As a final installment in trying to estimating pace before 1974 — that is, before turnovers and offensive rebounds allowed us to make such calculations — I’ve finally dug into the nitty gritty and created a Complex Formula for pace estimation. Although the changes are subtle, I believe it to be the best estimation yet.

Neil Paine (basketball-reference) suggested an offensive rebounding component based on the league averages between 1974-1976 – the first three seasons of available data before the NBA-ABA merger – however the results were a bit peculiar. We’ll call his formula (presented in the link above) the Offensive Rebounding Percentage Method, or OReb% when referring to it below.

**Offensive Rating and TS%**

Across league averages on a yearly basis, the correlation between True Shooting percentage (TS%) and Offensive Rating (ORtg), which is points scored per 100 possessions, is an unbelievably strong **0.94**. This means there is a massive historical precedent for TS% and ORtg to almost always behave in concert. This shouldn’t come as a surprise, since most of a team’s efficiency on offense is predicated by what it does the most, which is *shoot* the basketball.

In a typical 2012 game, there are about 91 true shooting attempts (field goal attempts plus two-shot free throw attempts). About 11 of those will be offensively rebounded to continue a possession, and roughly 15 times a game teams will lose their possession via turnover. Teams can make up a small (and meaningful) fraction of efficiency by excelling at rebounding or ball-protection, but for the most part, it’s the ability to shoot that dictates offensive strength. **78% of all possessions this year have ended with a true shot attempt.**

Which brings us back to the Simple Method of pace estimation. If we compare it to Neil’s rebounding adjustment, it looks a lot more reasonable despite a slightly higher absolute mean error rate when tested up the 1974-1976 years.

In the 16 seasons TS% increases between 1974 and 2011, only once has ORtg not also increased. That was in 1993, when there was a 0.5% improvement in league-wide TS%, but ORtg dropped -0.2 points from the year before. Incidentally, 0.5% is the exact TS% increase we *know* occurred from 1973 to 1974, the first year we can start estimating pace. (It’s also a year we have the luxury of having opponent data for, increasing our estimation accuracy.) Therefor, from 1973 to 1974 we are most likely to see an *increase* in ORtg, especially given that this was the first year turnovers were tracked, and recording turnovers coincided with a steep decline in turnover rates in the following decade. Recording performance tends to improve performance. (For example, all but one PS team in 1974 greatly reduced their turnovers from the regular season.)

*Test 1: Offensive Rating from 1973 to 1974*

If we don’t see an increase from 73 to74 in ORtg, the decrease better be small. From 1973-1974, we estimate ORtg to change by the following amount using the following methods:

- +0.5 with the
**Simple Method** - -0.3 with the
**Offensive Rebound% method** - +0.3 with the
**Complex Method**

I posit that something is off about the middle number. It’s not improbable, but unlikely that we see a decrease there.

**Test 2: The 1970 Offensive Explosion**

The five biggest jumps in TS% since 1974 have been (league-wide increase in ORtg in parentheses)

- 1995 +1.5% (+2.0 ORtg)
- 1979 +1.5% (+2.9 ORtg)
- 2005 +1.3% (+3.2 Ortg)
- 2000 +1.2% (+1.9 ORtg)
- 1984 +1.2% (+2.9 ORtg)

So it’s reasonable to expect a fairly enormous league-wide jump in 1970, when we have the biggest change in league history in TS% (+2.0%). Here’s how the three methods estimate the jump from 69 to 70:

**Simple Method**: +4.1**OREB% Method**: +3.1**Complex Method**: +3.7

Again, the OREB% Method is producing the least consistent result; The league-wide change in offensive rating is on the same order of jumps in TS% that were only 75% as large as what occurred in 1970.

**The Complex Method**

So what exactly is this Complex Method? Well, first and foremost it’s still basic math, but it’s just quite a large formula based on the Basketball-Reference (and Dean Oliver) method for pace calculation. We set (i.e. guess) the rebounding and turnover numbers and use a separate offensive rebounding estimation method from 1971-1973.

Complex Method of Pace Estimation: FGA + 0.4 * FTA – OREB% * (FGA – FG) + (-TOV% * (FGA + 0.44 * FTA) / (TOV% – 1))

Adjust for the total minutes a team played divided by their number of games and voila. From 1971-1973, we can average the result using opponent data as well.

- For 1956-1970, OREB% is set to 30.3% (estimated league average in 1971) and TOV% set to 16.1%.
- For 1971-1973, Opponent’s OREB% is set to 31.9% and TOV% set to 15.8%.

**Tests at the Team Level**

Our first two tests looked at league average behavior, but we can dig deeper to the team level. After all, the league averages are being generated by the individual team results in our estimates.

If we return to the original example about the typical NBA game in 2012, roughly 78% of the relevant data we collect for possessions and efficiency (true shooting attempts, offensive rebounds and turnovers) were comprised of true shooting attempts. It’s good then, at the team level, that we see a correlation of **0.73 **in the change in TS% to the change in ORtg yearly for each team (data from 233 team-seasons between 1974-1985). We see a correlation of 0.38 in OReb% change in the same period and of -0.27 for TOV%. So without knowing offensive rebounding and turnovers, there will be some uncertainty in the estimation (we’ll discuss that later), but we have a strong anchoring barometer in TS% with which to compare our estimated Offensive Ratings.

The top OREB% teams (top-35, 35% or more) have a weaker correlation between TS% and ORtg than everyone else (0.76). Teams under 35% have a correlation of **0.89**. In other words, the more frequently you grab offensive rebounds, the less of your ORtg will be explained by your shooting. This is (thankfully) what we would expect, and helps us since the league average in offensive rebounding was about 30% when we started tracking it in 1974. It ramps upward steadily before the 3-point shot takes over in the late 80′s, which means it’s unlikely that we have to deal with any teams yanking 35% of their misses down. This is good for us because it results in a stronger correlation between TS% and ORtg.

As for the other unknown, turnovers, the lowest TOV% team in 1974 (first year TOV recorded) was the Knicks at 15.1%. In 1975 they were down to 14.2%. We know there is a small correlation between pace and turnover percentage (0.33), which suggests that speeding up might increase TOV%.

*Test 3: Variation in year-to-year team changes*

Perhaps the most interesting test we can run at the team level is on the individual team fluctuations in TS%. We can compare the *change* in TS% to the *change* in ORtg for every team from 1974-1985 (233 team seasons). We can then compare that shooting data to the shooting data we have from 1956-1973 and see how the variance/behavior in our estimations looks next to the post-pace sample. Here are the results...

Get the rest of this article over at Back Picks.