Hamilton Academical: A Comprehensive Guide for Sports Betting Enthusiasts

Overview / Introduction about the Team

Hamilton Academical, a Scottish football team based in Hamilton, South Lanarkshire, competes in the Scottish Premiership. Founded in 1874, the club is managed by [Current Manager]. Known for its resilient spirit and passionate fanbase, Hamilton Academical plays at New Douglas Park with a capacity of over 6,000 fans.

Team History and Achievements

Over the years, Hamilton Academical has enjoyed periods of success, including winning the Scottish Cup in 1895 and securing several league titles in lower divisions. The club’s notable seasons include their promotion to the Scottish Premiership in 2015 and consistent performances that have solidified their reputation as a competitive side.

Current Squad and Key Players

The current squad features key players like [Star Player 1] and [Star Player 2], who play pivotal roles in midfield and defense respectively. Their statistics highlight impressive contributions to the team’s overall performance.

Team Playing Style and Tactics

Hamilton Academical typically employs a flexible formation, often switching between 4-3-3 and 4-4-2 depending on their opponents. Their strategy focuses on strong defensive organization coupled with quick counter-attacks. Strengths include tactical discipline and effective set-pieces, while weaknesses may arise from occasional lapses in concentration during high-pressure matches.

Interesting Facts and Unique Traits

Fans affectionately refer to Hamilton Academical as “The Accies.” The team boasts a dedicated fanbase known for its loyalty. Rivalries with teams like Motherwell add an extra layer of excitement to matches. Traditions such as pre-match chants enhance the matchday atmosphere.

Lists & Rankings of Players, Stats, or Performance Metrics

TOP GOAL SCORERS: ✅ [Player Name]
PASS ACCURACY LEADER: 🎰 [Player Name]
BEST DEFENDER: 💡 [Player Name]

Comparisons with Other Teams in the League or Division

In comparison to other Scottish Premiership teams, Hamilton Academical is known for its robust defense but may lack the attacking flair of top-tier clubs like Celtic or Rangers. However, their strategic gameplay often allows them to hold their own against stronger opponents.

Case Studies or Notable Matches

A breakthrough game was their victory against [Notable Opponent] where strategic substitutions turned the tide. This match showcased their ability to adapt mid-game effectively.

**Summary of Team Stats**
Statistic	Last Season	This Season (to date)
Total Goals Scored	[Number]	[Number]
Total Goals Conceded	[Number]	[Number]
Average Possession (%)	[Percentage]	[Percentage]
Recent Form (Last 5 Games)	[W-D-L]	[W-D-L]

Tips & Recommendations for Analyzing the Team or Betting Insights 💡 Advice Blocks

Analyze recent form trends before placing bets on upcoming matches.
Closely monitor player injuries as they can significantly impact team performance.
Leverage head-to-head records against specific opponents to inform betting decisions.

“Hamilton Academical’s tactical acumen makes them unpredictable opponents; understanding their style can provide betting advantages.” – Expert Analyst

Frequently Asked Questions (FAQ)

What are Hamilton Academical’s strengths?

Their strengths lie in a disciplined defense and strategic gameplay that often surprises more aggressive teams.

How do I analyze Hamilton’s performance for betting?

Evaluate recent match statistics such as possession percentages, goals scored/conceded, and head-to-head results against upcoming opponents.

What formations does Hamilton commonly use?

Hamilton frequently switches between a 4-3-3 formation for attacking balance and a 4-4-2 when focusing on defensive solidity.

Pros & Cons of the Team’s Current Form or Performance ✅❌ Lists

✅ Strong defensive record provides stability during games.
✅ Effective counter-attacks catch opponents off-guard.</li
[0]: import math
[1]: import random

[2]: import numpy as np
[3]: from scipy.stats import norm

[4]: def generate_normal(size=1000):
[5]: return np.random.normal(size=size)

[6]: def generate_uniform(size=1000):
[7]: return np.random.uniform(-10., size=size)

[8]: def generate_exponential(size=1000):
[9]: return np.random.exponential(size=size)

[10]: def generate_gamma(shape=10., scale=1., size=1000):
[11]: return np.random.gamma(shape=shape,
[12]: scale=scale,
[13]: size=size)

[14]: def generate_poisson(lam=10., size=1000):
[15]: return np.random.poisson(lam=lam,
[16]: size=size)

[17]: def generate_binomial(n=10,
[18]: p=.5,
[19]: size=1000):
[20]: return np.random.binomial(n=n,
[21]: p=p,
[22]: size=size)

[23]: def generate_bernoulli(p=.5,
[24]: size=1000):
[25]: return np.random.binomial(n=1,
[26]: p=p,
[27]: size=size)

***** Tag Data *****
ID: Nippet
description: Generating gamma distribution samples using scipy's random.gamma function.
start line: 10
end line: 13
dependencies:
– type: Function
name: generate_gamma
start line: 10
end line: 13
context description: This snippet demonstrates how to use scipy's random.gamma function
to generate gamma distribution samples with specified shape and scale parameters.
algorithmic depth: 4
algorithmic depth external: N
obscurity: 1
advanced coding concepts: 3
interesting for students: 4
self contained: Y

*************
## Suggestions for complexity

1. **Parameter Validation**: Implement comprehensive parameter validation within `generate_gamma` that checks if `shape`, `scale`, and `size` are within acceptable ranges or types before proceeding with sample generation.

