Hit Me With Your Best Shot
Does this theory work in theory?
Consider a common adage in sports that the best teams always get everyone's best shot. In other words there is no rest for the weary when the weary are the top dogs—someone is always trying to take you down, and they are giving it all they got to do so.
We hear it all the time, but should we believe it? How would we measure it? What would it even mean? Why would teams respond this way?
Sometimes this borders on excuse making when a favorite underperforms—whether they lose or simply underwhelmingly win.
Here are some thoughts in support of this conventional wisdom:
More focused preparation by the opponent because of [reasons] . . . maybe they want this more than a typical win, maybe they feel compelled to focus more because of the competition, maybe they know there is asymmetrical opportunity—a loss is expected but a victory (moral or actual) brings disproportional gains
More/broader following of the favorite yields more (greater and more diverse) efforts made and tested to discover and expose weaknesses
More reason to share ideas and info by common opponents (espionage and coordination)
Willing to try more radical approaches given the low expectations; however, coaches again and again don’t usually do this (e.g., failure to go for it on 4th downs, etc.) being more willing to lose conventionally than to win unconventionally
Being the conventional wisdom, this becomes a self-fulfilling mind game working psychologically against favorites and for underdogs
Are there benefits from spending more resources on the top opponent such that it spills over into other games favorably?
But:
Why put in so much more effort and work for what is likely a losing effort? Assuming an ability to do this, is it an indictment of bad coaching, player effort, etc. generally—why not give this effort and focus in all games and just be better? Or does it say something about limited resources and asymmetric outcomes (dovetailing with the point above and see below regarding slack).
How do players if not coaches avoid being easily discouraged offsetting the focus and other benefits—at least at the first signs of adversity or setback?
How much slack is there actually that can be overcome by effort, focus, and just wanting it more? Worse teams are in fact worse.
Resources being limited, even if they could, should they do what it takes to give the best shot? Is it not more rational to channel that into achievable goals? Again, coaches and players dependably don’t operate totally rationally in terms of victory maximization (losing conventionally is safer for reputation and career risk) so I’m not sure how powerful this point is other than a criticism assuming the underdogs are pursuing a best-shot effort.
Does trying your best against the top foe not cost more than it gains—countering the direct opposite point made above?
Continuing on these lines of thinking, can it really be the case that it is better to pursue a big win (moral or actual) against a top dog rather than do your best to maximize all other chances of game successes?
Does risk taking (trick plays, high risk/high reward schemes, and general strategy) change much at all in these games for the underdogs? I don’t see it.
I suspect any hunts seeking evidence of this truism will be as fruitless as those for momentum, the mythical force that all sports fans and commentators evoke but none can define much less give evidence for. Like an incantation people say, “we got/lost/kept the momentum”, “you could feel the momentum turning”, and “once they had momentum, there was no stopping them”. Once you think about it, momentum is either a tautology or utter nonsense.
Back to the discussion at hand, this is basically begging for a model, which probably exists in the literature but I am too lazy to go look for. Basically we would want to compare two outcomes from a utility standpoint: “success” from pursuing the “give your best shot” strategy versus pursuing the “put more eggs in the obtainable baskets” approach.
We would want to know things like:
the probability of success against top opponents in each strategy (there must be a tradeoff between strategies to some extent)
the probability of success against other opponents in each strategy (there likely are some positive spillovers in one or the other to some extent)
the gain from success against each type of opponent in each strategy (remember this would be total utility not just win = 1, loss = 0; assumptions made here can justify any use of resources, i.e., either strategy)
the additional cost of attempting each strategy (the total outcome of the model (one side of the equation) for each strategy versus the other is the true opportunity cost, but if pursuing one has a greater exogenous cost (e.g., we have to buy more [something] to pursue one or the other) we would need to capture it here)
The helpfulness of this model would not be in giving us “the” answer as to which strategy to pursue. It would be in telling us the necessary assumptions to make one or the other preferrable.
How you answer the points/questions I raised above in support and opposition to the conventional wisdom should guide your answers to #3 in the model. For the record I am going to come down against the common adage in terms of what is optimal most of the time (i.e., it isn’t worth the cost to pursue a “give ‘em your best shot” strategy). Further I am going to tend to believe it either isn’t possible to pursue it or it generally is not actually pursued.