Existing TS% Metrics in the NBA

In the NBA, efficiency metrics like True Shooting Percentage (TS%), Relative True Shooting Percentage (rTS), and True Shooting Plus (TS+) have been ubiquitous for evaluating player performance. However, these metrics have limitations that a Z-score normalized metric can address.

But before I get to these limitations, a brief review for what these metrics set to achieve -

True Shooting Percentage (TS%):

TS% is a shooting efficiency metric that accounts for field goals, three-point field goals, and free throws.

Limitations

• TS% is a raw percentage and does not account for the context within the league or the variability among players. Nor does it account for league-wide growth
• It treats all players equally without considering how they compare to the league average.

Relative True Shooting Percentage (rTS%):

rTS% measures a player’s TS% relative to the league average TS%.

Limitations

• While it contextualizes a player’s performance, it does not account for the distribution or variability of TS% within the league.
• It can be influenced by extreme values (outliers), skewing the perception of a player’s efficiency based on outliers.
• Harder to interpret due to the lack of a normalized metric.

True Shooting Plus (TS+):

TS+ is an index where 100 represents the league average, and values above or below 100 indicate better or worse performance, respectively. It is widely considered the gold standard for comparing efficiency metrics across NBA eras, although it has similar limitations to the rTS%, it does normalize to some extent.

Creating the Z-score normalized TS%

Z-score normalization converts individual data points into a measure of standard deviations away from the mean which accounts for the distribution of scores and the variability.

Z-scores are a superior method for normalizing efficiency metrics in the NBA due to their ability to provide contextual relevance, robustness to outliers, enhanced comparability across eras, and clearer interpretation. While traditional metrics like TS%, rTS, and TS+ are valuable, they lack the depth and robustness that Z-scores offer. By adopting Z-score normalization, we can achieve a much more accurate and comprehensive understanding of player performance across eras with ease of interpretation.

To understand the process behind the estimation of the metric, here’s a stepwise list -

1. All TS% scores filtered ordered and the top 90% based on the possession’s played were filtered for further analysis to remove smaller sample sizes and extreme outliers.

2. All filtered TS% scores were scaled and centred based on the gaussian(normal) distribution. To examine how well the scores distributed, Shapiro-Wilk test for normality was conducted across 32 seasons and was significant at p<0.001. (NOTE: Shapiro-Wilk is fairly flawed but still a good rudimentary judge for examining the distribution).

3. All the Z-scores were converted back to percentile norms for ease of comparison using the normal distribution. You can refer to the probabilities of a standard normal distribution to get a better idea for the conversion.

4. The final output was a new zTS% metric that allows easier comparison across eras.

How is it an improvement?

• Robustness to Outliers:
  • Outliers are extreme values that can disproportionately affect statistical analyses.
  • Z-scores reduce the impact of outliers by contextualizing each player’s performance within the league’s overall variability. Extreme values have less influence on the mean and standard deviation compared to how they would skew simple averages or ratios.
• Enhanced Interpretability:
  • Z-scores standardize the scale of measurement, making it easier to compare performances across different seasons or contexts. A Z-score of 1.0, for example, consistently indicates one standard deviation above the mean, regardless of the underlying distribution’s specifics.
• Translating Z-Scores into Percentiles:
  • By converting Z-scores to percentiles, we provide an intuitive measure of performance. A player with a zTS% of 85% is more easily understood as being in the top 15% of efficient players in the league.

Kobe, an inefficient chucker or a product of his era?

The only thing left was to put this new method to the test using the most controversial player of the modern era - Kobe Bryant. Kobe, who’s often considered an inefficient player compared to several stars.

PLAYER_NAME	NICKNAME	GP	MIN	POSS	year	TS_PCT	TS_PCT_Z	TS_PERC
Kobe Bryant	Kobe	71	15.5	2211	1996-97	0.54	0.37	64.48
Kobe Bryant	Kobe	79	26.1	4157	1997-98	0.55	0.73	76.79
Kobe Bryant	Kobe	50	37.9	3676	1998-99	0.55	0.83	79.61
Kobe Bryant	Kobe	66	38.2	5047	1999-00	0.55	0.70	75.87
Kobe Bryant	Kobe	68	41.0	5460	2000-01	0.55	0.91	81.93
Kobe Bryant	Kobe	80	38.3	5991	2001-02	0.54	0.72	76.47
Kobe Bryant	Kobe	82	41.5	6699	2002-03	0.55	0.88	81.00
Kobe Bryant	Kobe	65	37.7	4853	2003-04	0.55	0.94	82.72
Kobe Bryant	Kobe	66	40.8	5196	2004-05	0.56	0.90	81.63
Kobe Bryant	Kobe	80	41.0	6371	2005-06	0.56	0.74	77.06
Kobe Bryant	Kobe	77	40.8	6263	2006-07	0.58	0.94	82.65
Kobe Bryant	Kobe	82	38.9	6488	2007-08	0.58	0.92	82.04
Kobe Bryant	Kobe	82	36.1	5911	2008-09	0.56	0.59	72.31
Kobe Bryant	Kobe	73	38.8	5570	2009-10	0.54	0.23	59.12
Kobe Bryant	Kobe	82	33.9	5361	2010-11	0.55	0.33	62.82
Kobe Bryant	Kobe	58	38.5	4332	2011-12	0.53	0.21	58.42
Kobe Bryant	Kobe	78	38.6	6020	2012-13	0.57	0.85	80.23
Kobe Bryant	Kobe	35	34.5	2434	2014-15	0.48	-0.94	17.42
Kobe Bryant	Kobe	66	28.2	3820	2015-16	0.47	-1.34	9.07

