'd be curious to see:

2FGM
3FGM
0.44*FTM
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If the statistical revolution won't be televised, I need to call my cable provider, pronto!

[WizardsKev]

[gabefarkas]

awesome. i'm looking forward to it. if you want to share the raw data at all, i'd be happy to take a crack at it.

my thinking was this: since 2FGM, 3FGM and FTM all affect Total Points differently, a change in each affects Total Points (and thus each's % of "Source of Points") in a different magnitude.
_________________
If the statistical revolution won't be televised, I need to call my cable provider, pronto!

[WizardsKev]

Okay -- here's the graph you requested:



Very similar to the pts source graph I posted above. Free throw makes are slightly higher in recent years than they were in the 70s even as 2pt makes have given way to 3pt shooting. It's also interesting that there was a slight uptick in FTs when 3pt shooting surged abruptly in the 90s. I don't remember precisely, but that was probably when the league went to the shorter 3pt line.

I'd be happy to share the raw data. Just email me at kevinbroom@realgm.com and I'll send back the spreadsheet.
_________________
If you can't explain it simply, you don't understand it well enough.

-- Albert Einstein

[mathom]

Using FTM/2pFGM/3pFGM etc clouds the issue because FGM is a function of both FGA and FG%. If FG% over the given period were constant, it would not be an issue. Let me give a quick example to demonstrate:

Say 10000 total shot attempts were taken in the league in 1970 (all 2pers since its 1970). Suppose also that a player gets to the line once for every 4 FGA, ie 2500 FTA were taken in 1970. If you say that 50% of FGA are made and 75% of FTA are made, then FTM/FGM+FTM = .1579. Now, flash forward to present, where tempo has died down considerably, where say 8000 total shots are taken. Suppose 7000 are 2pFGs and 1000 are 3pFGs. You still get 1 FTA per 4 FGA, but now also suppose that you get 1 FTA per 10 3pFGA. Suppose that 2pFG% has dropped to 45%, 3pFG% is 35%, and FT% is still 75%. That means there were 1387.5 FTM, and 7000*.9 + 1000*1.05 + 1850*.75 points scored, so FTM/points = .1588. FTM are now a higher portion of total points scored, but the fact that FTA/FGA has decreased is entirely masked.

While I did make up the numbers, the effect is the same. If you want to find a correlation between 2pFGA, 3pFGA and FTA, using FTM/2pFGM/3pFGM is deceiving because 2pFG%/3pFG% have also changed over time and will give you an incorrect view of things.

Edit:

[WizardsKev]

mathom: I just took a look at (.44*FTM)/oting has increased and 2pt shooting has decreased.

I also just took a look at FTA/FGA, which is dopossessions as one more way of looking at what you're talking about in the first post of this thread. The data looks basically the same as the other graphis I posted -- that free throws have remained fairly constant even while 3pt shown over the past few years, but which also went up when 3pt shooting spiked to its highest level in the 90s. You may be right that teams & players may be costing themselves efficiency with 3pt attempts. I'm asking Roland if he has data on foul rates by shot type. Of course, this data wouldn't be historical so we're still kinda in the same place we're in now.

You could well be right about this, but I think we're going to need more information to prove it.
_________________
If you can't explain it simply, you don't understand it well enough.

-- Albert Einstein