"Make it, take it" Simulations

In a discussion on Tom Tango’s blog, Phil Birnbaum was speculating about whether switching basketball to “make it, take it” might change the balance of the game, and he thought it might help the underdog win more often. After reading his comment, I thought of a rather simple simulation I could hack up to test his hypothesis, and so I wrote one to see what would happen.
Phil came up with a separate, but very similar, simulation, and he’s written about his testing here. I figured I should add some of my own findings to follow up. The short story is that I can replicate Phil’s results…

One difference between Phil’s simulation method and mine was how we treated games tied after regulation. Phil’s model assumed a 200 possession game, and if the game was still tied, he continued playing until one team scored again, a “sudden death”  overtime. My model used a 22 possession OT following a 200 possession game, roughly analogous to a 5 minute OT after a 40 or 48 minute game. This makes a small but noticeable difference in the results, because a longer OT (or game) favors the stronger team more.
I ran 10 million trials each matching Phil’s parameters, but using my OT method, and found the stronger team won 7183214 times when alternating possessions, but just 7159595 times in “make it, take it” (which I’ll call MITI from now on). So my model found MITI favors the underdog even more than Phil’s given his parameters.
In addition to computing a winner, I had my simulation output additional data, including the average scores for each team, and counts of how many games ended in regulation or in each overtime period. So here’s the output of my two long runs. Team1 is the underdog, with a 48% chance of scoring in each possession, while Team2 is the favorite, with a 52% chance of scoring.
First traditional alternating possessions:

Game is 200 possessions total, doing 10000000 simulated games.
Teams alternate possessions.
Total 10000000 Team1 wins  2816786  28.2% avg  96.6 pts, Team2 wins  7183214  71.8% avg 104.7 pts. Tot avg 201.3
Reg:   9519637 Team1 wins  2619066  27.5% avg  95.8 pts, Team2 wins  6900571  72.5% avg 104.2 pts. Tot avg 200.0
1 OT:   401058 Team1 wins   165038  41.2% avg 110.5 pts, Team2 wins   236020  58.8% avg 111.5 pts. Tot avg 222.0
2 OT:    66173 Team1 wins    27199  41.1% avg 121.5 pts, Team2 wins    38974  58.9% avg 122.6 pts. Tot avg 244.1
3 OT:    11027 Team1 wins     4632  42.0% avg 132.5 pts, Team2 wins     6395  58.0% avg 133.5 pts. Tot avg 266.0
4 OT:     1744 Team1 wins      695  39.9% avg 143.4 pts, Team2 wins     1049  60.1% avg 144.5 pts. Tot avg 287.9
5 OT:      306 Team1 wins      136  44.4% avg 155.5 pts, Team2 wins      170  55.6% avg 156.4 pts. Tot avg 311.9
6 OT:       47 Team1 wins       19  40.4% avg 165.7 pts, Team2 wins       28  59.6% avg 167.2 pts. Tot avg 332.9
7 OT:        8 Team1 wins        1  12.5% avg 181.0 pts, Team2 wins        7  87.5% avg 184.2 pts. Tot avg 365.2

Now the make-it, take-it simulation:

Game is 200 possessions total, doing 10000000 simulated games.
Teams scoring on a possession get the next possession
Total 10000000 Team1 wins  2840205  28.4% avg  92.4 pts, Team2 wins  7159795  71.6% avg 108.4 pts. Tot avg 200.9
Reg:   9760216 Team1 wins  2739090  28.1% avg  92.0 pts, Team2 wins  7021126  71.9% avg 108.3 pts. Tot avg 200.3
1 OT:   220186 Team1 wins    92800  42.1% avg 109.6 pts, Team2 wins   127386  57.9% avg 111.5 pts. Tot avg 221.1
2 OT:    17954 Team1 wins     7622  42.5% avg 120.1 pts, Team2 wins    10332  57.5% avg 121.9 pts. Tot avg 242.0
3 OT:     1486 Team1 wins      621  41.8% avg 130.4 pts, Team2 wins      865  58.2% avg 132.2 pts. Tot avg 262.7
4 OT:      146 Team1 wins       69  47.3% avg 141.8 pts, Team2 wins       77  52.7% avg 143.6 pts. Tot avg 285.4
5 OT:       12 Team1 wins        3  25.0% avg 147.3 pts, Team2 wins        9  75.0% avg 154.0 pts. Tot avg 301.3

A few things stand out. First, the underdog’s average points per game drops from 96.6 to 92.2 in MITI, yet its chance of winning actually rose slightly, from 28.2% to 28.4%. Second, in the MITI simulation there were far fewer overtime games than in traditional alternating possessions. It’s also interesting to note that the underdog’s chances to win in either regulation (27.5% to 28.1%) or in overtime (41.2% to 42.1% in 1OT) both rose much more than the chance to win overall.
In my model, overtime is simply a 22 possession game, which gets replayed as needed if there are still ties, and so in theory the chances of winning any specific overtime period should remain constant. Of course multiple overtimes happen much less often the further out you count, and the very small sample sizes for many OT games don’t converge as well to the true probability of winning.
But it does seem paradoxical that MITI improves the underdog’s chances of winning in regulation *AND* your chances of winning in overtime more than it improves their chances of winning overall. The answer to the paradox is that MITI also greatly reduces the number of overtime games, and that largely offsets the advantages it gives the underdog in any specific game.
Update January 10: For those interested in the code, e-mail me – geoff at rotovalue dot com. I’ve now posted the code and done a follow-up discussion of running many more simulations here.

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