APBRmetrics

By DSMok1's projections of rookie and sophomore year APM projections, only the very top pick in the draft helps a team in his rookie season on average and only the top 3 do so in year 2. How many in year 3 and 4? Would 8 and 14 be about right respectively using Mike G's convention of a .9 improvement on APM? Based on who actually played minutes. What is the actual average improvement from year 2 to 3 and 3 to 4? Does it accelerate or stay steady compared to the projected improvement from year 1 to 2? The data is out there to calculate this but I haven't done so previously. It would be interesting to see the average career APM curve. Has anyone done / shared that? If so, I am not immediately recalling it. If the rate of improvement is a steady +0.9 for first rounders that would mean only about the top 5 guys drafted help a team net over the first 4 years of the rookie contract. I think only about 35-40% of players in the league are estimated as positive on RAPM so that is valuable but I am not sure it lives up to the conventional wisdom of draft pick value, at least in the first 4 years. The vast majority of first round picks hurt their teams net over the first 4 years by RAPM when they played. But hurt them less than a lot of vets and at a lower price on average? A comparison would be useful.

Evan said "Replacement level was set at -3.3 for players that were not rookies and did not have over 500 possessions or so in either of the last two seasons..." Only about the top 18 draft picks beat replacement level in their year 1 on average and about 28 do so in year 2 by DSMok's projections. It takes year 3 or 4 for a lower first round pick to beat a constant replacement level fill for those 3 or 4 years? Again that doesn't make those draft picks sound that good from a win now or fairly soon perspective. How does the salary of the average replacement level player compare to lower first round picks over their first 3-4 years?



Mike G: "Also, Evan: You don't list some players I've figured for major minutes: Krstic (Bos), Pachulia (Atl), Dante Cunningham and Reggie Williams (Cha), ... Are they not under contract?"

Krstic is playing in Russia for the year or more. Pachulia signed overseas and probably isn't coming back this season. Cunningham is in an offer sheet / match situation currently but will play in the NBA. Williams is hurt I think but will probably play later.

First year SPM averages over the last 12 years for respective picks.
I can't see any linear trend here. In fact I got the best approximation by using polynoms. Late first round picks are doing better than mid lotto to late mid first round picks. My explanation: Lottery teams are rather picking players with supposed upside (while upside means most times young, athletic and raw), and better teams at the end are picking the best available players to fit into team needs.

I didn't check the sophomore performances.

DSMok1 APM estimate for year 1 - SPM estimate for year 1 is -0.3 for the top pick on average and is generally small for the top 15 picks but becomes -1.5 to -2.5 for most of the bottom 15 picks in the first round. Those lower picks are better on SPM than APM outright and better on SPM than APM when compared to the relationship between those metric estimates for the top 15. The top half of the draft may have better "intangibles" than the bottom half and their APM performances show it while their SPM does not show as much difference. At least in year 1. And GMs are showing the ability to see it, value it in draft picks who might have boxscore stats fairly similar to the top picks? Even without NCAA APM? I guess that says something about talent / impact evaluation. Still might be some benefits to be had from a customized NCAA APM that focused on / weighted heavier top teams, top players, and when playing top teams & players. If GMs are going for best player available with later picks, they might also be going more for best SPM available over best APM available. And getting the first but not the second. If they are going for best fit with top picks, it seems they are doing better on APM there, as a consequence of either having a better pick and better picks intrinsically having better APM or having better APM when picked with more attention to fit and more attention to overall impact instead of just boxscore stats. It would be worth checking how all this looks in year 3, 4, 5 and beyond on both SPM and APM.

Crow, my values are the average results. I guess, the values DSMok1 presented are based upon a regression of the "real" APM values on pick numbers. DSMok1 is using a linear model in order to project the performance of the draft picks. I think the R^2 is maybe around 0.4 to 0.5, while a polynomical approximation can probabily give 0.6+. The linear model thinks that later draft picks are per se worse, while the reality shows that a lot of mid first rounders are wasted on "upside". It could also show the differences in the abilities of different teams to evaluate talent.

Btw: http://82games.com/nbadraftpicks.htm

Those are career values and it seems the pattern is pretty similar to my result for the first season. The linear model (adjusted for minutes) would give a R^2 of 0.54, while a logarithmical approach gives 0.67 and a polynomical up to 0.73.

I used Beech's values adjusted for minutes played, then I subtracted the average value for the Top30 draft picks.



