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Year-to-Year Four Factor Correlations

Posted by Neil Paine on September 28, 2009

I know we haven't talked about Dean Oliver's Four (Eight?) Factors here in a while, but that hasn't been deliberate. I actually like the 4 factor methodology for evaluating teams' strengths and weaknesses, although there's a quite a gordian knot to deal with when you start trying to link team factors to their respective metrics for individual players. Hmm... maybe that's the reason why I haven't invested so heavily in them recently, because we've been all about trying to establish expectations for teams in 2010 based on their current rosters, and last year's 4 factor data wouldn't help you get very far in that direction. But it occurs to me that another way to look at team trends is to see which stats are historically sustainable from year to year, and which aren't. So, with that in mind, here are year-to-year correlations for each of the 4 factors, on offense and defense, since 1973-74 (the first year the NBA kept turnovers, offensive rebounds, etc. at the team level):

Factor r
oORb% 0.790426
ORb% 0.720865
TO% 0.703134
oTO% 0.696372
eFG% 0.693140
oeFG% 0.658823
oFTr 0.632391
FTr 0.620854

Rebounding ability seems to be the most consistent aspect of the four factors from season to season, followed by the ability to prevent and force turnovers. Interesting how the non-shooting areas (Reb% and TO%) are more consistent than the ones that deal either completely (eFG%) or partially (FTr) with putting the ball in the basket... I have no numbers to back this up, but I always felt like shooting was by far the place in the game where luck had the biggest impact. You never hear about "streak rebounders" or "streak ballhandlers", but streak shooters have been in the lexicon practically as long as the game has been around. There's something about the act of tossing a ball into a stationary target 10 feet off the ground that lends itself to that kind of randomness, I suppose.

Now, free throw rate is a strange case because it combines several different aspects of the game. Shooting accuracy is obviously a large part, and drawing fouls is a function of your own offensive aggressiveness (rarely do they call fouls on 20-foot jump shots), but you also have to rely on the officials to give you the calls when you do attack the basket. So here are the year-to-year correlations of the two separate metrics that make up free throw rate:

Stat r
FTA/FGA 0.6330263
FT% 0.5813185

You might think that free throw percentage would stay relatively constant year-to-year, since the conditions never change and the defense can't bother you when you're shooting... However, chalk this up as more evidence that shooting a basketball accurately is very tough to do on a consistent basis, even if you're all alone in a gym. Finally, I wanted to know which field-goal shooting numbers varied the most, 2-pointers or 3-pointers, but I wanted to filter out the early years of the 3-point era (when few players and teams seemed to understand the value of using the new shot) as well as the brief 22-foot arc in the mid-1990s. So these numbers are only going to be on seasons after 1996-97, the final year before the NBA went back to a 23'9" arc.

Stat r
2FG% 0.6251018
3FG% 0.4251931
o2FG% 0.6231809
o3FG% 0.2249165

So, as you probably expected, it's a lot easier to shoot with consistency the closer you get to the basket, but even I'm surprised at the low year-to-year correlation we see for opposing 3-point %. One team that was unusually fortunate in that regard was Cleveland, who allowed a league-low 33.3% shooting from the arc, almost a full percentage point better than the 2nd-place Magic; conversely, the Sacramento Kings allowed a staggering 40.5% mark from downtown, which helps explain some of why they had the worst defense in the NBA, more than 1 pt/100 poss. worse than Washington, the 2nd-worst D. Here are more teams who performances in certain categories are sure to regress -- and progress -- towards the mean:

Top 5 o3FG%
CLE 33.3%
ORL 34.2%
LAL 34.5%
CHI 34.7%
BOS 34.9%
Bottom 5 o3FG%
PHO 38.3%
WAS 38.7%
MIA 38.9%
NJN 39.1%
SAC 40.6%
Top 5 3FG%
BOS 39.7%
CLE 39.3%
SAS 38.6%
POR 38.3%
PHO 38.3%
Bottom 5 3FG%
DET 34.9%
UTA 34.9%
OKC 34.6%
WAS 33.0%
PHI 31.8%
Top 5 oFT%
HOU 74.9%
LAL 75.3%
ORL 75.5%
CHA 75.6%
SAC 75.6%
Bottom 5 oFT%
TOR 78.4%
CHI 78.6%
MIL 79.1%
DAL 79.9%
POR 80.3%
Top 5 FT%
TOR 82.4%
DAL 81.9%
IND 80.7%
NOH 80.7%
HOU 80.5%
Bottom 5 FT%
PHO 74.4%
CHA 74.0%
ATL 73.7%
LAC 73.6%
ORL 71.5%

Finally, keep in mind that even though these are lists of teams that got unusually "lucky" or "unlucky" last season, regressing these numbers to the mean will result in only relatively small improvements/declines in W-L%, because free throws & 3-pointers only account for roughly 40% of all points and 30% of all possessions. But even so, those small changes can be very important to teams that are close to playoff contention.

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5 Responses to “Year-to-Year Four Factor Correlations”

  1. Jason J Says:

    Out of curiosity on how very bad free throw shooters who took a lot of FTAs effected overall league percentages for a season, I ran the numbers on Shaq’s effect in 2000 and Wilt’s effect in 1961. Dropping Shaq would have improved the league average from 75% to 75.3%. Dropping Wilt would have improved the league average from 73.3% to 75.1%.

    Clearly the impact has to do with the size of the league. There were an additional 21 teams in 2000. Shaq took just 1.4% of the total league-wide free throws in 2000 (I was surprised too), while Wilt took 4.5% of the total league-wide free throws in 1962. Shaq shot 52.4% from the stripe, and Wilt shot 50.2%.

    It’s worth noting though that the next season Wilt shot over 60% from the line and only had a 0.6% negative impact on league-wide FT% despite taking over 5% of the total FTAs.

  2. Charrua Says:

    A factor here is the change in team rosters. We could interpret the results as suggesting that rebounding and turnovers are less susceptible to personnel changes and more a product of coaching strategy, for example.

  3. Jason J Says:

    That jives with all the diminishing returns info that ABRmet produced regarding adding and subtracting great rebounders from teams. Basically rebounding doesn't vary THAT much regardless of personnel (though that's not to say that having a great rebounder doesn't promote winning by freeing up other players to run the break or get back on defense).

  4. Ryan J. Parker Says:

    What's the range of values for these? As Jason J suggested, the higher correlation for rebounding likely comes from the fact that it doesn't vary all that much.

    Also, I'd love to see stuff like the mean absolute error to get a sense of how much the error is on average when using last year's data to predict next year's data.

  5. Bronn Says:

    Sure it's odd for me to comment a month after the fact, but don't you find it more than a coincidence that 4 of the 5 top teams in opposition 3FG% were also the 4 best teams in the NBA last year?

    Seems to me that part of being a team that can win 60 games is solid perimeter defense-limiting your opponents' open looks. There's still going to be variance year to year, but it can't entirely be luck when the best teams end up at the top of the list.