### NBA home field advantage larger when home team is behind

In the NBA, the home team advantage declines steadily over the course of a game. From 2002-03 to 2003-04, the advantage is 1.28 points in the first quarter, but only 0.45 points in the fourth:

1st quarter: 1.28 points

2nd quarter: 1.07 points

3rd quarter: 0.89 points

4th quarter: 0.45 points

The total, including overtime, is about 3.74 points.

All this comes from a study by Marshall B. Jones (fakeable self-identification required for download) in the just-released new issue of JQAS. It's called "Home Advantage in the NBA as a Game-Long Process."

Why does the home field advantage (HFA) decline? It could be because, when the home team is ahead early in the game, it doesn't play as hard. Here are the HFAs, by quarter, when the home team is ahead at the beginning of the quarter (Jones gave the results separately for the two seasons – I averaged them out):

2nd quarter: +0.05 points

3rd quarter: +0.27 points

4th quarter: -0.43 points

But when the home team started the quarter *behind*, the HFA is strong:

2nd quarter: 1.71 points

3rd quarter: 1.77 points

4th quarter: 1.84 points

So is this true, that a team doesn't try as hard when it has the lead? Perhaps teams are more likely to bench their stars when they have the lead. Or maybe they play a different style – trying to use up the clock? – to maximize their chance of winning. Or maybe the players don’t care as much, which Bill James suggested as a possibility in a slightly different context.

None of these explanations have to do with HFA explicitly, but, rather, with the fact that when the stronger team is trailing, it performs especially well. The paper doesn't distinguish between the possibilities, but I'd bet it's a "stronger team" effect and not a "home team" effect.

Regardless of the explanation, I found this to be a highly unexpected result. I would have expected a bit of a letdown, perhaps, in the fourth quarter, when the game is almost certainly won. But after one quarter? What's going on? Does anyone have any ideas?

By the way, in overtime, the HFA per minute was about the same as in the first quarter. This is what you'd expect for any of the above theories.

One thing I disagree with in the paper is this:

"An NBA team playing at home should be leading at the end of the first quarter. If it is behind, it has lost much of the advantage it had when the game started. Before the game starts, the home team can expect to win the game roughly 62.0% of the time. If the home team is behind at the end of the first quarter, that percentage drops to 44.2% in 2002-03 and 43.8% in 2003-04. The home advantage is not something that the home team retains regardless of how it performs during the game. If the home team lets itself be outscored in the first quarter, then the advantage it had when the game started is lost."

The implication is that the first quarter is especially critical when it comes to HFA. But I don't think it is. First, as we have seen, a team that's behind after one quarter has a high HFA in the rest of the game. And, second, a home team that falls behind in the first quarter is probably the victim of a much stronger team. That would always be the case, regardless of whether the HFA is "frontloaded" or not.

Labels: basketball, home field advantage, NBA

## 9 Comments:

Phil:

What strikes me about this data is how efficiently basketball turns relatively small point advantages into wins. A 3.74 point edge becomes a .600 win%. That's a scoring advantage of about 4%. In baseball terms, that's a 4.7 RS / 4.5 RA team, which would be only a .518 team.

Has anyone studied the correlation between points scored and allowed in the NBA? The data you show here that indicates "coasting" with a lead, together with the very high win payoff for each extra point differential, certainly suggests a high correlation. (While in baseball, RS and RA are essentially independent).

BTW, the fact that a 4% scoring difference can be worth .018 in win% in one sport, but .100 in another, is another piece of evidence for your point that the structure of games determines the level of competitiveness as much or more as the player talent pool.

Guy, agreed. It's all a function of the standard deviation of the difference in score, relative to the average score.

In most sports, the SD of the score is quite large (compared to the average score). In basketball, it's small.

Another way of saying that is that in the NBA, the score is a more accurate reflection of the team's talent than in other sports. And that's why the better team wins more often.

