How to Utilize the Markov Model in Predictive Analytics

A Markov model is a statistical model that can be used in predictive analyzes that rely heavily on probability theory. (It is named after a Russian mathematician whose primary research was in probability theory.)
Here’s a working scenario showing how it works: Imagine you want to predict whether Team X will win tomorrow’s match. The first thing to do is to collect the past stats about Team X. The question that may arise is how far in history should you go?
Let’s say you were able to access the last 10 previous results of the game in sequence. You want to know the probability of Team X winning the next match, given the results of the past 10 matches.
The problem is that the more you want to go back in history, the more difficult and complicated it becomes to collect data and calculate probabilities.
Believe it or not, a Markov model simplifies your life by providing you with a Markov hypothesis, which looks like this when you put it in words:
The probability of an event occurring, given n past events, is approximately equal to the probability of such an event occurring given only the last event in the past.
Written as a formula, Markov’s assumption looks like this:

Either way, the Markov Assumption means that you don’t need to go too far back in history to predict tomorrow’s outcome. You can just use the most recent past event. This is called the first-order Markov prediction because you’re considering only the last event to predict the future event.
A second order Markov prediction includes just the last two events that happen in sequence. From the equation just given, the following widely used equation can also be derived:

This equation aims to calculate the probability of some event occurring in a sequence: event 1 after event 2, and so on. This probability can be calculated by multiplying the probability of each event (given the event before it) by the next event in the sequence. For example, suppose you want to predict the probability of team X winning, then losing, and then relationships.
Here’s how a typical predictive model based on the Markov model works. Consider the same example: Suppose you want to predict the outcome of a soccer match played by Team X. The three possible outcomes – called states – are win, lose, or draw.
Suppose you collected past statistical data on the football results of Team X, and Team X lost its last match. You want to predict the result of the next football match. It’s all about guessing whether Team X will win, lose or draw – just based on data from previous matches. Here’s how to use a Markov model to make this prediction.

• Calculate some probabilities based on past data.

For example, how many times has Team X lost matches? How many times has Team X won matches? For example, imagine if Team X won 6 matches out of a total of ten matches. Next, Team X wins 60 percent of the time. In other words, the probability of Team X winning is 60 percent.

• Calculate the probability of loss and then the probability of tie in the same way.

 

• Use the Naïve Bayes probability equation to calculate the probabilities such as the following:

>>The probability of Team X winning, given that Team X lost the last match.
>>The probability of Team X losing, given that Team X won the last match.

• Calculate the probabilities for each case (win, lose or draw).

 

• Assuming the team only plays one game per day, the odds are as follows:

P (Win | Loss) is Team X’s probability of winning today, given that they lost yesterday.
P (Win | Tie) is Team X’s probability of winning today, given that they tied yesterday.
P (Win | Win) is the probability of Team X winning today, given their win yesterday.

• Using the calculated probabilities, create a chart.

The circle in this diagram represents a possible state that team X could achieve at any given time (win, lose, draw); The numbers on the arrows represent the probabilities of team X moving from one state to another.

For example, if team X just won today’s match (its current state = win), the probability of team X winning again is 60 percent; The probability that they will lose the next match is 20 percent (in this case they will go from the current state = win to the future state = loss).
Let’s say you want to know the chances of Team X winning two games in a row and losing the third. As you might imagine, this is not a straightforward prediction.
However, using the graph just created and the Markov assumption, you can easily predict the chances of such an event. You start with the win condition, cross the win condition again, and score 60 percent; Then you move into a loss situation and score 20 percent.
The chances of Team X winning twice and losing the third game are simple to calculate: 60 percent x 60 percent x 20 percent 60 percent * 60 percent • 20 percent, which equals 72 percent.
So what are the chances that Team X wins, then draws, and then loses twice after that? The answer is 20 percent (going from win to tie) 20 percent (going from tie to loss), multiplied by 35 percent (going from loss to loss) multiplied by 35 percent (going from loss to loss). The score is 49 percent.