Andy Chang asked the most important question about my baseball investment strategy:

How did I come up with the probabilities in my chart?

For example, if the Angels are projected by Baseball Prospectus to win 86 games, and they are projected by the Vegas oddsmakers to win 92.5 games, how would I determine the probability that they will win 92 or fewer games?

It is important that I answer this question, because all of my assumptions about expected profit and profit % are based on these probabilities.

In my previous post, I simply guessed what they might be.

But after doing more research today, I can now generate a more accurate value for these probabilities.

In order to determine the probabilities, I needed to look at past data and find out how each team's actual number of wins differed from their expected number of wins.

I used the Diamond-Mind pre-season projected team standings from 1998-2004. The Diamond-Mind projections have proven to be more accurate than most other projections, and this data should be comparable to the results from Baseball Propsectus (for which I don't have data).

The following is part of the cumulative distribution chart for the difference between actual wins and expected wins for 210 data points (30 teams over 7 years):

W - E(W)	Cumulative Distribution
-10	17%
-9	20%
-8	22%
-7	25%
-6	29%
-5	33%
-4	35%
-3	40%
-2	43%
-1	47%
0	51%
1	55%
2	59%
3	62%
4	68%
5	72%
6	75%
7	80%
8	82%
9	85%
10	86%

The chart above can help us create a new chart.

If we go back to our question about the Angels, what we need to do now is add the Angels' expected win total to the first column, and then we will have the distribution of the Angels' win totals.

2005 Angels Win Total	Cumulative Distribution
76	17%
77	20%
78	22%
79	25%
80	29%
81	33%
82	35%
83	40%
84	43%
85	47%
86	51%
87	55%
88	59%
89	62%
90	68%
91	72%
92	75%
93	80%
94	82%
95	85%
96	86%

Now we have the answer to our original question:

According to Baseball Prospectus' expected win total and my cumulative distribution of win differences, the Angels will win 92 or fewer games approximately 75% of the time.