Market Watch: Rams/Lions

 

Rams played Seahawks in the evening match, and Lions and Packers met later on Sunday.  If Rams won their match then Lions needed to win to make the play off, if Rams lost then Lions had less motivation.  In other words the matches were related - and so combining the odds by multiplying as bookies do to create a double will be just plainly wrong.  Some books still allowed this however.  Although the double lost, was it still value?

I tracked the movements of odds during the Rams/Seahawks match and noted the before and after odds.  I wanted to answer two questions. Was brodders bet value?  How does motivation affect a team?

You can see below, that just at the end of the match the Lions drifted out a bit, this made sense, with the Rams losing they had less motivation to win their game.  They are pros, they still have motivation to win (for the sake of winning, to eliminate the Packers).  However when it comes to the crunch does the coach/players really put their bodies on the line as they would if going for the big prize?  Do they play at 100%?

The odds move wasn't huge, but lets look at it.  Before the Rams/Seahawks result the Lions were 3.1 to win, after the Seahawks won they were 3.45 (on betfair exchange).  There is a tiny margin on the exchange but lets remove it anyway to give estimated true probabilities:

P[Lions] = 32.52% ... (implied probability based on 3.1 with margin removed)

P[Lions | Seahawks] = 29.16% ... (implied probability based on 3.45 with margin removed)

The market doesn't tell us is what the odds for Lions would have been if the Rams won.  But from the Law of Total Probability we know:

P[Lions] = P[Lions|Seahawks]xP[Seahawks] + P[Lions|Rams]xP[Rams]

The market - as the Seahawks win played out - gives us good estimates for most of these terms, so we can just rearrange to solve for P[Lions|Rams] (I get 39.66%) and hence calculate the estimated true odds of the double (I get 7.87).

Typically the books would have been paying about 8.17 I guess on the double when you account for the likely margin they would add to betfair odds.  So this was value (based on this analysis).  Well done brodders.

Warning: The odds drift may have been for other reasons, but it did happen exactly on the Rams/Seahawks result.  But that moment there could also have been specific teams news unrelated to the result, or any other information.  Maybe the big punters were waiting for the result before making their big bets, so perhaps the pre-Ram's match odds for Lions were just not the best estimate for the Lions probability and it was just corrected at the result. Note how the Lions odds barely moved during the other match despite Rams going favourites at one point.

Anyway, lets keep running with it.

We know from the Elo Rating System that the probability of the Lions winning depends on their ratings difference between them and the Packers.  Since we know the probabilities we can infer the ratings.

We would have witnessed a fully motivated Lions team vs a fully motivated Packers team if Rams had won, that is the top row.  Giving Lions their true potential 963 inferred Elo Rating. This drops to 882 when they are not fully motivated.  So the Lions in effect were playing at 91.56% of their full potential.

Conclusion

This all seems reasonable enough.  A small +EV in the double, not big enough that the books (who remember have already weeded out smart players) to be running scared of. Many books may have made the decision to allow the doubles so as not to cause any friction with their regular accounts.  It saves them the cost and effort of creating rules in their tech to handle this kind of rare exception.

Its uncommon enough for matches to be played sequentially like this, so to be able to look at the odds for different scenarios.  Typically in World Cup and the Premier League "deciding matches" will be played at the same time.

It's an initial attempt for me to quantify motivation and maybe apply this motivation factor to the Premier League.  For example in the run in it can matter alot if you have a team fighting relegation and highly motivated, rather than a mid table team.  On paper you would expect you want to play weaker teams in the run in, but you also have to take account what they are all playing for toward the end of the season. 

Every case though will be considerably different.  We have got 91.56% in this case.  It will depend on how much motivation is removed, you may be out of the title race, but still playing for Champions League.  It also depends on how good your second string players are in comparison to your fully motivated top team.  For Man City giving a few second string players time in a meaningless game the fall off from their full potential might not be the same as another team with less strength in depth.