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# Simulating Kovi

I put together a series of simulations to see what spread of shooting production we might expect to see from average players and how the variability in that production compares to what we might expect from Kovi. In looking at the data over the last few years, it appears roughly 500 players have had greater than 20 even strength shots each season, with the maximum shots around 200. I used these as the basis for my models. I'm using a coin-flipping model, with every one of the 500 players other than Kovi having a known shooting percentage of 8.0%

Model 1

Each player takes 110 shots in a season. Data analyzed after 1 and 5 seasons.

 Analysis Average Std. Dev. 25% percentile 75th percentile 1 year 2.58 2.52 2.63 5 years 1.16 1.13 1.18

For comparison, if each player takes 200 shots in a season

 Analysis Average Std. Dev. 25% percentile 75th percentile 1 year 1.92 1.88 1.96 5 years 0.86 0.84 0.87

Model 2

Each player was assigned a random number of shots between 20 and 200. The number of shots was distributed uniformly. The same number of shots were taken by that player each season.

 Analysis Average Std. Dev. 25% percentile 75th percentile 1 year 3.06 2.97 3.14 5 years 1.18 1.16 1.21

At one year, the standard deviations are about 20% greater. At 5 years, however, the standard deviations are only slightly greater than Model 1.

Model 3

Like Model 2, each player was randomly assigned a number of shots between 20 and 200. The player took this many shots in year 1. In the subsequent years, they took 1.2, 1.1, 0.9 and 0.8 times as many shots. Hence the player with 200 average shots took 200 shots in the first season, then 240, 220, 180, and finally 160 shots in the fifth season.

 Analysis Average Std. Dev. 25% percentile 75th percentile 1 year 3.06 2.97 3.14 5 years 1.37 1.33 1.41

This obviously results in a substantial increase in the standard deviation of the 5 year estimate .

Kovi versus the models

In the first Model, the confidence interval of the average one year estimate of average runs from [2..94, 13.06]. At 5 years, it runs from [5.73 ,10.27] In Model 2, one year is [2.00,14.00] and 5 years is [5.69, 10.31]. In Model 3, one year is the same as model 2 and 5 year is [5.31, 10.69]. So in Model 1, at 5 years, he is at +1.69 SD. In Model 2, he is at +1.65 SD. In Model 3, he is at +1.42 SD.

Gabe had looked at this in an earlier post. He got a standard deviation of 0.44. Working with Model 1, I increased the number of shots in each season until the average standard deviation came down to 0.44. It took 750 shots per player per season for 5 seasons for the average standard deviation to reach this level. In Model 3, it takes about 1950 shots on average per player per season for 5 seasons to reach this level.

Conclusion

In these models, in the land of 8% shooters, the 10% shooter is less than 2 SD above the mean.