Make-It/Take-It Game Simulation

[Arkady]

This is possibly of interest to nobody else, but I thought I'd share.

In another thread, I said I preferred the version of half-court basketball where when a team scores, the other team gets the ball, rather than the "make it, take it" variety, where you keep getting the ball back as long as you keep scoring on each possession. My preference is based partly on that being more consistent with real basketball (the other team gets the ball after a basket), but also based on my impression that it rewards more balanced play. My gut feeling was that make-it/take-it favors offense over defense, by allowing someone who is a weak defender to hide that defect by often being able to stay on offense for long periods.

To check whether that gut feeling was correct, I programmed a quick simulation. I assigned each of two players a skill number for offense and defense. Player A had a 60 offense and 30 defense, and Player B had 50 for each. Player B, therefore, was the overall better player (total skill of 100, versus 90 for his opponent). Then I had the computer simulate possessions for each. On each possession, the computer would roll a random number from 0 to the relevant skill number. So, if player A was on offense and Player B on defense, Player A would be 0-60 and Player B would be 0-50. If the offensive player's random number exceeded the defender's, he gets one point, otherwise the ball gets turned over and a new possession gets calculated based on the other player on offense. The first to 15 points "wins."

I ran two simulations, first based on "losers outs" rules (where after the offensive player scores, the other player gets possession), and second based on make-it/take-it (the scorer keeps getting new possessions until the defender wins the random number face-off). It took about 15 minutes to program, but once I was done, the computer could run tens of thousands of simulated games in seconds.

What I found confirmed my gut feeling. In the "losers out" simulation, the better offensive player (the worse player overall) wins about 23% of the time -- about what we'd expect for "dumb luck" letting a somewhat less skillful player win, in a game to 15. In the "make-it/take-it" simulation, on the other hand, the better offense/worse overall player wins about 77% of the time. Make-it/take-it makes a huge difference in allowing some weaker overall players to dominate stronger ones, by giving greatly disproportionate importance to offense. I suspect it also magnifies the randomness of the result, though I'd need to run a whole lot more simulations and do statistical tests to confirm that).

This has some relevance to the setting up of rules in an economic "game." If you want a meritocracy, where the harder-working, more skillful person tends to come out on top more often, some rules will favor that more than others. Think of offense and defense as analogous to the skills of "capitalizing on advantages" and "overcoming hardship" respectively. If you have a "make-it/take-it" economic system, where things are relentlessly set up to reward short-term successes, you put huge weight on one skill (capitalizing on advantages), allowing victories even for someone who is very weak on another area (overcoming hardship), through the same kind of "streak" dynamics as in make-it/take-it basketball. If, on the other hand, you have rules that give someone who suffered a short-term setback "the ball", you favor long-term success by whoever has greater overall skill, rather than letting someone build up momentum that allows him to avoid being tested in areas of weakness.

If you take the rules of the "game" to extremes that are too great, in either direction, you ruin the game. People will stop really even trying. If, for example, any success will be punished so harshly that extra skill and effort mean almost nothing, and the victory ends up little better than a coin toss, nobody will bother making an effort. But, in the same way, if you so reward early success that a little initial luck can result in an insurmountable streak (and a little early bad luck puts people into a rut they can never get out of), people won't try hard there, either. Sporting leagues get that, which is why they often institute drafts where the worst teams go first, and scheduling where worse teams get easier schedules, and salary caps that keep the best teams from leveraging early success to monopolize all the talent. And it's why real basketball isn't "make-it/take-it". If you want to keep the games interesting and hard-fought, the rules have to be built to do that. That doesn't mean you're dictating the outcome. It just means that you're recognizing that certain rules are going to result in more competitive games than others.

 

[BitterPill]

Interesting post, and I think it makes your point.

Nonetheless, when playing pick-up games by whichever format, there is typically another team, sometimes several, waiting to play the winner. At some point fatigue will become a factor as the team that wins consistently becomes more and more fatigued with each win.

One advantage of the winner-takes-out rule is that it tends to cycle through games more quickly, thus allowing more teams to participate.

 

[resident_evil]

Interesting post, and I think it makes your point.

Nonetheless, when playing pick-up games by whichever format, there is typically another team, sometimes several, waiting to play the winner. At some point fatigue will become a factor as the team that wins consistently becomes more and more fatigued with each win.

One advantage of the winner-takes-out rule is that it tends to cycle through games more quickly, thus allowing more teams to participate.

And "make it, take it" creates hustle pressure to make the defense move to gain possession. Which in turn puts more pressure on the guys playing offense.

I wonder what system yields better results not for but from capitalism?

 

[BitterPill]

And "make it, take it" creates hustle pressure to make the defense move to gain possession. Which in turn puts more pressure on the guys playing offense.

I wonder what system yields better results not for but from capitalism?

I suppose the added incentive of money would make some players more likely to hustle. Where getting paid would make the most difference is in pre-game conditioning and preparation. For example, if I got paid to play, I'd likely hustle about the same, I was always a hustler to compensate for my limited athletic ability, yet the money incentive would find me conditioning as if it were a job; I'd watch my diet, stop smoking and so forth. Furthermore, I'd be willing to engage in organized practice with my team as if it were a job.

 

[resident_evil]

I suppose the added incentive of money would make some players more likely to hustle. Where getting paid would make the most difference is in pre-game conditioning and preparation. For example, if I got paid to play, I'd likely hustle about the same, I was always a hustler to compensate for my limited athletic ability, yet the money incentive would find me conditioning as if it were a job; I'd watch my diet, stop smoking and so forth. Furthermore, I'd be willing to engage in organized practice with my team as if it were a job.

I wish you'd quit smoking.

 

[fairsheet]

The top study/scenario is useful - up to a point. But, "scoring" a half-court game is easy. One point per made shot and first to 15 wins. A win's a win's a win. If we play winners out or losers out, the outcome is the same. The first one to 15 is the winner. The difference/question is, which team "wins"? The more skilled one or the less skilled one? But, what difference does it make if the outcome is the same? - the first one to 15 wins? For all practical purposes, the winner is by definition, the more skilled team.

What we need, is a scenario in which the more skilled team doesn't just "win", but they produce a better outcome than the other team could. This is where I think our current socioeconomy has lost its way. We're not doing a very good job of defining our preferred outcomes.