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Are all 10 point leads the same?

Posted by Chase Stuart on January 29, 2009

Over at the Advanced NFL Community, the claim was made that not all 10 point leads are the same. Here's the meat of the argument:

Let's say your team is up by 10 with 8 minutes remaining. That's a pretty good lead, right? Well, if it's a 13-3 game, it's a VERY good lead -- if their poor opponents couldn't muster more than a field goal in 52 minutes, they're unlikely to close a 10 point gap now. On the other hand, if it's a 42-32 shoot-out, it's still anybody's ballgame[.]

That sounds reasonable, but whenever I hear arguments like this I always raise an eyebrow and wonder if common perception matches reality. After all, ten points is ten points, and maybe it's equally likely that a team trailing 13-3 will win its game compared to a team trailing in a shootout. A touchdown and a field goal can be scored by almost any team in a short time, and the small sample size of less than one game may not be that telling of the team's offensive prowess.

So how do we measure this?

I checked every NFL game from 1993-2007 and noted the scores at the end of the third quarter and the end of the fourth quarter. There were 299 games in which there was a 10 point lead heading into the fourth quarter. Some games were high scoring, like the 2006 Chargers-Bengals game where San Diego came back to win after trailing 38-28; some games were low scoring, like the 1999 Cowboys-Eagles game where Philadelphia won after trailing 10-0 at the start of the fourth and the, uh, 2000 Cowboys-Eagles game where Philadelphia won after trailing 10-0 at the start of the fourth. So this gives us a nice sample to view how likely or unlikely a given team is to come back from a 10 point deficit.

Teams trailing by 10 had a 47-252 record in those games, an .157 winning percentage. So is a 38-28 lead less safe than a 17-7 lead? There are several ways to measure this. I checked the correlation coefficient of points scored in the game through three quarters by the trailing team and number of wins in the game by the trailing team. If high scoring games are more likely to have those late lead changes, the CC should be closer to 1 (more points, more wins). If low scoring games are likely to produce late drama, the CC should be closer to -1. It turns out the CC was 0.07, which isn't large in either direction. However, a more detailed breakdown gives us a more interesting result:

        #gm   #win   win %
20+     17      5     0.29
15-17   17      3     0.18
13-14   56      7     0.13
10-12   52     10     0.19
6-9     67     10     0.15
0-3     90     12     0.13

This means that teams that had scored 20 or more points through three quarters but trailed by 10 points won five of their seventeen games. Not exactly known for their offensive prowess, the Ravens have two of those games, with Jim Harbaugh leading a comeback against the Colts and Anthony Wright thwarting the Seahawks. There looks to be at least some small benefit to trailing in a high scoring game -- the teams that scored more than two touchdowns through three quarters won almost a quarter of their games while teams that hadn't scored more than a field goal won only two in every fifteen games.

I also looked at the significance of being at home. For example, is a 20-10 lead by the host tougher to overcome than a 20-10 lead by the visitor? We would expect it to be, although Doug and JKL have shown that home field advantage isn't worth that much by the fourth quarter. Unsurprisingly, a majority of the teams that are up by 10 through three quarters are the host -- 136 of the trailing teams were at home, 162 of the trailing teams were on the road, and 1 game was at a neutral site. The correlation coefficient between being at home and winning the game was 0.19, which signals a weak connection. However, home teams went 32-104 (23.5%) while road teams went 15-147 (9.3%) so being at home greatly improves your odds of winning that game, even if overall you're pretty unlikely to win.

I then ran a regression using home/road as one variable (home = 1, road = 0) and the trailing team's score after three quarters as the other input. Because the output is binary (win/lose), we should use a logit regression and not a linear regression. The logit regression formula that best fit the data was:

1 / (1 + e^(2.53 - 1.22*HOME - .025*3QPTS))

While the home variable was significant (0.0005), the 'points through three quarters by the trailing team' variable was not statistically significant (0.39). If it *was* statistically significant, how meaningful would it be practically? A road team trailing 10-0 would be expected to win just 7.4% of the time; if that team was instead losing 30-20, its odds of winning would jump to 11.6%. A team losing 13-3 at home would win 22.5% of the time while a host losing 27-17 would win 29.2% of the time.

So a trailing team (through three quarters) in a very high scoring game would be slightly more likely to win than a trailing team in a really low scoring game. The points variable was not statistically significant so we can't be confident in this based on the data, although conventional wisdom seems to support this. While you might prefer your team to be trailing 30-20 through three quarters, I'd much rather my team be at home down 13-3 then on the road down 30-20.

But there's another thing we could look at. If we run a logit regression using the same 299 games, and using as variables "points through three quarters" and the "vegas line", we get this:

1 / (1 + e^(1.75 - .016*3QPTS + .155*VEGAS))

where VEGAS is negative for the favorite. We don't need a home field variable here because the point spread would have already taken the location of the game into account. The '3QPTS' is still nowhere near significant while VEGAS is massively significant (.000005).

Here are some sample scenarios -- do these seem right to you?

7-point favorite, trailing 10-0: 34%
7-point dog, trailing 10-0: 5.5%
7-point favorite, trailing 30-20: 41.5%
7-point dog, trailing 30-20: 7.5%

So we know that the point spread of the game is a good indicator of a team's likelihood of winning even after three quarters, and to a lesser extent, home field advantage is also a good indicator as well. The number of points scored through three quarters was not shown to be an indicator of eventual success. That said, if you believed that to be true before reading this, nothing shown here would convince you to think it's better to be trailing in a low scoring game. If there is any real difference in likelihood of winning, it's more likely that a team is better to be trailing in a high scoring game, but the effect is certainly very small.

This entry was posted on Thursday, January 29th, 2009 at 8:13 am and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.