I don't quite know how it works in the rulebook.
The way it's been done in the rulebook has changed from edition to edition. When I first started playing Blood Bowl, it used to be that you'd pick three players on your team and roll a d3 to determine who'd get it. The following edition had it such that it was strictly determined by d16 (you get a 16-sided dice in each set) according to where on the team roster the player was listed. Haven't checked what it will be for the new edition, but my group is ignoring it anyway in favour of our own MVP selection method.
Wouldn't it make sense to award the MVP to the player that earned the most SPP in the game? They clearly had the greatest impact. It might make the player level up too quickly, but it would be more realistic.
Not necessarily, especially if a team has the misfortune of not scoring any SPP over the course of the game.
How we do it is based on which player impressed us the most by its actions over the course of the game. Obviously, priority picks typically go toward players who scored SPP that game, but they're just as valid as the player who ran a lot of interference, were key to pulling off a ridiculously difficult play (with or without scoring any SPP themselves), did something that stands out as being unexpected, or otherwise did the most to help their team try to win the game.
It's also worth remembering that not all sources of SPP reward players equally either. At its most basic level, Completions are worth 1SPP, Casualties are worth 2SPP, and Touchdowns are worth 3SPP. Incidentally, some teams in the new edition have the Brawlin' Brutes special rule, which switches the SPP gains for Casualties and Touchdowns by players in that team.
Depending on the team you're playing, touchdowns are the easiest to get, as it's just getting the ball to the end zone after either catching or picking up the ball, with outside interference being the only obstacle in the way.
Completions are more involved and a little more difficult to pull off, requiring a Pass roll by the player throwing the ball and a Catch roll by the player receiving it, even before accounting for outside interference. Still manageable if you have 2+ PA and/or relevant skills though.
Casualties are notoriously unreliable to get by comparison. First you need to knock another player down via block dice, then you need to roll to break armour on 2d6, then you need to roll an injury result of a 10+ on 2d6. A few factors can modify this - the Claws trait treats natural rolls of 8+ as a success when breaking armour, Mighty Blow allows you to add +1 to either armour or injury roll if you so choose, Stunty players can be made casualties on a 9+, etc - but you're still relying on dice rolls that give you a relatively small chance of success by comparison to other means of getting SPP, and unlike nearly every other roll made in the game there is no way to re-roll the 2d6s.