>> Being a numbers guy, I couldn’t resist calculating the odds of making four sell recommendations on what ends up being the four best performers out of 749 different stocks. Can we have a drum roll? The odds are 1 in 13.1 billion
> The odds are actually 1 out of 16
Both of these look likely wrong to me.
The first, from a CBS article, is, I believe, based on there being 13008631251 ways to pick an unordered collection of 4 items out of a set of 749. But where does that 749 come from? It's the number of stocks listed on the Wilshire U.S. Large-Cap Index.
There's nothing in the CBS article that ties this to Cramer. The author wanted data on the top performing stocks to see how Cramer did. He asked the S&P Dow Jones Indices people for the data from the S&P 500, and they didn't have what he needed. Then he asked the Wilshire people, and they had it.
If the S&P Dow Jones Indices had the data, he presumably would have used the number of stocks on the S&P 500, ran the computation using 500 instead of 749, and came up with 2573031125 instead of 13008631251.
1 out of 16 also seems wrong. That would be the odds that a given set of 4 stocks Cramer picked would all go the opposite way that Cramer picked, if Cramer's picks were no better than random chance.
I think what we actually want here is to look at all of Cramer's picks in the applicable time frame, and determine what fraction of them, f, were ones he picked to go down. The odds that the 4 stocks that turned out best would be in his down list if his picks were by chance would then be 1 out of 1/f^4. This is only 1 out of 16 if Cramer picked half the stocks to go down and half to go up.
On first read, I also thought that the CBS article is actually including the odds than 4 randomly selected stocks will be the best market performers. But I didn't take the time to compute those ;-)
Nevertheless, it's totally ill-placed to blame Cramer for this. The journalist is using this low-probability to say:
"Thus, picking the four best performers as stocks to sell is the next closest thing to being statistically impossible. [...] By any measure of statistics I can think of, these four awful stock calls are telling of Cramer's incredibly poor ability to call stock sells. It not only surpassed my wildest imagination of just how bad anyone could be..."
For the 1 out of 16, you're also right. I was just keeping the same hypothesis as the one in the article of a uniformly random distribution.
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[ 3.1 ms ] story [ 11.6 ms ] thread> The odds are actually 1 out of 16
Both of these look likely wrong to me.
The first, from a CBS article, is, I believe, based on there being 13008631251 ways to pick an unordered collection of 4 items out of a set of 749. But where does that 749 come from? It's the number of stocks listed on the Wilshire U.S. Large-Cap Index.
There's nothing in the CBS article that ties this to Cramer. The author wanted data on the top performing stocks to see how Cramer did. He asked the S&P Dow Jones Indices people for the data from the S&P 500, and they didn't have what he needed. Then he asked the Wilshire people, and they had it.
If the S&P Dow Jones Indices had the data, he presumably would have used the number of stocks on the S&P 500, ran the computation using 500 instead of 749, and came up with 2573031125 instead of 13008631251.
1 out of 16 also seems wrong. That would be the odds that a given set of 4 stocks Cramer picked would all go the opposite way that Cramer picked, if Cramer's picks were no better than random chance.
I think what we actually want here is to look at all of Cramer's picks in the applicable time frame, and determine what fraction of them, f, were ones he picked to go down. The odds that the 4 stocks that turned out best would be in his down list if his picks were by chance would then be 1 out of 1/f^4. This is only 1 out of 16 if Cramer picked half the stocks to go down and half to go up.
Nevertheless, it's totally ill-placed to blame Cramer for this. The journalist is using this low-probability to say: "Thus, picking the four best performers as stocks to sell is the next closest thing to being statistically impossible. [...] By any measure of statistics I can think of, these four awful stock calls are telling of Cramer's incredibly poor ability to call stock sells. It not only surpassed my wildest imagination of just how bad anyone could be..."
For the 1 out of 16, you're also right. I was just keeping the same hypothesis as the one in the article of a uniformly random distribution.