Based on the above, you can say that Kobe has always been around 80th percentile in terms of league efficiency across most of his prime, or you can simply state that he was more efficient than 80% of the league during his prime.

Similarly for Lebron -

PLAYER_NAME	NICKNAME	GP	MIN	POSS	year	TS_PCT	TS_PCT_Z	TS_PERC
LeBron James	LeBron	79	39.6	6053	2003-04	0.49	-0.36	35.85
LeBron James	LeBron	80	42.3	6423	2004-05	0.55	0.72	76.45
LeBron James	LeBron	79	42.5	6404	2005-06	0.57	0.92	82.08
LeBron James	LeBron	78	40.9	6124	2006-07	0.55	0.40	65.67
LeBron James	LeBron	75	40.4	5831	2007-08	0.57	0.77	78.06
LeBron James	LeBron	81	37.7	5769	2008-09	0.59	1.18	88.17
LeBron James	LeBron	76	39.0	5728	2009-10	0.60	1.40	91.94
LeBron James	LeBron	79	38.8	5916	2010-11	0.59	1.23	89.03
LeBron James	LeBron	62	37.5	4533	2011-12	0.60	1.60	94.53
LeBron James	LeBron	76	37.9	5549	2012-13	0.64	2.16	98.48
LeBron James	LeBron	77	37.7	5634	2013-14	0.65	2.28	98.86
LeBron James	LeBron	69	36.1	4889	2014-15	0.58	0.98	83.66
LeBron James	LeBron	76	35.6	5344	2015-16	0.59	1.10	86.44
LeBron James	LeBron	74	37.8	5655	2016-17	0.62	1.48	93.11
LeBron James	LeBron	82	36.9	6250	2017-18	0.62	1.41	92.11
LeBron James	LeBron	55	35.2	4218	2018-19	0.59	0.70	75.76
LeBron James	LeBron	67	34.6	4910	2019-20	0.58	0.32	62.68
LeBron James	LeBron	45	33.4	3145	2020-21	0.60	0.67	74.88
LeBron James	LeBron	56	37.2	4380	2021-22	0.62	1.04	85.11

You can see that he’s hovered around the 90th percentile during his prime and that number jumps up to 98th percentile during 2012-13 and 2013-14.

Finally, for my favourite player Nikola Jokic -

PLAYER_NAME	NICKNAME	GP	MIN	POSS	year	TS_PCT	TS_PCT_Z	TS_PERC
Nikola Jokic	Nikola	80	21.7	3488	2015-16	0.58	0.98	83.58
Nikola Jokic	Nikola	73	27.9	4264	2016-17	0.64	1.90	97.10
Nikola Jokic	Nikola	75	32.6	4983	2017-18	0.60	1.05	85.43
Nikola Jokic	Nikola	80	31.3	5140	2018-19	0.59	0.72	76.37
Nikola Jokic	Nikola	73	32.0	4733	2019-20	0.60	0.80	78.91
Nikola Jokic	Nikola	72	34.6	5084	2020-21	0.65	1.47	92.93
Nikola Jokic	Nikola	74	33.5	5136	2021-22	0.66	1.77	96.18
Nikola Jokic	Nikola	69	33.7	4873	2022-23	0.70	2.14	98.40
Nikola Jokic	Nikola	79	34.6	5599	2023-24	0.65	1.42	92.17

He’s an efficiency god, with multiple seasons in the 90th percentile.

How to Access the data

Unfortunately, I am still in the process of creating the app so all the data is publicly available but in the meantime if you’re interested in data for a single player, I created a hacky solution for you - https://codepen.io/Gareth-Bale-the-bashful/pen/qBzZejW