toonces' free throw analogy

KenSmith

KenSmith

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From another thread:
So, I've been trying to come up with an analogy to the TBJT vs. EBJ debate in a real-world statistics sense. And my first thought is a free-throw shooting contest.

Imagine a lineup of 6 free-throw shooters shooting simultaneously. In the TBJT event, each gets 50 shots and the winner is the one who makes the most. In the EBJ event, we eliminate the low shooter after every 10 shots until the final 10 shots are determined head-to-head.

Now aside from the fact that the EBJ event seems more exciting, I think that if we ran simulations, we would find that the winner in the TBJT contest was more likely to be the best overall shooter than the EBJ contest, arguing that the EBJ event has more "luck" and less "skill" even though in the EBJ event each free-throw feels more critical, due to the cutthroat nature.

The problem with this analogy is that unlike the free-throw shooting contest, the first 75% of any TBJT event can be played on autopilot. Playing better than average in the first 75% of the hands has only a marginal effect on your final result, while in the EBJ event, those 75% of the hands were just as important as the final 25%.

So, to return to our analogy, I think a TBJT event is like a free-throw shooting contest where the first 35 shots can be lay-ups, and only the last 15 shots are actually free-throws (and perhaps the final shot is from the 3-point line for 2 points). The first 35 shots make a minor skill difference, but since almost all of the event comes down to skill in the final 15 shots (especially the last shot), the variance is actually higher and the skill level lower in an TBJT game.
Click to expand...

I got curious, and implemented a quick simulation of this free throw contest idea.

Player 1 is an 0.60 free throw shooter, and he competes against 5 other players who are all 0.50 shooters.

In a straight 50-shot playoff, Player 1 wins nearly 60% of the matches.
If we eliminate the lowest scorer after every ten shots, Player 1 still wins 57% of the time. This is closer than I expected.

It's tough to draw any conclusions from the analogy, but it is clear that it is similar to EBJ in some ways and dissimilar in others. The main difference is that free throws are independent events, while blackjack hands are correlated due to the shared dealer hand.
 
netball

I thought the free-throw contest was a good analogy but don't know enough about basketball to feel comfortable commenting on it.

Ken, when you said you were suprised how close the simulation was, what did you mean? Did you mean you thought there would be more or less of a difference? How far off the mark was your best guess?

Cheers

Simon
 
KenSmith said:
From another thread:

I got curious, and implemented a quick simulation of this free throw contest idea.

Player 1 is an 0.60 free throw shooter, and he competes against 5 other players who are all 0.50 shooters.

In a straight 50-shot playoff, Player 1 wins nearly 60% of the matches.
If we eliminate the lowest scorer after every ten shots, Player 1 still wins 57% of the time. This is closer than I expected.

It's tough to draw any conclusions from the analogy, but it is clear that it is similar to EBJ in some ways and dissimilar in others. The main difference is that free throws are independent events, while blackjack hands are correlated due to the shared dealer hand.
Click to expand...

After reading about your simulation, I wasn't all that surprised about the answer you got. The only times that the format would make a difference is when the good shooter gets eliminated just before he was about to go on a big run. In general, in a free-throw shooting contest, if you are in last place at any point, it's quite hard to catch up. Not true in EBJ, where you can increase your variance when it suits you to come back with a big bet from behind.

Perhaps a better model would be a contest where the baskets are worth a variable amount of points, and you are trying to finish #1 or #2. For Example:
EBJ: 11111223<ELIM>22222334<ELIM>333333446<ELIM>44558
TBJT: 1111111111/1111111111/2222233458

My guess is that in this simulation, TBJT would be a worse bet for the 60% shooter than the EBJ contest, but I'm too far removed from my programming past to test it.
 
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