Slams, Games & Partscores
     
HCP total and LTC & Distribution & Knowledge of Controls are what determines conclusion of bidding.
So first lets examine these concepts individually.

HCP count is what every bridge player knows about

Let's look at the detail:
The popular count is 4-3-2-1 for A,K, Q & J
Nevertheless this count is very approximate and incidentally 7531 actually provides a more realistic measure giving the pack a 65 total count rather than 40 of the 4321 count.
Nevertheless all stick to the 4321 which leaves me the task of explaining where its inaccuracies lie.
First Aces are undervalued. 4 1/4 is more realistic than 4. There also seems to be an old wives tale that says a hand of 3 Aces is not a good opening - i beg to differ and value it at 13 and will always open it.
At the other end of the scale Jacks are overvalued 3/4 a more accurate evaluation, This is especially true of isolated Jacks  count them as 1/2 would be wise, however when  they combine with other honours  like A, K or Q  and perhaps a Ten their value  could be  1, 1, 1, 3/4  respectively.
Most know that singleton or doubleton K or Q's are to be devalued initially to 2 & 1 for singletons and 2 1/2 & 1 1/2 for doubletons. However if ever in the bidding partner shows that suit thn they may immediately revert to their full value - even a previously discounted J.
A humble Ten or 9  has a value in a suit when supporting honours should give a plus value especially in flat distributions.
So what do we do with the count: First of all revise its evaluation as the bidding progresses, secondly combined with partners apparent values (according to system) it gives part of the reasoning as to what the partnership may obtain.

Balanced hands &  NT  contracts

In NT contracts a game is odds on with 25HCP even with 24 probabilities are reasonable but distribution and controls will determine the answer not just HCP. How many times have opponents defeated your 3NT by running a 5 card suit? I know you get away with it sometimes but with good opposition it would be a foolhardy to dream of making it if opponents have 9 cards or even 8 in a suit in which you have no control. Of course with less than 24 3NT can make with a good suit to run.
So distribution and controls are the deciding factor - HCP is just a guide.
What of 1NT contacts. Here there is no doubt that declarer has the edge - its far easier for declarer to determine his best chances then the defenders can theirs. Therefore even with a combined 19 HCP value declarer can succeed more often than not - therefore unless distribution indicates otherwise do not disturb a balanced 1NT opening with 7-8 points! One cannot expect to do better at the 2-level in a suit - unless you have the distribution to underwrite it.
With 21, and no better fit to play in a suit with BetaACOL we may find ourselves unfortunately forced into  2NT after partner makes a 2/1 response in a minor. This situation is not ideal and the contract may  fail by 1 trick. We have accepted this knowing that structurally we have great benefits from bidding in this way. Partner making a 2/1 is therefore asked to take care and realise that 10HCP is the gold standard rather than 9 and plus values like 5 cards or good intermediates are required with a 9 count and if otherwise the case to devalue the hand to 8 - especially at adverse vulnerability. So 22-23 is the gold standard for a 2NT and 19-21 acceptable for 1NT and probabilites bear this out in flat hands. However, as with 3NT, as long as some control is available a long suit can make all the difference and lower these standard ranges.
NT contracts is all about making your required tricks before opponents can muster a setting trick.

Let's now turn our attention to a suit contracts.

HCP counts are still quoted for suit contracts. Unfortunately they are now very unreliable! The more the hand is distributional the more they are unreliable.
Still figures like 26 HCP for a Major game are quoted and this is approximate for a moderately balanced hand with a fit. Even then a poor guide.
Distribution, the trump fit and controls are the decisive factors - NOT HCP counts.
First we look at the trump suit fit. Without a good fit suit contracts regularly fail. Losing control of a hand when the trump suit proves inadequate is one major reason for losing a contract.
5-4 fits or better can rarely prove insufficient so we will concentrate on the more frequent 4-4 and 5-3 fits. BetaACOL will always find these fits unless made difficult by opponent interventions. Nevertheless the more opponents intervene the more distributional the whole hand is likely to be. Distribution favours suit contracts as long as an adequate trump fit can be found. When intervening opponents demonstrate fits in their suit the probailities of having a fit yourself is mathematically enhanced.
The right kind of HCP is also often decisive.
First it is critical to have top controls in your longer side suits - missing A & K can lead to a third round ruff.
Good fit of an 8 card trump suit is not enough - again without a sufficient HCP count the opponets may reduce your trumps sufficiently to give you much trouble - Holding the Ace of trumps is really useful to reduce the risk of trump attacks.
A lot is said about 4-4 versus 5-3 fits. One is not necessarily better than the other - dispel the often stated idea that 4-4 is superior.
The LTC becomes far more important a measure than just HCP

Let's turn our attention to how is LTC determined:-
Examine each of your 4 suits in turn and consider just the 3  highest cards held:
Partner will also be aware of his count and all trump suit raises agreements will be limit bids based on LTC.
This is calculated by taking from 18 your own LTC count and what your partner's bidding tells you of his LTC count.
Some assumptions can be made:

However LTC is not enough in itself for slams - indeed it can be very misleading - now adequate controls are necessary - otherwise one can suffer the ignomy of losing A & K off the top or even 2 Aces!

