Diagonal Speed Boost

You're headed north, he's headed northeast, he suddenly turns northwest halfway to the destination, the race ends in a tie. You both traveled at identical speeds the whole way. Or at least you would have, were it not for the diagonal speed boost.

Common in square grid based games, the diagonal speed boost is when it takes the same amount of time or turns to move to a diagonal square as it does to a horizontal or vertical square. This means that diagonal movement is about 40 percent faster^note specifically, it's √2, or approximately 1.414 than movement in a straight line. This allows whatever's moving on the grid to cover more ground in the same amount of time.

Not just a problem with grids; most older first-person games implement diagonal movement in a similar way: moving forward in any direction gives normal speed, while a combined sideways movement adds to the speed. It's arguably even worse, as you can change which direction you're facing to get a diagonal speed boost in any direction.

Savvy players can use this to outmaneuver and flank opponents unless there's a rule against it. The unreality of this trope is why some games use hexagonal grids, where the distance from the center of one hex to that of an adjacent hex is always the same regardless of the direction of travel. As such, this trope can qualify as an Advanced Movement Technique.

The Other Wiki calls this Chebyshev distance.

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Examples:

• The Réti endgame study in Chess (published in 1921, but based on a 1914 game) is a candidate for Trope Maker. The white king is able to chase black's pawn on one side of the board while simultaneously approaching his own pawn on the other. The trick is that black's pawn can only move vertically, but white's king can move diagonally.
• Descent: Trichording—a diagonal slide (e.g. up/down + left/right) combined with forward thrust. This gives up to a 73% speed boost, not counting the afterburner added in Descent II. The justification for this is that several of your ship's thrusters are being used simultaneously to move it in one direction, which results in a combined thrust that is greater than full forward/reverse thrust.
  • As Descent serves as the Trope Codifier for any video game that features six degrees of freedom, most video games released after it that also feature six degrees of freedom, such as Elite Dangerous, Overload, Star Citizen, and Sublevel Zero, allow the player to trichord to varying degrees.
• Doom: Straferunning (SR)—strafing sideways and running forwards at the same time—is 30% faster than just moving forward or strafing. The most common method of SR is called SR40, named so because internally your sideways acceleration will be 40 (in arbitrary units, unrelated to length units), as compared with forward/backward acceleration of 50. It is also possible for a further speed boost known as SR50, where you turn and strafe in the same direction, with "strafe on look" on. Combined with moving forward, this gives the full ~41% speed boost (but prevents you from turning), and is used in many speedruns.
  • Speed runs of GoldenEye (1997), its Spiritual Successor Perfect Dark and The World Is Not Enough pretty much require you to strafe-run everywhere.
  • Quake fixed the straferunning exploit in Doom by capping your movement input, but introduces a very peculiar issue in the way it caps your acceleration: rather than checking how fast you'd end up going period, it only checks how fast you're moving in the direction you're accelerating. You could be moving at truly ridiculous speeds straight forward, but none of your velocity is pointed to the left or right or whatever other direction, so you can still accelerate to full speed in any direction but forward. This quirk is the source of the most fundamental of Quake's movement tricks, from Quake 1's bunnyhopping, to Quake 2 and beyond's strafejumping, to Quake 4 and Champion's crouchsliding as a form of acceleration. This is also why you can do 180 degree midair turns in Quake 1 and gain speed in the process.
  • The GoldSrc and Source engines (of Half-Life and Team Fortress 2 fame), being directly based off the Quake engine, displays the same acceleration quirk Quake does, but tightens up jump inputs and makes bunnyhopping harder as a result. On the other hand, it introduces the ability to strafe and walk up ladders simultaneously, with the results you'd expect on this page. Custom maps have even used this as a puzzle element since you can jump from the top of a ladder with more upward velocity than your legs can provide. Even the recent Left 4 Dead series only sports new ladder code for survivors; the zombie team can still climb walls 50% faster with this trick.
    • Team Fortress 2 in particular takes the air movement of Quake 1 and runs with it. The Soldier and Demoman have explosive jumping as core features, and the characteristic air movement gives them both great speed, surprising mobility, and a very high skill ceiling just for moving around the map. More towards this trope, a Demoman that replaces the Stickybomb Launcher with the Tide Turner's Dash Attack allows a technique called trimping, which combines Quake's acceleration quirk with constant, heavy forward acceleration even in midair, and the result can only be described as absolutely ludicrous.
  • Battlezone, on the other hand, retains this. In fact, going forward, strafing, pitching your hovertank forward (auto-stabilizing needs to be turned off or the tank will try to level out by itself) and using the jump thrusters all at once gives much faster movement - to say nothing of a physics glitch that allows hovertanks to float high enough to be out of range for most weapons. Naturally, all versions of Battlezone 2's unofficial 1.3 patch nerfed the ability to fly, to much rage from the veteran players.
• Dungeons & Dragons:
  • When 3rd edition introduced the 5-foot square grid, it came with the rule that diagonal movements alternate between costing 1 and 2 squares' worth of regular movement, making diagonal movement about +6% slower rather than +41% faster in the long run. (At typical movement rates, this will frequently result in a speed boost anyway, since the alternation starts with the cheap cost every turn.)
  • 4th edition relieves a bookkeeping burden by counting diagonal moves equally to orthogonal ones, giving the diagonal speed boost in its classic form.
  • 5th edition also has this, and the rules section about grid movement actually mentions that it may seem strange but you should ignore it as the grid is an approximation anyway. There is an optional rule to mitigate this by reverting to the 1.5 rule above.

