Is it wrong to estimate its moment probability with Bayes, beta parameter 
*

*As far as I know I can decide beta parameter for Bayes estimation. 
Let’s say we estimate probability of coin flip distribution, and choose Uniform Distribution as Beta(1,1)
If 9 of 10 flips will come up heads, beta parameter would be Beta(1+9, 1+1). After next new trial, we would to update Beta parameter. I believe that these result in approaching to true probability rate. 


My question
1. I wondered if I can apply to baseball batter hitting rate
Can we estimate batter’s hitting rate?? 
For example, I  use past score of batter as prior distribution, and use score of this season to get posterior distribution. 
The batter have the 100 of times at bat, and 30 hits. (In my country, calculate like 30/100 as hit rate). Then, beta would be Beta(30, 70)
Next, we gonna add this season’s score like 10 of times at bat, and 9 hits. Then, beta parameter would be Beta(39, 70).
Is it ok??
2. I wondered if I can estimate this moment hitting rate.
Is it ok that we take most recent several score to estimate this moment hitting rate??  
After the batter got the new result(hit or mis-hit), ignore the prior(=past posterior) distribution, and use original prior distribution with new recent score to get posterior??
If we decide to take recent 4 score and get this score for the batter. it would looks like this
1: mis-hit 
2: hit 
3: hit 
4: hit 
Beta(30, 70) as prior distribution would be Beta(30+3, 70+1)
And, after he got the new result for 5th (ignore 1st result cuz we assume most recent 4 score). It would look like 
2: hit 
3: hit 
4: hit 
5: hit 
Beta(30, 70) as prior distribution would be Beta(30+4, 70+0)
I want to estimate this moment hitting rate, not approaching to true probability rate. 


Any advice would be helpful such as baseball hitting rate in not fitted to modelling. 
Cheers
 A: Taking aside the technical aspects of applying the math, why would you want to do this? What you're basically saying is that each time you see new data point, you want to forget everything that you have learned until now and assume that you know nothing about your data besides the very recent history. Assume that your batter mis-hit one thousand times in a row and then had four hits, would you be prone to assume that he is a very good better because among the recent four bats he had 100% success rate? Unless you could assume that after four tries batter "forgets" all his previous skills and he becomes a totally different player, i.e. his past history tells you nothing about the current state, then your approach would be very flawed.
If you want to take consideration the recent history and the changes over time, where past history has somehow less "weight" on the recent outcomes, then the current history, then you should probably consider some kind of time-series model that takes those factors into consideration. I doubt that discarding valid data does any good in here.
Speaking more Bayesian, if you know the previous history, then you should adapt your prior to it, since prior tells you about your prior knowledge about the data. In this case, the past history is your prior knowledge. By discarding it you basically say that you don't care about the history and you know better what the batter's ability is -- this doesn't sound reasonable. This is the idea behind Bayesian updating. 
A: I'm working on a similar case.  I have a program that gives the user the same questions over and over again, and they slowly learn the answers.  It takes them 3 or 4 attempts on average to 'learn' an answer.
I can easily calculate their probability based on data from the start of time.  The problem is that assumes the user never improves.  In reality their old answers need to be thrown out.
It is possible to add a weighting to newer events and still use this Rule of Succession method: probability = (success + 1) / (total + 2) .  But it means you have a trade off between punishing users for past mistakes or having a long and detailed memory about the user.
What i've found best so far is the same as you put originally in your question: Just use a history size of 10 questions and forget ones that are older.  The historic weighting / damping doesn't matter that much unless you want to avoid having sharp jumps in your results when the history buffer empties.