There are 2 approaches:
  1. Best is cue bidding as it pin-points location and can be initiated even before game level where it can help too. However once cue-bidding is reaching 4NT, Beta uses TURBO.
  2. Then there is the 'Big Bang' 4NT ERKCB.

How do HCP, LTC & Controls influence determination of what is possible?

Let's first get an understanding where these measures (that's just what they are) fail.

1) Mirror hand patterns

Some simple examples:

A singleton opposite a singleton gets counted TWICE in an LTC count giving a higher result than is correct.
However this could work for you in another way - that all your values are concentrated in 3 suits rather than 4 suits - that is giving you a better HC count per cards held in that suit  ratio- this is always a good sign in suit contracts (disasterous in NT contracts!).
Same goes for xxx opposite xxx your 3 losers are coinciding - In suit or NT contract this can be very bad news.
Doubled HCP strength is wasted strength e.g e.g AQ opposite Kx Thats 9 points making just 2 tricks just where you might expect more e.g AQx opposite K.
In NT contracts a Quality suit opposite a  poor suit of similar length is far from helpful e.g. AKQJ opposite xxxx to take an extreme example to make the point makes 4 tricks, but AKQJ opposite x would also make 4 tricks while the 3 other cards could make a huge difference elsewhere in the  hand.
So  HCP  or LTC can easily have pitfalls. And the pitfalls are all due to  SHAPE and location of Honours!

Beta has a number of fundamental aids in determination of Shape and location of Honours. E.g Trump requests, Control requests, cue-bidding, very accurate determination of shape, location of honours in short suits, use of techniques that determination of suits, guards, controls in 2 suits at a time. A thorough examination of Beta will throw light on these claims.

As may be understood from the discussion on duplication of Honours and length,  HCP count, LTC is there another type of measure may be more accurate? Well that's difficult.

One thing Beta style bidding does very  well is: - determing shape accurately in most auctions - especially reasonably free auctions  - but even up to a point in contested auctions too.
This in turn in conjunction of rebids gives length  and a good idea of the LTC lower limit. Now shape is beginning to emerge giving you knowledge of the distribution of your partner and the nature of the fit (suspicion of duplication may also becoming obvious and will often need a 3rd round of bidding to know one way or the other for sure)

So now you have the chance of deducing the FIT of the hands.
For a measured evaluation take the sum of known cards in the trump suit and the secondary suit, (at least 4-3 in the second suit), subtract 2 for 2-2 or longer in the other 2 suits, add 3 for a useful singleton and 5 for a useful void. An 18 count is to be considered as average for a major game or higher level contracts,  each point above 17 is a plus point,
If other indications primarily controls & HCP  indicate some doubt in a small or grand slam 3+ additional  points as explained above should sway you in favour.

For balanced hands we provide this rough table of HCP  normally required  for the level  stated  playing in a suit or NTs. This table is not valid for distributional hands with 6+ card suits (see below). Valid for trump fits of 4-4 or 5-3. Distributional points (DP)  are  additional points for useful shortages (singleton 2 and void 4)

Level
NT contract HCP required
Suit  contract DP required
1
20-22
16-19
2
22-24
19-21
3
25-27
22-24
4
27-29
25-27
5
29-31
27-29
6
32-35
29-32
7
36+
33+

In NT contracts good controls and a long  6+ cards establishable suit for loss of at most 1 trick, can significantly reduce the above points required. So such a 6 card suit can reduce CP requirements by up to 2 points and such a 7 card suit by up to 4 HCP on the condition that it is establishable before opponents can setup their best suit.

In Suit contracts presence a 6+ card suit, shortages, useful singletons & voids and additional trump cards 9+,  will reduce the HCP requirements. In these cases we re-value hands with Distributional points DP once a fit is established.

DP = HCP + Distributional points

Distributional points for suit contracts in unbalanced hands with a 6+ card suit and at least 9 trump cards:
Notice with less balanced hands, maximum a 5 card suit, our additions for shortages are shaved by a point.