• Secret of Evermore: Running diagonally is visibly faster.
• Sid Meier's Pirates!: Land battles allow diagonal movement in this manner. When combined with the flanking bonus a unit gets for attacking from the side it can allow for victory against overwhelming odds.
• Almost all Roguelikes.
  • One of the earliest creatures in NetHack, the grid bug, cannot take advantage of the diagonal speed boost. The "grid bug conduct" is an unofficial Self-Imposed Challenge to voluntarily apply the same limitation to your character, which is much more important and potentially lethal than it sounds.
  • The Pokémon Mystery Dungeon series not only follows this logic, it also comes with a button input to lock yourself into diagonal movement to help you do this.
  • In Dwarf Fortress diagonal movement on the x-y plane takes 362/256 times as long as orthogonal movement, which is as close as the game engine can get to the square root of 2. Z movement, however, will just add the extra axis movement space.
  • DRL uses the so-called Angband metric; the distance between two points is the length of the long axis plus half the length of the short axis, rounded down. That's still a speed boost within the Moore neighbourhood used for movement (1 + 0.5 rounds down to 1), but it has consequences when determining range for weapons.
  • One Way Heroics allows you to have a key, that, when held down, restricts your movement to the four diagonal directions, for those playing on a pad or with the arrow keys. Of course, you can use a numpad instead. Given that the premise revolves around outrunning an Advancing Wall of Doom, diagonal movements are extremely important and can make the difference between "phew, barely escaped the autoscroll, onward for another few hundred kilometers!" and "gods dammit, Yet Another Stupid Death!"
• Deadly Towers plays this straight in the first place, but there is also an item (called the Hyper Shoes) that increases your move speed...but only if you're moving diagonally.
• Occurs in Marble Blast Gold. Hold down two direction keys at once and the marble will travel faster than normal. This is sometimes needed to beat the gold times.
• "Zig-zagging" is the best way to run in the open field in Tecmo Super Bowl and its sequels because you don't lose speed when rushing diagonally.
• Youju Senki AD 2048 has an odd variation: moving one space diagonally is considered the same as moving one space vertically or horizontally (counted as one space when moving or shooting), but the characters cannot move like this if the spaces next to them are occupied by enemies or obstructions (to put it simply, if you can't move there without diagonal movement, you can't move there period). However, this limitation does not affect attacks (meaning that even if a character can't move diagonally into a space, they can still shoot that space if they're in range).
• Halo: Oddly present in Halo 3 and Halo: Reach. Picking up a turret normally causes you to move slower, but moving diagonally negates that speed decrease entirely.
• Gunrox, an online turn-based, grid-based, squad-based tactics game, has this. Making use of it is an easy way to gain the advantage over an inexperienced player.
• The prototype Ninja Gaiden for the Sega Genesis was a belt-scrolling Beat 'em Up where Ryu could only move diagonally unless hemmed in by the top or bottom. This was likely a bug which would have been corrected had it received a final release.
• In Minecraft, minecarts travel diagonally over curved rails. If you place rails on two adjacent diagonals, you get a zig-zagged track, which you can travel over as if it were a straight diagonal. This results in a speed boost.
• In the Heroes of Might and Magic IV-VI combat screen, diagonal movement takes 1.5 times the amount of movement points for horizontal and vertical movement. (The first three games used a hexagonal combat grid.) But there's no extra cost for moving diagonally on the overland map, like in most TBS games.
• Similarly, in tactical combat of the pre-reboot XCOM games, time unit and energy costs (including terrain penalties) are multiplied by 1.5 and rounded up.
• In both PlanetSide games, the Vanu Sovereignty's Magrider tank moves significantly faster when strafing and moving forward - to the point where a Magrider can actually keep up with a Terran Republic Prowler tank. Aircraft in PS2 likewise can fly much faster when the nose is angled down, and the vertical lift thruster is engaged.
• In the X-Universe series, the player use the (player-exclusive) strafing thrusters to give them a small speed boost while using the main engines. Strafing speed is generally much slower than most Space Fighters, but on the slow-as-molasses Space Trucker transports, it can make a world of difference. However, in practice it is rarely used outside of combat since for travel it is far faster to just turn on the autopilot and engage the Singularity Engine Time Accelerator to speed up the game. In X: Rebirth, the Albion Skunk has very powerful strafe thrusters which are handy for maneuvering without using the shield-sapping Nitro Boost.
• Undertale applies this not just to moving around areas, but also the Bullet Hell attack-dodging interface. This can take a little getting used to if you frequently play scrolling shooters, most of which avert this trope.
• A feature of Blood Bowl, which is played on a pitch divided up into squares, where moving diagonally costs no more points of movement that moving straight forwards. Because movement in open squares is one of the few actions that doesn't risk ending your turn, understanding how to move your players efficiently is a key skill.
• In South Park for the Nintendo 64 and PlayStation, the player can run faster by pressing C Left or Right as well as C Forward while looking downwards.
• The square in The World's Hardest Game moves faster diagonally. Some levels require you to exploit this, such as level 6 of the second game.
• In Forbidden Island, the Explorer is the only Adventurer who can move diagonally, which allows for faster movement. They can also shore up tiles diagonally.
• Paper Mario: The Thousand-Year Door: An unusual example. Because the game was built around an odd perspective, Mario has more x-axis speed than z-axis speed. However, speed is still calculated as a function of inputs in both directions, so provided there's a wall to restrict your movement in the z-direction, it's marginally faster to run at a slight forward diagonal than simply left or right.
• Everybody Edits Flash provides a Platform Game example. Horizontal and vertical speed are calculated separately, resulting in more distance being covered when moving diagonally.

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