Latrinsorm
03-05-2014, 07:13 PM
When Chris Paul invented the pass, the NBA changed forever. But what does an assist even mean? According to some guy at the WSJ (http://online.wsj.com/news/articles/SB123855027541776617), the NBA defines an assist as "a player tossing the last pass leading directly to a field goal, only if the player scoring the goal responds by demonstrating immediate reaction to the basket." There is no box score entry for a player tossing such a pass that leads only to a field goal attempt, so for thousands of years it has been impossible to determine how useful assists are outside of awkward regressions between assist rate and ORtg. How awkward? I'm glad you asked: so far this year the equation is Ast rate = 0.000 * ORtg + .590 with an R^2 of 0.000. (This is a terrible, horrible, very bad, no good regression.) This is probably why Dean Oliver's famous Four Factors make no reference to assists whatsoever, although you could still sneak it in by demonstrating that a higher assist rate will result in a higher eFG% without compromising TOV%.
But now with stats.nba.com we have assist opportunities! Where an "opportunity" is defined as a player taking a shot that would generate an assist if made. It is relatively easy to sum up all the assists and opportunities: 42,750.5 out of 85988.2 (of course there is no such thing as .5 assists, but nba.com only lists per-game, so we'll have to make do) for an assisted FG% of 49.72%. If we rounded every case of [assists per game * games played] we would get 49.76%, so we're probably fine just calling it 49.7%.
The average NBA team has shot 2,258 of 4,992 for 45.2%, so clearly being assisted is a big deal. We can subtract out and see that unassisted field goals and unassisted field goal attempts are something like 24,989.5 of 63771.8 for 39.2%.
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Field goal percent is all well and good, but what if assists are disproportionately generated on the basis of location? It turns out that they are:
rim 3-9 10-15 16-23 3
0.428 0.107 0.076 0.211 0.179 %fg
0.392 0.077 0.056 0.215 0.261 %a
But because the proportion is weighted away from the basket, this makes the FG% advantage even more stark. We can further demonstrate this by tabulating the "points created" column, dividing it by assists, and comparing the quotient to (points - free throws made) divided by (field goal attempts). It's not clear if the FT Assists that stats.nba.com tabulates are included in the Points Created column, but we can treat the problem both ways. FT Assists only count if the player misses the field goal and makes at least one free throw, so we can get a reasonable estimate of points created on FT Assists by doing...
[FT Assists] * [2 * (probability of making both free throws) + 1 * (probability of making only one free throw)]
= 93,438.6 points
= 1.087 points per assist opportunity
And for the NBA as a whole, we get 149,250 points over 149,760 field goal attempts, so the unassisted version works out to 0.875 points per unassisted attempt.
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Thus an assist adds 0.212 points to the points otherwise generated by a shot attempt, but does attempting an assist carry a higher chance of being turned over? Unfortunately stats.nba.com does not have a breakdown of turnovers, which are even more subjective than assists. Dwyane Wade is notorious for attempting a shot, recognizing it won't go in, and trying to pass on the way down from his jump - not all passing turnovers are aiming for assists. You might be tempted to count all offensive fouls as attempting to score, but what about illegal screens?
In any event, if we say that turnovers can only happen on assist attempts we can see that if a player exceeds .875/.212 = 4.14 assists per turnover, they are definitely living right. This is an extremely rare accomplishment for an NBA player with a decent volume of passing (say 500 assists): Muggsy Bogues has 7, Chris Paul will have 5 by the end of this year, everyone else put together has 11 (recognizing that turnovers have only been tracked since 1974). The reality that turnovers sometimes happen otherwise means the bar is set lower to some degree, but I would be surprised if it got below 3. Unselfish basketball is important to encourage, especially with today's NBA defensive rules, but at the same time the casual fan might overemphasize the relevance of assists.
But now with stats.nba.com we have assist opportunities! Where an "opportunity" is defined as a player taking a shot that would generate an assist if made. It is relatively easy to sum up all the assists and opportunities: 42,750.5 out of 85988.2 (of course there is no such thing as .5 assists, but nba.com only lists per-game, so we'll have to make do) for an assisted FG% of 49.72%. If we rounded every case of [assists per game * games played] we would get 49.76%, so we're probably fine just calling it 49.7%.
The average NBA team has shot 2,258 of 4,992 for 45.2%, so clearly being assisted is a big deal. We can subtract out and see that unassisted field goals and unassisted field goal attempts are something like 24,989.5 of 63771.8 for 39.2%.
.
Field goal percent is all well and good, but what if assists are disproportionately generated on the basis of location? It turns out that they are:
rim 3-9 10-15 16-23 3
0.428 0.107 0.076 0.211 0.179 %fg
0.392 0.077 0.056 0.215 0.261 %a
But because the proportion is weighted away from the basket, this makes the FG% advantage even more stark. We can further demonstrate this by tabulating the "points created" column, dividing it by assists, and comparing the quotient to (points - free throws made) divided by (field goal attempts). It's not clear if the FT Assists that stats.nba.com tabulates are included in the Points Created column, but we can treat the problem both ways. FT Assists only count if the player misses the field goal and makes at least one free throw, so we can get a reasonable estimate of points created on FT Assists by doing...
[FT Assists] * [2 * (probability of making both free throws) + 1 * (probability of making only one free throw)]
= 93,438.6 points
= 1.087 points per assist opportunity
And for the NBA as a whole, we get 149,250 points over 149,760 field goal attempts, so the unassisted version works out to 0.875 points per unassisted attempt.
.
Thus an assist adds 0.212 points to the points otherwise generated by a shot attempt, but does attempting an assist carry a higher chance of being turned over? Unfortunately stats.nba.com does not have a breakdown of turnovers, which are even more subjective than assists. Dwyane Wade is notorious for attempting a shot, recognizing it won't go in, and trying to pass on the way down from his jump - not all passing turnovers are aiming for assists. You might be tempted to count all offensive fouls as attempting to score, but what about illegal screens?
In any event, if we say that turnovers can only happen on assist attempts we can see that if a player exceeds .875/.212 = 4.14 assists per turnover, they are definitely living right. This is an extremely rare accomplishment for an NBA player with a decent volume of passing (say 500 assists): Muggsy Bogues has 7, Chris Paul will have 5 by the end of this year, everyone else put together has 11 (recognizing that turnovers have only been tracked since 1974). The reality that turnovers sometimes happen otherwise means the bar is set lower to some degree, but I would be surprised if it got below 3. Unselfish basketball is important to encourage, especially with today's NBA defensive rules, but at the same time the casual fan might overemphasize the relevance of assists.