The pattern upto pick #15 seems to be very similar. Interesting, the #2 pick performs worse than #3 to #5 pick, not only in the first season. Also, the worse performance of the #6 and #8 pick is also seen in their career averages. The figure shows also that a linear model is unlikely to be the best fit, logarithmic or polynomical are better solutions.

I would say that the assumption it would be a linear trend is wrong. The performance of drafted players are not best represented by using a linear model.

Crow wrote:By DSMok1's projections of rookie and sophomore year APM projections, only the very top pick in the draft helps a team in his rookie season on average and only the top 3 do so in year 2. ...

I'd have thought any player above replacement level (-3.3 or -3.5, say) helps a team.
Even the best teams have to give minutes to some below-average players.

Now, if anyone using a plus-minus model (boxscore or pbp based) should add that 3.3 or 3.5 to their player rates, we'd more readily visualize what each player brings. It feels more real than "what he brings, minus NBA average".

mystic wrote: Interesting, the #2 pick performs worse than #3 to #5 pick, not only in the first season. ..

I doubt this is meant to be a predictive statement, but merely recognizes a circumstance of the recent past. The people who draft may take Darko or Wade at #2, regret it now or regret it later, and it doesn't imply that you should trade your #2 for the #3-5, just because #2 picks have a recent history of being duds.

Why not just average your 2,3,4 picks and call that #3; etc? Do that over longer intervals for later picks. Realistically, a player taken 10th could have been taken 8th to 12th. The exact draft number isn't an aspect of the player but of some other circumstances.

Even averaging 7 picks in the #15-and-after range, I found an anomalous dip around #22-23 and an equally odd rise around 26-27; later bottoms at #38 and re-peaks at 46.
And still, one wouldn't advise trading down to get that later pick.

Mike G wrote: Now, if anyone using a plus-minus model (boxscore or pbp based) should add that 3.3 or 3.5 to their player rates, we'd more readily visualize what each player brings. It feels more real than "what he brings, minus NBA average".

Do you want to say that scoring negative values in such plus-minus models would suggest a player is not helping and can be replaced easily? Because I would not interpret the results like that at all. But I can understand when you are saying that it may "feel" that way. Especially when we consider that average last season was worth $5.8m. A team consisting of only average players would win 41 games, that is more than the worst teams in the league are winning. And that average team was worth overall $72.5m in total salaries.

In my model in average a team would win basically no games, if it consists only of players with -2xS.D. (in average -6.16 over the last 15 years). Each player better than that would at least help his team win at least 1 game. Well, that is the reason my salary model is based upon the assumption that a player should get no salary, if he is a -2xS.D. player.

Hmmm, ...
Some people interpret a negative value as a negative contribution. Even veteran observers seem to still suggest it.
My suggestion was that if positive contributors had positive ratings, this confusion could often be avoided.

A baseline of -6.16 for zero-value players is a lot different than -3.3 or -3.5 replacement level, and it describes a different player.
The definition I assume is that replacement level = zero wins added, in whatever minutes.

If you add 6.16 to every player's rating, do you get his rate of win contribution?

Mike G wrote:I doubt this is meant to be a predictive statement, but merely recognizes a circumstance of the recent past.

That statement is trivial, given the fact that the numbers used are generated by players picked in the past.

Mike G wrote: The people who draft may take Darko or Wade at #2, regret it now or regret it later,

They may regret that now, but similar people still picked Thabeet at #2

Mike G wrote: And still, one wouldn't advise trading down to get that later pick.

That is NOT the implication at all. As I said earlier, it can be explained by different goals of the teams. While lottery teams usually are looking for the next "big" thing, the better teams at the end are rather looking for fitting players who are ready to play now. I suspect that those players are usually older, maybe junior or seniors instead of freshmen or sophomores like the earlier picks. That would also agree with the difference in the development curve of the later picks. If we look at the first year performance of the later picks, they are outperforming mid first rounders, but later those mid first rounders are actually ending up at least on a similar career level. The later picks don't have much upside anymore. If a team wants to fill a team need, it can easily trade down to #25 to #30 (or even early 2nd round) instead of picking that player already at #20 or so. The Knicks in 2006 are a pretty good example. They picked Balkman with their #20. Balkman ended up being the #5 in terms of SPM among the 2006 draftees in their 1st season, but had no upside at all. That was a pick for a contender, not a pick for a team like the Knicks. The Knicks should have went for upside here rather than playing level right now. They overpaid for Balkman, while not helping their future.

And basically all teams are picking in such a manner, the Pistons picked Milicic over Anthony, Wade, Bosh, etc., because he was supposed to have the biggest upside (some even thought more than James!). The Lakers picked Bynum with their #10 pick, a player clearly not ready to do anything in the NBA in 2005/06. They still went for the upside. And I suspect that will be the same pattern in the future as well.

