Fantasy Premier League player prices operate much like a stock market. Although there appears to be some manual invervention by the team behind the FPL game, player prices rise or fall based on the volume of purchases or sales of each player.
Price changes generally occur around 1:30am UK time. Price changes occur in increments of £0.1m and a player can only rise or fall once per day and 3 times in one gameweek.
If you wish to build or retain the value of your team, it's important to be on the ball with player prices. It's frustrating to plan a transfer, only to discover that you've been priced out by £0.1m because the player rose in price or your existing asset dropped in price since you last looked.
Conversely, early ditching of your injured/underperforming assets, and early investment in rising assets can have a significant effect on your team value. For example if the players are "hot" and "cold" enough to change price twice in a gameweek, an early switch could mean a significant £0.4m swing in your team value.
The downside of early transfers, of course, is that circumstances often change during the gameweek. Players may become injured or unavailable, or midweek performances may affect your decision. International breaks can wreak havoc with injury and illness. So early transfers are a gamble in that respect, and many managers prefer to accept a loss and wait until press conferences and late team news before making their transfers. You can find very brief press conference summaries at Premier Fantasy Tools.
The FPL "bank" keeps half of your profit. You can think of it like a 50% sell-on fee. Despite this, it's possible to increase your team value during gameweeks when you wildcard. If you're sure you want to wildcard, do it early. Get rid of your unwanted players before they drop in price and transfer in players that you think are most likely to rise twice in a week. Even if you don't want to keep them, you can transfer them out after a double rise and make £0.1m on them without them ever playing for you.
But be wary of "hokey cokeying" a player out and in during a wildcard gameweek if there is a risk that player will rise in price while you don't have them. The price you pay is their price when you sign them last, so it's easy to mess up and lose £0.1m or even £0.2m.
Also worth noting is this observation from @FPLPriceChanges: When a player'd status changes from 'Unavailable' to 'Available', FPL locks their price for a period of time (usually a week or until the next GW if less than a week). That means it doesn't matter how many transfers IN or OUT, they will not change in price until the lock expires.
The websites below do a good job of predicting when player prices are likely to rise or fall. As the price-change algorithm is mysterious and prone to change and manual intervention, the sites' predictions usually don't match precisely, and the predictions often don't come true. So use them as a guide only. Also note that these sites can struggle to maintain accuracy in weeks where there is a high volume of wildcard transfers, such as blank and double gameweeks.
This website has been around for a long time and boasts good accuracy for FPL player price changes. Click the "Target" column header to toggle between prospective risers and fallers . Hit F5 to refresh the page for the latest data. It's worth reading the Notes for insight into FPL price changes. fplstatistic.co.uk - Fantasy Player Price Change Predictions...
Click the "Change time" column header to bring players with imminent price changes to the top. Cyan progress bars indicate risers, while deep orange progress bars indicate fallers. Fantasy Football Fix Price Change Predictor...
The FPL Plus by fantasyfootballfix.com Chrome browser extension also adds a new tab to your FPL page, showing these price change predictions.
A newer option than the previous 2, currently with no explanation of what the figures mean in terms of when players' prices are likely to rise or fall. Fantasy Football Hub Price Change Predictions...
To simply track FPL price changes, and see why you now can't afford the player you were planning to buy at the start of the week, try these: