I don’t intend to transform my writings here into a low-key sports mathematics blog. I just happen to have run across a couple of interesting problems and, after all, sports do offer a lot of neat questions about probability and statistics.
benperreira here makes mention of “Lawler’s Law”, something I had not previously noticed. The “Law” is the observation that the first basketball team to make it to 100 points wins the game just about 90 percent of the time. It was apparently first observed by Los Angeles Clippers announcer Ralph Lawler and has been supported by a review of the statistics of NBA teams over the decades.
benperreira is unimpressed with the law, regarding it as just a restatement of the principle that a team that scores more than the league average number of points per game will tend to have a winning record in an unduly wise-sounding phrasing. I’m inclined to agree the Law doesn’t seem to be particularly much, though I was caught by the implication that the team which lets the other get to 100 points first still pulls out a victory one time out of ten.
To underscore his point benperreira includes a diagram purporting to show the likelihood of victory to points scored, although it’s pretty obviously meant to be a quick joke extrapolating from the data that both teams start with a 50 percent chance of victory and zero points, and apparently 100 points gives a nearly 90 percent chance of victory. I am curious about a more precise chart — showing how often the first team to make 10, or 25, or 50, or so points goes on to victory, but I certainly haven’t got time to compile that data.
Well, perhaps I do, but my reading in baseball history and brushes up against people with SABR connections makes it very clear I have every possible risk factor for getting lost in the world of sports statistics so I want to stay far from the meat of actual games.
Still, there are good probability questions to be asked about things like how big a lead is effectively unbeatable, and I’ll leave this post and reblog as a way to nag myself in the future to maybe thinking about it later.
Lawler’s Law states that the NBA team that reaches 100 points first will win the game. It is based on Lawler’s observations and confirmed by looking back at NBA statistics that show it is true over 90% of the time.
Its brilliance lies in its uselessness. Like NyQuil helps us sleep but does little to help our immune systems make us well, Lawler’s Law soothes us by making us think it means something more than it does.
Why is it so useless, one may venture to ask?
This is a graphical representation of Lawler’s Law. Point A represents the beginning of a game. This team (which ultimately wins this game) has roughly a 50% chance of winning at that point. As the game goes on, and more points are scored, the team depicted here increases its chance of victory based on the number of points it has scored. Point B…
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