Stuttering and buffering on streams is normally due to insufficient bandwidth. Please see the Recommended Bandwidth FAQ page here (quality is based on the connection rate).
If the bandwidth is fine, exit the game and re-launch it. If that does not help, exit and then re-launch the MLB app.
If bandwidth is a problem, power cycle the router and modem to try to improve the connection. (Power Cycling is turning off the power to the Modem and Router then powering back on, in an attempt to refresh the Internet connection.) Also, limit the amount of devices sharing your Internet connection. If you continue to have issues, try to connect your device to your router with an ethernet cable.
How to Update Your MLB Application
The MLB application should automatically force the most recent update. To ensure this, we recommend updating to the latest firmware on your Sony PlayStation® device.
PlayStation® 4: To update software, from the function screen, select Settings > System Software Update.
Upon launching the MLB App, your PlayStation® device will automatically download and install the latest version.
If you are unable to view a game and see a message stating that you need to update your account information or are having issues accessing content, go to the Payment Profile section of your account settings on MLB.com and enter the most current information here. Then log out and log back into your device in the "My Account" tab of the MLB app.
Try a hard reboot of your PlayStation® device. Remove your device from its power source for 30 seconds, and then turn it back on.
To force an update on a PlayStation® device, you can attempt to delete the MLB app from your device. After deleting the app, re-download it from the App store and re-link it to your registered MLB account.