BTW, the correlation between points scored and allowed is probably already high because of the fact that both teams have the same number of possessions. Maybe the correlation between points scored and allowed *per possession* would tell us more.

I still wonder why teams coast, though, even after one quarter. Any ideas?

"BTW, the correlation between points scored and allowed is probably already high because of the fact that both teams have the same number of possessions."

I don't think I agree. After all, baseball teams also have the same number of possessions (9), yet RS and RA are uncorrelated (relative to mean RS and RA for each team). I think basketball probably is different, in that once a team has a substantial lead they can afford to play lesser players. What makes this possible is 1) a team with a lead can slow the pace of the game and reduce number of possessions, and 2) the maximum score per possession is low (3 pts.). In baseball, even a weak team can score 5-6 runs in an inning, so few leads are truly "safe." (We know that in about 1/2 of baseball games one team scores more runs in one possession than the other team scores in the whole game. It's safe to say that will never happen in the NBA!)

Another way of saying this is that great NBA teams could run up the score more than they do against weaker teams. They may outscore their opponents by 6 or 7 points on average, but if you gave them an incentive to maximize the spread it could be a lot larger. At least, that's my guess.

"... baseball teams also have the same number of possessions (9), yet RS and RA are uncorrelated (relative to mean RS and RA for each team)."

Yes, but they have 9 possessions *every game*. Basketball teams have a different number of possessions every game, and so some of any correlation you find will be due to that factor.

Can NBA teams run up the score a lot more than they do? Yesterday, I would have been skeptical that it's a big effect (except maybe for fourth-quarter blowouts), but this study suggests that it might be.

Phil:

Fair point on possessions. So we want to know if teams' points-per-pos. and points-allowed-per-pos. are correlated at the game level, right? My guess is the answer is yes. Surely someone in the APBR crowd has studied this already?

Yeah, I bet someone's studied that ... I agree with you that the answer is probably yes.

2 things:

1. my take on the RS/RA correlation for baseball and basketball. i agree that the variance in # possession would have to be controlled first. also, i imagine the difference is almost uniquely due to the fact that basketball allows for more adjustment of strategy whether winning or losing compared to baseball.

2. back to the original question of why does hfa decrease over quarters? my gut reaction is to believe that the primary cause is shift in style of play. a leading team will bleed the clock (reduce # possessions) and attempt more high % 2 point shots (that decrease expected value of the shot, but also decrease the variance of points scored). And I think this change could occur as early as the 3rd quarter.

however, isn't the losing team employing the opposite strategy? speeding up possessions and chucking up more 3s than is optimal?

one would think that these strategy effects would balance out, but the data show otherwise.

maybe leading teams are better able to dictate the flow of a game than losing teams. (their conservative slow play outweighs the aggressive fast play of the losing team)

this would be interesting to test on football as well - who has more power to dictate the flow of a fourth quarter, the leading team running off-tackle every down or the losing team going no-huddle and throwing 15 yard out patterns all the way?

Late to the party, sorry.

"So we want to know if teams' points-per-pos. and points-allowed-per-pos. are correlated at the game level, right?"

I can't comment on that, unfortunately. But to an APBRian, pts.scored/pts.allowed is equal to (pts.scored/possession) / (pts.allowed/possession) -- there are roughly equal number of possessions in a game/quarter for each team.

Another way to think about this is in terms of the pythag equation for basketball vs. baseball. In baseball, the pythag equation is consistent with complete independence of RS and RA. Is that also true in basketball? That is, are teams' win% consistent with random scoring for any given ability to score and prevent points, and the accompanying SDs? My guess is that a team that outscores opponents by, say, 3 points will win more than they "should" under an assumption of random scoring. If Sal B swings by here, he might be able to shed light on this.

However, that isn't the whole story, because that analysis would take the SDs for points and points allowed as a given. If strong teams with a lead "coast," then their SD for points will be artificially constrained because they aren't running up the score as much as they could. Still, looking at pythgag in basketball would be an interesting starting point.

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