Why? For the winning team, if they just beat a division rival, they will be flying high and have extra rest. If they beat a non-rival, they will still have some confidence from winning, and extra time to prepare. For the losing team, they don't have confidence but should be taking advantage of extra days rest.
I went through the data from the last three seasons, since the Thursday night games started. I was looking for teams that played a division game on Thursday or played a division game following a Thursday game. I wanted to see if a team had an extra psychological edge for the game.
Here are the results to the game following the Thursday night games:

The contrast in these numbers are amazing. Teams that win on Thursday night do incredibly better the next week than the loser of that game. Especially if either the Thursday night game or following Sunday game is a division game. For the losing team, the numbers are pretty bad, but a trend is forming.
Look at the year by year split:



Very interesting for the Thursday loser. As more teams are getting experience with the Thursday night game (as opposed to teams just playing on Thanksgiving once in 10 years), both the winners and losers are playing much better. The losing teams are playing to a .500 pace when the past two years were .250. And the winners were really using the extra days to prepare. 14-2 overall the last 2 years for the Thur winners? I'll take those odds.
The obvious question is: Maybe the Thursday night winners have a good record because they are good and the Thursday night losers a bad record because they are bad.
Well, here is the research with spreads for the game following Thur night:
[For those not wanting to read the charts, here is a summary: Since it seems like teams are getting used to the Thur night game more, I believe the 2007 and 2008 data is more important than 2006.] In the last 2 years,
Winners
14-2 overall
8-1 as favorites (only loss being -4 with no division or prev division add on)
4-1 as underdogs (all wins being +5.5 to +6.5, loss +7)
Losers
7-9 overall [taking out a week 17 game I accidentally included before]
5-1 as favorites
2-8 as underdogs (7 of the losses were +5.5 or more underdogs)
2008
2007
2006
So, what do we learn from all of this?
You can have confidence in the previous Thursday night winner, especially as a favorite, and even if they are an underdog by less than a TD. (And it helps if one of the 2 games is a division game).
You can have confidence in the previous Thursday night loser, if they are favored or a small underdog. [I don't think any system will tell you to take a team that is +7 or worse on a consistent basis].
Earth shattering? No. But this should come in handy in close spread games during the season.
Here will be games to note for the upcoming season. (They are the Sunday games after a Thursday game)

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