My buddy Tony and I have been trying to figure out how to quantify Jeremy Lin’s recent five games. He suggested I figure out the likelihood of his start, assuming that Lin is “just” an above average point guard. So, I identified all the point guards who averaged between 16 and 18 points per game in the 2009-10 or 2010-11 season. In 2009-10, that included Devin Harris, Rodney Stuckey, Russell Westbrook, Stephen Curry, Steve Nash, and Tony Parker. In 10-11, the list is Brandon Jennings, Chauncey Billups, Gilbert Arenas (before the suspension), John Wall, Raymond Felton (while with the Knicks), and Tony Parker again.
I collected the game logs for all these guys for the relevant year(s); here’s the histogram of points scored in each game (including playoffs to bump the sample up):
In a total of 832 games, these players scored 30 or more points on 38 separate occasions (this is the total of the last three bars on the right). Likewise, they scored fewer than 5 points in 32 different games. These two tails each capture about 4-5% of the total distribution.
Using this distribution, we can answer the following question: if Lin is a 16 to 18 point per game point guard (above average), what are the chances that he would rip off 25, 28, 23, 38, and 20 points once he got meaningful playing time? Under the assumption that Lin is similar to the guys above, the approximate percentiles for these point totals are 90, 95, 85, 99.5, and 74. In other words, 16 to 18 point guys score 25 points or more around 10% of the time, 28 points or more 5% of the time, 23 or more 15% of the time, 38 or more 0.5% of the time, and 20 or more 26% of the time.
The chance that such a point guard would start with these five games in exact sequence is the product of all the probabilities: 0.1*0.05*0.15*0.005*0.26 = 0.000098%. The order in which the games occur isn’t really important for assessing quality, so we can multiply this by 120 (the number of different permutations of the five games), which yields 0.01%. That’s still pretty unlikely!
I can be a little more conservative. What’s the probability that a 16 to 18 point guy would put together a streak like this at some point during the season? I simulated 10,000 seasons and found at least five games in a row above the 90th percentile in only 0.04% of seasons. Based on these numbers, it looks like 16 to 18 points per game is too conservative for Lin.
However, if I generate the distribution using only 17 to 18 point guys, the probability that he would start as he did (in some order) is 0.02, or about one out of every 50 seasons. That’s not so unreasonable, considering that there are three or four guys in that range each year. We should expect a point guard that scores 17 to 18 points per game to start with a stretch like Lin’s every 15 or 20 years.
So, is Lin above average? Almost surely so. Is he better than that? On points alone, he could be, but we’ll have to wait and see. He’s shooting well above his college percentage from two point range, but he could continue to improve — after all, he’s a rookie. I also slipped an assumption by you. By multiplying all the probabilities to figure out the chance that they would occur in order, I assumed that each game was independent. In reality, once a guy starts scoring, he probably takes more shots in future games, increasing his point totals. That could make a streak more likely.
This will be my last Jeremy Lin post for awhile — to get a more solid answer, we need him generate some more data, starting with tonight. If you just have to have more Lin, check out his effect on the stock of the Knick’s ownership company (thanks to Tony for the link). Pretty impressive.