{"id":433,"date":"2013-01-07T13:27:35","date_gmt":"2013-01-07T18:27:35","guid":{"rendered":"http:\/\/blog.rotovalue.com\/?p=433"},"modified":"2013-01-07T13:27:35","modified_gmt":"2013-01-07T18:27:35","slug":"make-it-take-it-simulations","status":"publish","type":"post","link":"https:\/\/blog.rotovalue.com\/index.php\/2013\/01\/07\/make-it-take-it-simulations\/","title":{"rendered":""Make it, take it" Simulations"},"content":{"rendered":"

In a discussion<\/a> 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.
\nPhil came up with a separate, but very similar, simulation, and he’s written about his testing here<\/a>. I figured I should add some of my own findings to follow up. The short story is that I can replicate Phil’s results…
\n
\nOne 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” \u00a0overtime. 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.
\nI 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.
\nIn 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.
\nFirst traditional alternating possessions:<\/p>\n

Game\u00a0is\u00a0200\u00a0possessions\u00a0total,\u00a0doing\u00a010000000\u00a0simulated\u00a0games.\nTeams\u00a0alternate\u00a0possessions.\nTotal\u00a010000000\u00a0Team1\u00a0wins\u00a0\u00a02816786\u00a0\u00a028.2%\u00a0avg\u00a0\u00a096.6\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a07183214\u00a0\u00a071.8%\u00a0avg\u00a0104.7\u00a0pts.\u00a0Tot\u00a0avg\u00a0201.3\nReg:\u00a0\u00a0\u00a09519637\u00a0Team1\u00a0wins\u00a0\u00a02619066\u00a0\u00a027.5%\u00a0avg\u00a0\u00a095.8\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a06900571\u00a0\u00a072.5%\u00a0avg\u00a0104.2\u00a0pts.\u00a0Tot\u00a0avg\u00a0200.0\n1\u00a0OT:\u00a0\u00a0\u00a0401058\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0165038\u00a0\u00a041.2%\u00a0avg\u00a0110.5\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0236020\u00a0\u00a058.8%\u00a0avg\u00a0111.5\u00a0pts.\u00a0Tot\u00a0avg\u00a0222.0\n2\u00a0OT:\u00a0\u00a0\u00a0\u00a066173\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a027199\u00a0\u00a041.1%\u00a0avg\u00a0121.5\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a038974\u00a0\u00a058.9%\u00a0avg\u00a0122.6\u00a0pts.\u00a0Tot\u00a0avg\u00a0244.1\n3\u00a0OT:\u00a0\u00a0\u00a0\u00a011027\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a04632\u00a0\u00a042.0%\u00a0avg\u00a0132.5\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a06395\u00a0\u00a058.0%\u00a0avg\u00a0133.5\u00a0pts.\u00a0Tot\u00a0avg\u00a0266.0\n4\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a01744\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0695\u00a0\u00a039.9%\u00a0avg\u00a0143.4\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a01049\u00a0\u00a060.1%\u00a0avg\u00a0144.5\u00a0pts.\u00a0Tot\u00a0avg\u00a0287.9\n5\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0306\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0136\u00a0\u00a044.4%\u00a0avg\u00a0155.5\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0170\u00a0\u00a055.6%\u00a0avg\u00a0156.4\u00a0pts.\u00a0Tot\u00a0avg\u00a0311.9\n6\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a047\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a019\u00a0\u00a040.4%\u00a0avg\u00a0165.7\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a028\u00a0\u00a059.6%\u00a0avg\u00a0167.2\u00a0pts.\u00a0Tot\u00a0avg\u00a0332.9\n7\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a08\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01\u00a0\u00a012.5%\u00a0avg\u00a0181.0\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a07\u00a0\u00a087.5%\u00a0avg\u00a0184.2\u00a0pts.\u00a0Tot\u00a0avg\u00a0365.2<\/pre>\n
Now the make-it, take-it simulation:<\/p>\n
Game\u00a0is\u00a0200\u00a0possessions\u00a0total,\u00a0doing\u00a010000000\u00a0simulated\u00a0games.\nTeams\u00a0scoring\u00a0on\u00a0a\u00a0possession\u00a0get\u00a0the\u00a0next\u00a0possession\nTotal\u00a010000000\u00a0Team1\u00a0wins\u00a0\u00a02840205\u00a0\u00a028.4%\u00a0avg\u00a0\u00a092.4\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a07159795\u00a0\u00a071.6%\u00a0avg\u00a0108.4\u00a0pts.\u00a0Tot\u00a0avg\u00a0200.9\nReg:\u00a0\u00a0\u00a09760216\u00a0Team1\u00a0wins\u00a0\u00a02739090\u00a0\u00a028.1%\u00a0avg\u00a0\u00a092.0\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a07021126\u00a0\u00a071.9%\u00a0avg\u00a0108.3\u00a0pts.\u00a0Tot\u00a0avg\u00a0200.3\n1\u00a0OT:\u00a0\u00a0\u00a0220186\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a092800\u00a0\u00a042.1%\u00a0avg\u00a0109.6\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0127386\u00a0\u00a057.9%\u00a0avg\u00a0111.5\u00a0pts.\u00a0Tot\u00a0avg\u00a0221.1\n2\u00a0OT:\u00a0\u00a0\u00a0\u00a017954\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a07622\u00a0\u00a042.5%\u00a0avg\u00a0120.1\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a010332\u00a0\u00a057.5%\u00a0avg\u00a0121.9\u00a0pts.\u00a0Tot\u00a0avg\u00a0242.0\n3\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a01486\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0621\u00a0\u00a041.8%\u00a0avg\u00a0130.4\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0865\u00a0\u00a058.2%\u00a0avg\u00a0132.2\u00a0pts.\u00a0Tot\u00a0avg\u00a0262.7\n4\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0146\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a069\u00a0\u00a047.3%\u00a0avg\u00a0141.8\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a077\u00a0\u00a052.7%\u00a0avg\u00a0143.6\u00a0pts.\u00a0Tot\u00a0avg\u00a0285.4\n5\u00a0OT:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a012\u00a0Team1\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03\u00a0\u00a025.0%\u00a0avg\u00a0147.3\u00a0pts,\u00a0Team2\u00a0wins\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a09\u00a0\u00a075.0%\u00a0avg\u00a0154.0\u00a0pts.\u00a0Tot\u00a0avg\u00a0301.3<\/pre>\n
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.
\nIn 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.
\nBut 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.
\nUpdate January 10:\u00a0<\/strong>For those interested in the code, e-mail me – geoff at rotovalue dot com.<\/span> I’ve now posted the code<\/a>\u00a0and done a follow-up discussion of running many more simulations here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
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… Continue reading "Make it, take it" Simulations<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,14],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/posts\/433"}],"collection":[{"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/comments?post=433"}],"version-history":[{"count":0,"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/posts\/433\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/media?parent=433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/categories?post=433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.rotovalue.com\/index.php\/wp-json\/wp\/v2\/tags?post=433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}