Yesterday, Aaron Schatz issued a challenge to his readership to prove the existence of a “trap game” or a “letdown game”. Both terms are thrown around in the media for almost every sport all the time, but I have not seen a hard definition or analysis of whether or not either phenomenon is real. This post defines and examines both types of games to see if there is evidence for either one’s existence.
Let me begin with trap games. As Schatz writes, there is no widely-accepted definition of a trap game, only the mushy understanding that sometimes good teams lose to bad teams when they have a “bigger” game against a better opponent the following week. In this narrative, the good team doesn’t take the bad team seriously, and is focused on the good team coming up the following week. For this study, I defined a “trap game” as a game between a team that finished the season above .500 against a team that finished the season below .500 that occurred one game before the above .500 team played another team that finished the season above .500. (From here on, I use the terms “above/below .500” to refer to a team that finished the season above/below .500.) There are many other ways to define a trap game, but I think this one is true to the soft understanding of the term without overly restricting the sample size.
Using Pro-Football-Reference’s wonderful game finder, I observed every game where a team above .500 played a below .500 team over the past 10 seasons (2002-2011). Over 1359 games, the above .500 team won 79.5% of the time. We must compare the above .500 team’s win percentage in trap games to this base rate of 79.5% in order to see if good teams lose at a statistically significantly higher rate.
Limiting the sample to our trap game definition (n=515), the above .500 team won 80.5% of the time, a full percentage point higher than in the full sample. Far from a losing more frequently, as we would expect by the trap game logic, good teams tend to do even better against worse teams the week before they play a good team. However, this difference is not statistically significant: a difference of means t-test yields a t-value of just 0.60. So we fail to reject the null hypothesis that good teams have a different win percentage in trap games than they do in any game against a sub-.500 team.
We can also use this data to examine whether or not letdown games exist. A common story behind letdown games is that the team was so excited over their big win from the previous week that they do not prepare for their upcoming game against a worse opponent. To fit this idea, I define a letdown game as a matchup between above and below .500 teams that occurs the week after the above .500 team beats another above .500 team.
Our baseline comparison is the same as in the trap game sample: above .500 teams have beaten below .500 teams 79.5% of the time from 2002-2011. In possible letdown games, the above .500 team won 82.2% of the time over 242 games – 2.7 percentage points higher than in the overall sample. Like the difference in trap game win percentage, this difference is not statistically significant (t = 0.30). Again, we fail to reject the null hypothesis that good teams beat bad teams at a lower rate when coming off of a good win than they do in any other game against a below .500 team.
This analysis does not prove that individual losses were not in part due to some psychological factor like the “trap game” and “letdown game” ideas suggest. However, claiming that a specific mentality is directly responsible for a particular loss is completely unfalsifiable, and so not worth arguing over. What we can say from this analysis is that the rate at which good teams beat bad teams does not depend on whether they beat a good team the week before or whether they play a good team in the coming week.
So if the Ravens lose to the Chargers this week, it’s not because they beat a winning team last week. And Denver Broncos: don’t worry about Kansas City being a trap game. If Denver does lose, the loss will have much more to do with Arrowhead than the Buccaneers game next week.
Most importantly: Happy Thanksgiving everyone – enjoy all the football today.
The Harvard Sports Analysis Collective 
There’s probably some selection bias in the ‘trap game’ analysis — teams above .500 that are coming off a win over another above-.500 team are, on average, probably better than the total group of teams above .500. (i.e., you’d see the 13/14/15-win teams show up more frequently in that group than the 9/10-win teams, so it makes sense that they’d win more frequently.)
I’m sure there wouldn’t be a meaningful difference anyway, but I don’t think it’s a perfect baseline.
sorry, I meant the ‘letdown game’ analysis. The ‘trap game’ study doesn’t have the same problem, since it’s not conditional on wins.
Perceptively, in a true psychological qualitative sense, I think anecdotally most coaches (as I was a high school baskeball varsity coach for 13 years) do believe in the trap game. Statistically and quantitalively, I am not sure this even exists, and as your study within the NFL suggests, none was found. But what was perceptibly true when my team did narrowly lose a so-called trap game, I believe the magnitude of “felt” failure seemed greater to me and most of my players, and the recovery for the next opponent was psychological more difficult, than a close loss to a higher quality opponent did. Interestingly enough, I often heard coaches exhort another sports adage: Narrowly beating an inferior opponent,even in an ugly manner, is always better than any loss, even if the loss occurred against a higher quality opponent. I would venture to state that, while most coaches will state this position publicly,conversely in private many coaches feel differently. Why? All coaches want their teams to primarily play well first, for playing well is believed to decisively lead to more wins. Notwithstanding, I hasten to add that this belief can be quite susceptible to numerous nuanced perspectives…hope this makes sense.
I think the conclusion is that “trap games” exist in the same way that “clutch” or a player’s comments “giving the opposition motivation” do. In that they exist only as some nebulous concept rolled out by writers when they actually happen, and ignored when they don’t.
I’ve not heard anyone praising New England for successfully negotiating either a trap game or a letdown game last night, depsite them beating the Colts last week and the playing the Texans next week.
Its almost as if good teams usually beat bad teams, but don’t always beat them.
Great analysis, perhaps the next thing you could investigate is how teams did against the spread or some other objective pregame prediction. Last week, even though the Texans won the game vs. the Jags, it was still somewhat of a “letdown” game for them.
How about using DVOA variance, ie, do teams play worse relatively to other games? Win loss is too binary and doesn’t tell you if a team played worse necessarily.
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You purposely omitted the effects of emotional exhaustion on a team. When a team wins a very emotional game then it is common for them to suffer from emotional exhaustion if not properl;y prepared. https://psychcentral.com/blog/avoiding-emotional-exhaustion-filling-our-emotional-tank/
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