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.