I think I have heard this during more or less every game this year – “Well as you know [other broadcaster], the Sixers are the best team in the NBA in first quarter scoring”. I seem to specifically remember hearing that in games we then go on to lose, although the Pacers and Nets games feature prominently in my memory. I wonder though, does it actually mean anything to be a good first quarter team? I wrote something previously about the “critical moments” in games, but this is a look at longer and more defined time periods.

## 76ers Quarter Scoring in Context

In order to understand our illustrious first quarter scoring number (via NBA Stats), we need to put it into context as seen below in Table 1 (data as of 12/15/2018). I love this table, because it fits all kinds of narratives depending on your particular axe to grind. The numbers are raw counting stats, unadjusted for possessions or anything like that.

### Table 1: Philadelphia 76ers Quarter Scoring and +/- Rankings

Quarter | Avg. Points | NBA Rank | Plus/Minus | NBA Rank |
---|---|---|---|---|

Quarter | Avg. Points | NBA Rank | Plus/Minus | NBA Rank |

Q1 | 30.4 | 1 | +3.3 | 2 |

Q2 | 28.2 | 15 | +0.05 | 13 |

Q3 | 27.3 | 15 | -0.1 | 17 |

Q4 | 26.5 | 19 | -1.8 | 28 |

## Assumptions & Hypotheses

#### Quarter Leads & Game Outcomes

- Having a lead at end of Q1 is positively associated with winning the game
- Having a lead at end of Q2 is positively associated with winning the game and more strongly predictive than Q1 lead
- Having a lead at end of Q3 is positively associated with winning the game and more strongly predictive than Q1 or Q2 lead

#### Quarter Leads & Other Quarter Leads

- Having a lead at end of Q1 is positively associated with having a lead at end of Q2
- Having a lead at end of Q2 is positively associated with having a lead at end of Q3
- Having a lead at end of Q1 is positively associated with having a lead at end of Q3

#### TL;DR

- Having leads at ends of Q1, Q2, or Q3 is predictive of winning and having leads at end of Q1 or Q2 are predictive of a lead at end of Q3

## End of Quarter Margins and Game Outcomes

I am going to compare the Sixers and the Celtics throughout the article because they have relatively similar records and seem to be approximately the same quality of team. First, let’s take a look at the Q1, Q2, and Q3 margins in wins and losses in Figure 1, 2, and 3.

Interesting that Philadelphia’s median Q1 margin is approximately +2 in losses, whereas Boston’s median Q1 margin in losses is approximately -5. Keep this in mind for later when we do some modeling.

Figure 2 appears to show that Q2 margins by wins/losses are nearly the same for both the Sixers and Celtics. Nothing jumps off the page for me here.

According to Figure 3 (and the underlying distribution), the Sixers 70th percentile of Q3 margin in losses is +0. Of the Sixers losses so far, 3/10 have occurred with a lead starting Q4. Basic information on these losses is presented in Table 2, and unsurprisingly all three were away games.

### Table 2: Losses with end of Q3 leads

Date | Opponent | Location | Q1 Margin | Q2 Margin | Q3 Margin | Q4 Margin | Final Score |
---|---|---|---|---|---|---|---|

Date | Opponent | Location | Q1 Margin | Q2 Margin | Q3 Margin | Q4 Margin | Final Score |

10/23/2018 | Detroit Pistons | Away | +1 | +3 | +7 | +0 | 132 – 133 (OT) |

11/10/2018 | Memphis Grizzlies | Away | +5 | +13 | +6 | +0 | 106 – 112 (OT) |

11/14/2018 | Orlando Magic | Away | +3 | -1 | +11 | -5 | 106 – 111 |

Now to be fair, two of the three games went to OT, and I am not sure I would be writing this piece if they won both of those games, but here we are nonetheless. Now we have an idea that there might be something here worth investigating, so lets make a quick model or two. We’ll be using logistic regression to assist us with this. Each will be a univariate model using exclusively the margin after Q1, Q2, Q3^{3}.

#### Model #1a: Philadelphia 76ers Q1 margins and game outcome

Figure 7 presents the outcome from this initial model which is mostly entirely useless from a statistical and non-statistical perspective^{1}. This should square with the visual inspection of Figure 1 as the two Q1 margin distributions seem rather similar.

#### Model #1b: Boston Celtics Q1 margins and game outcome

Similar to the 76ers Q1 model, it is not a statistically meaningful^{1} (nor particularly non-statistically useful) model.

#### Model #2a: Philadelphia 76ers Q2 margins and game outcome

This model has verged into statistical meaningfulness^{1}, but still misclassified^{2} games approximately 37% of the time on average.

#### Model #2b: Boston Celtics Q2 margins and game outcome

Similarly to the 76ers model, this is statistically meaningful^{1} but still misclassified^{2} about 39% of the time.

#### Model #3a: Philadelphia 76ers Q3 margins and game outcome

Still statistically meaningful^{1}, but with a far improved average classification error^{2}.

#### Model #3b: Boston Celtics Q3 margins and game outcome

Again, still statistically meaningful^{1} with an improved average classification error^{2}.

## Relating Quarter to Quarter Margins

This is a similar and related measure, so I will go easy on some of the text.

Figure 15 again seems to show the lack of strong relationship between the 76ers’ first quarter success (or failure) with Q3 margins. We know that Q1 margins are not particularly useful predictors of game outcome (Figure 7/8), and that Q3 margins are much better predictors of game outcomes (Figure 11/12).

## Thoughts & Discussion

My two primary concerns with this piece is that I did not include any sort of game context/line-up data, and that I only have about 29 games of data to work with. I do not know if either would materially impact the results, but both are too important to not mention. What I did find interesting was essentially the lack of meaning of Q1 leads/deficits, especially given how hard the viewing audience has been hit over the head with the “best first quarter team in the league” statistic. For the 76ers, it seems hard to believe but it’s almost as if the first quarter scoring margin does not really matter that much in determining the game outcome. However, it would be nice if they could stretch out that first quarter success into the following quarters.

## Testing the Models in Action

Moving forwards, I’m going to run the model at the start of each quarter of each game and see how well it does or does not perform.

^{1}Coefficent for quarter scoring margin was not statistically significant at p < 0.05^{}

^{2}Error based on ten-fold cross validation with 0.5 threshold for classification

^{3}Vegas betting lines were tested as for inclusion in model and uniformly did not improve model performance, and as such was not included in models used for presented results