Deeper Data Dive

Last time, we introduced the data available to us for analyzing the game of Sheepshead. We are ready to combine some of those data sets and look deeper into the data.

Data Preparation

Combining the Picker, Score, and Dealt tables, we have the picking team’s score for each hand, the picker’s hand, and thepicker’s place in the picking order. Our combined data set includes the columns mentioned on the 15,940 completed hands to date.

Once the data are combined, it is still difficult to say much about the picker’s hand with the data in their current format. In order to make much sense of the hand the picker has, we create 32 new indicator variables, one for each card in the deck. As an example, one of these variables is called isQC. It simply tells us whether the picker was dealt the queen of clubs or not. Variables isQS, isQH, and so on exist as well.

These new variables allow us to do things like count the number of trump in the picker’s hand and determine the value of having an individual card in one’s hand.

Analysis

Recall that our end goal is to know whether we are better off picking on a given hand or passing. We won’t be able to do that all at once, but the first step in that process involves building a predictive model that tells us the probability we will win the hand if we pick. Before we starting building a model, we want to examine the data a little closer to see whether there are any abnormalities in the data. We also want to see whether some basic reports tell us anything about what to expect of the model we are building.

The table below tells us the percentage of picking hands that contain the given card. This tells us what players find valuable when determining whether to pick. It doesn’t tell us what actually is valuable. With that said, the information is instructive.







































































































































Card % of Picking Hands
Queen of Clubs 42.5%
Queen of Spades 36.9%
Queen of Hearts 33.1%
Queen of Diamonds 30.0%
Jack of Clubs 25.7%
Jack of Spades 25.0%
Jack of Hearts 24.2%
Jack of Diamonds 10.0%
Ace of Diamonds 22.9%
10 of Diamonds 22.4%
King of Diamonds 21.3%
9 of Diamonds 20.9%
8 of Diamonds 21.0%
7 of Diamonds 20.8%
Ace of Clubs 15.6%
10 of Clubs 14.2%
King of Clubs 13.8%
9 of Clubs 12.9%
8 of Clubs 13.3%
7 of Clubs 12.6%
Ace of Hearts 14.4%
10 of Hearts 13.8%
King of Hearts 13.2%
9 of Hearts 12.6%
8 of Hearts 12.6%
7 of Hearts 12.9%
Ace of Spades 14.6%
10 of Spades 14.2%
King of Spades 13.6%
9 of Spades 13.2%
8 of Spades 12.8%
7 of Spades 13.1%

The first thing we notice is the difference in percentage of picking hands with a queen of clubs stepping down to the jack of hearts. If anything, it is suprising 10% of picking hands contain the jack of diamonds. One might expect that to be lower.

Another thing we notice is there is nearly no difference between having the ace of diamonds and a 7, 8, and 9 of diamonds, but there is a significant difference between an ace of fail and a 7, 8 or 9 of fail. There are a couple potential reasons for this: first, a fail ace is the most powerful card for that suit; second, pickers might plan to bury the ace of fail.

The relationship between the fail ace, fail ten, and the rest of the cards in that suit is constant across fail suits. Remember, this doesn’t tell us that an ace of clubs is more valuable than the 7, 8, and 9 of clubs. It only tells us that players on the website are behaving as if the ace is more valuable.

The table above is univariate. It could be that, by chance, players with an ace of fail have happened to have better than average trump while players with small fail have had worse than average trump. This is very unlikely given how many hands have already been played.











































# Trump Had JD No JD
0 0.2% 0.0%
1 2.1% 0.6%
2 10.5% 5.0%
3 34.2% 17.7%
4 41.0% 42.0%
5 11.2% 29.7%
6 0.8% 5.0%

It’s no suprise that players require more from a picking hand if they have the jack of diamonds. About 77% of picking hands with the jack of diamonds have at least four trump or more. Without the jack of diamonds, only 53% of picking hands have four trump or more.

We are now in great position to built a model that assigns a win probability to a hand prior to picking.