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Weighted Scoring

Before we enter the Sixers' back-to-back-to-back (should be fun!), here is a brief statistical interlude.  In the NFL, organizations like footballoutsiders.com have revolutionized statistics by treating different game situations differently.  For example, an 11-yard completion on 3rd-and-9 in the red zone with 2 minutes left in a one-score game is much more difficult (and valuable) than a 15-yard completion on 1st-and-20 in the 1st quarter.  That has gotten me to thinking: what if we were to try that in the NBA?  Not all points in an NBA game are equal.  A basket when your team is down 2 with under a minute left is "worth" much more than a basket in garbage time.  So to turn this idea into a workable system, we need to develop some weights based on game situations (the hard part) and then determine weighted statistics (it turns out that these follow naturally).

Here is the table of weightings based on game situations that I came up with.  Higher weightings reflect more important game situations, and vice versa.  There is a premium placed on close games in the 4th quarter, while points scored during "garbage time" are devalued.  A weight of 1.5 means that a 2-point basket is worth 3 points; a weight of 0.5 means that a 2-point basket is worth 1 point.

Weight Game Situation
1.5 +/- 0-3, < 24 s (4Q)
1.4 +/- 0-3, < 1 min (4Q)
1.3 +/- 0-3, < 2 min (4Q)
1.2 +/- 0-5, < 6 min (4Q)
1.1 +/- 0-5 (1Q-3Q) or +/- 6-10 (4Q)
1.0 +/- 6-10 (1Q-3Q)
0.9 +/- 11-15 (1Q-mid 4th)
0.8 +/- 16-20 (1Q-3Q), +/- 11-15 (< 6 min 4Q)
0.7 +/- 21-29 (1Q-3Q), +/- 16-20 (4Q)
0.6 +/- 30+ (1Q-3Q), +/- 21-29 (4Q)
0.5 +/- 30+ (4Q)

In addition to the table above, there are two "bonus" situations, where a weighting is promoted 10% to one level higher on the table than the game situation would otherwise dictate:  (1) when points stop a scoring run by the other team [defined as 6 points or more] and (2) when there are points scored at the end of the 1st-3rd quarters [points at the end of the 4th quarter are already given a premium in the table].

Now let's talk about how the weightings are used, using the Sixers' last game vs. the Raptors as an example.  Most of the first half was played within a 5-point range, so points scored in the first half were generally weighted at 1.1.  The Sixers led briefly by 7-10 points toward the end of the first half, so points scored during that time were weighted at 1.0.  The Raptors went on their only scoring run of the game (!) bridging the two halves, so Jrue's basket at 41-38 was weighted at 1.2.  And much of the 4th quarter was played during garbage time, so those points were weighted as low as 0.6 and 0.5.  For each player, we can multiply his points scored by the weighting of each of the points, to obtain a "weighted points raw" (WPR).  In this game, the Sixers' total WPR was 86.8, indicating that there were fewer "important" points (weightings 1.1 or higher) than unimportant (0.9 or lower).  But then we scale the team WPR total to the team's actual total (97) to obtain a "weighted points scaled" (WPS) that will show each players weighted contribution to the 97 points.

I've taken the weighted statistics further by counting misses as well and weighting them by game situations according to the table above.  In so doing, I can calculate a weighted true shooting percentage (WTSP).  "Raw" true shooting percentage (TSP) is calculated essentially as (points) divided by ([scoring possessions]*2).  A "scoring possession" is defined as a field goal attempt (2 or 3 points) or a set of (2 or 3) free throws, and it is not the same as a team possession.  Multiple players can have a scoring possession in the same team possession, if there are offensive rebounds. 

[Aside on TSP that you can skip if you're not interested:  The actual TSP definition contains a factor of 0.44 multiplied by free throws attempted in the denominator, an approximation meant to account for "and-one" situations and technical foul shots.  I essentially use a factor of 0.5 and count all "and-one" free throws in the same possession as the field goal attempted (I can do this because I am tabulating the results from the play-by-play; TSP is calculated from the boxscore).  The only situations that are not well accounted for are technical free throws and "and-one" free throws when someone else scored the basket (these are rare situations that did not occur in the Raptors game).]

Weighted TSP (WTSP) for any player is then calculated as his weighted points (raw, or WPR) divided by his weighted possession.  If the percentage is higher than his "raw" TSP, then that means he shot better in the relatively important situations in the game.  Let's look at the Sixers' weighted statistics from this game now:

JH 14 13.9 15.5 70.0 70.9
JM 7 6.0 6.7 29.2 26.1
AI 14 14.7 16.4 46.7 47.1
EB 10 10.1 11.3 62.5 60.8
SH 7 7.7 8.6 58.3 57.5
TY 12 9.7 10.9 60.0 56.4
LW 13 10.0 11.2 46.4 41.7
ET 9 7.6 8.5 50.0 49.4
NV 9 6.1 6.8 56.3 56.5
AN 2 1 1.1 50.0 45.5
TOT 97 86.8 97 50.5 49.5

Since the Raptors game turned out to be a blowout, the weightings mainly serve to devalue the points scored when the game got out of hand (and, in the scaled totals, bump up the value of the points scored when the game was relatively close).  Iguodala's 14 points were worth slightly more than Jrue's 14 points, because all of Iguodala's points were scored when the game was within 10 points.  Most of Jrue's 3rd-quarter points came when the margin was already 11-15 points.  WTSP totals show, for example, that Jrue shot slightly better on his important scoring possessions, while Meeks shot worse (recall that his made 3-pointer was in garbage time).

So for those who have made it this far, I'm most interested in whether you think the weighting system that I've developed is fair.  Do the weightings make sense to you, and do you agree with them?  Would you add any other game situations to the table?

by Statman on Jan 9 2012
Tags: Advanced Stats | Basketball | Sixers | Statman | Stats |