I don't see any reason to believe that this behavior can be very well approximated by using a linear model, the past showed that other ways are better fits.

Mike G wrote: If you add 6.16 to every player's rating, do you get his rate of win contribution?

Theoretically yes, but I didn't test that.

mystic wrote:.. If we look at the first year performance of the later picks, they are outperforming mid first rounders, but later those mid first rounders are actually ending up at least on a similar career level...

This brings up my next question. How does one average-in the "performance" of those who never played, or who played trivial minutes, in their rookie year or beyond?

While my own short study averaged the rates of rookies who actually got significant minutes, I also averaged their minutes, including those with zero and near zero.

In my super-averaging scheme, a playing #46 pick has been well better than a #37: In eWins/484, .57 to .40 .
But along with all the mid-2nd rounders who never played, that #46 has gotten just half the minutes of the #37 (3.7 mpg vs 7.3)
The upshot is that the mid-30s pick has contributed about 70% more 'equivalent wins' as a rookie, than the mid-40s guy has.

This corroborates your theme that rookies with bad teams are more likely to get more minutes, even if they're not really fit for the league. Mid and late rounders are less likely to get a shot, thus are represented mostly by the better players.

Here's my APM/SPM aging curve:


A cubic fitted the year-to-year deltas very nicely, indicating an overall quartic shape to the aging curve. The curve fit was weighted by the number of observations for each delta.

Note, of course, that the very young on that curve above were players drafted out of high school and thus may have had unusually high "potential". That said, when I did my draft analysis, the age of the player was not significant in predicting first-year performance. I would guess that most of the "potential" was realized in the first year, enough to bring up "potential" picks to the level of "safe" picks (I'm presuming age is an indicator of potential picks vs. safe picks).

If someone played their first year at age 18, I would be comfortable using this aging curve to bump up their age 19 projection by 1.9 points.

mystic wrote:Crow, my values are the average results. I guess, the values DSMok1 presented are based upon a regression of the "real" APM values on pick numbers. DSMok1 is using a linear model in order to project the performance of the draft picks. I think the R^2 is maybe around 0.4 to 0.5, while a polynomical approximation can probabily give 0.6+. The linear model thinks that later draft picks are per se worse, while the reality shows that a lot of mid first rounders are wasted on "upside". It could also show the differences in the abilities of different teams to evaluate talent.

I'm not using a linear model at all, Mystic. I'm using a logarithmic/linear model. The equation is of the form a*LN(Pick)+b*Pick+c. The curve, graphed, looks like this:


It appears to me that you are not adjusting for selection bias in your graph. For instance, only the best of the #30 picks end up playing significant minutes... Are you averaging only those who actually play, or adjusting for that issue?

DSMok1 wrote:

Code: Select all

Delta Age Deltas (Model)
18.5 1.898
19.5 1.506
...

Hey, this is great.
Are you calling this first column "Delta Age"? And does 18.5 mean "from age 18 to age 19"?

If so, it seems a cumulative yearly improvement would show an actual trajectory of performance. The magnitude would of course vary by player, but the curve itself might be equivalent for any level of player. (Or maybe not)

If an 18-yr old is just good enough to play in the NBA, perhaps he has a rookie ASPM of -3.00The peak age is 26; or 25 to 27; or 24 to 28, at which point we're talking about "plateau".
This is the same peak age range (24-28) that I've assumed for many studies, so it's gratifying to see corroboration.
I cut this one off at age 40, since the sample player has dropped below -3.5

Based on early research results from the effect of aging on RAPM values, this chart and the fact that recent NBA championship teams have been rather old, it is my opinion that a player's peak of impact is closer to 28/29 years than 25/26.
I don't doubt that a player's peak measured by BoxScore based metrics is closer to 25, but I think we see this effect simply because younger players care more about BoxScore statistics, or are more able to carry out actions that are subsequently recorded in a BoxScore. some extreme examples.
Younger players also care more about money, probably because they just haven't made that much yet, compared to older players. And I think they know that better BoxScore statistics lead to bigger contracts.

Examples of suboptimal strategy by younger players would be:
- going directly for the ball instead of boxing out
- block the ball from behind instead of getting in front of the man

More research is obviously needed, but time is sparse these days

Yep, that's the aging curve. This is, of course, variable player-to-player (Aaron McGuire hinted that experience and position also mattered in a Twitter conversation). You interpreted my numbers correctly.