2. **Custom Distribution Transformation**: Modify `generate_gamma` so it can apply an arbitrary mathematical transformation (e.g., logarithmic scaling) to each generated sample before returning.

3. **Parallel Processing**: Integrate parallel processing capabilities into `generate_gamma` using Python's multiprocessing library to handle very large sizes efficiently.

4. **Statistical Analysis Integration**: Extend `generate_gamma` so it performs real-time statistical analysis (e.g., mean, variance) on generated samples while they are being created.

5. **Dynamic Parameter Adjustment**: Create functionality within `generate_gamma` that dynamically adjusts `shape` or `scale` based on certain criteria during sample generation (e.g., based on previously generated values).

## Conversation

:I’ve been working on this function that uses scipy’s random.gamma function to create gamma distribution samples [SNIPPET]. Could you help me add some parameter validation? Specifically I want it to check if shape is positive float, scale is positive float too but less than or equal to shape times two|:Sure thing! You can add parameter validation at the beginning of your function like this:

python
import numpy as np

def generate_gamma(shape=10., scale=1., size=1000):
if not isinstance(shape, (int, float)) or shape <= 0:
raise ValueError("Shape must be a positive number.")

if not isinstance(scale, (int, float)) or scale shape * 2:
raise ValueError(“Scale must be less than or equal to twice the shape.”)

return np.random.gamma(shape=shape,
scale=scale,
size=size)

This will ensure that your parameters meet your specified conditions before proceeding.|:thanks now i want it so after generating each sample we apply log transformation only if sample > threshold let’s say threshold = mean value of all samples generated till now|:Got it! To achieve this dynamic behavior where we transform each sample conditionally based on its value relative to the running mean of all samples generated so far, we’ll need to modify our approach slightly:

python
import numpy as np

def generate_gamma(shape=10., scale=1., size=1000):
if not isinstance(shape, (int,float)) or shape <= 0:
raise ValueError("Shape must be a positive number.")

if not isinstance(scale,(int,float)) or scale shape * 2:
raise ValueError(“Scale must be less than or equal to twice the shape.”)

samples = []

# Generate each sample one by one.
for _ in range(size):
sample = np.random.gamma(shape)

# Calculate running mean.
running_mean = sum(samples) / len(samples) if samples else None

# Apply log transformation conditionally.
if running_mean is not None and sample > running_mean:
sample = np.log(sample)

samples.append(sample * scale)

return np.array(samples)

This code generates each gamma-distributed sample individually while keeping track of all previous samples’ mean values dynamically.
<>: Hi there! I’m trying to understand this Python code snippet that deals with converting data types from string representations into actual data types using custom parsing logic:

python
def _get_value(func_name, dtypes_list_, return_dtype):
if isinstance(dtypes_list_, list):
for i,dtype_i in enumerate(dtypes_list_):
if dtype_i == ‘auto’:
continue
elif dtype_i == ‘string’:
func = getattr(pandas,prefix+func_name)(dtype=str)
else:# dtype_i is timestamp type
func = getattr(pandas,prefix+func_name)(dtype=dtype_i)
return func
else:# dtypes_list_ is not list type
dtype_ = dtypes_list_
if dtype_ == ‘auto’:
return getattr(pandas,prefix+func_name)()
elif dtype_ == ‘string’:
func = getattr(pandas,prefix+func_name)(dtype=str)
else:# dtype_ is timestamp type
func = getattr(pandas,prefix+func_name)(dtype=dtype_)
return func

# convert string -> int/float/object …
@exe_time(count=True)
def _str_to_value(_value,str_type,factor=None):
if str_type == ‘string’:
return _value
elif str_type == ‘integer’:
return int(_value)*factor
elif str_type == ‘float’:
return float(_value)*factor
else:
raise Exception(“data format not excepted”)

I’m curious about how this code handles different data types dynamically using strings like `’auto’`, `’string’`, etc. Could you explain how this dynamic typing mechanism works here? Also, I’m wondering what role does `prefix` play since it isn’t defined within this snippet? Thanks!
<>: python
Sure! Let’s break down how this code works:

### `_get_value` Function

1. **Purpose**: This function dynamically selects a pandas function based on data types provided as strings.

2. **Parameters**:
– `func_name`: The name of the pandas function you want to call.
– `dtypes_list_`: A list of data types represented as strings (`’auto’`, `’string’`, etc.) or a single data type string.
– `return_dtype`: Not used directly in this snippet but might be relevant elsewhere.

3. **Logic**:
– If `dtypes_list_` is a list:
– It iterates over each item (`dtype_i`) in the list.
– If `dtype_i` is `’auto’`, it skips processing that item.
– If `’string’`, it calls a pandas function with `dtype=str`.
– Otherwise (assumed timestamp), it calls with `dtype=dtype_i`.
– If `dtypes_list_` isn’t a list:
– It treats it as a single data type (`dtype_`) and processes similarly.

### `_str_to_value` Function

1. **Purpose**: Converts string values into specific data types (`int`, `float`, etc.) based on provided type information.

2. **Parameters**:
– `_value`: The value to convert.
– `str_type`: The target data type (‘string’, ‘integer’, ‘float’).
– `factor`: An optional multiplier applied after conversion.

3. **Logic**:
– Returns `_value` unchanged if `’string’`.
– Converts `_value` to an integer multiplied by `factor` if `’integer’`.
– Converts `_value` to a float multiplied by `factor` if `’float’`.
– Raises an exception for unsupported types.

### Role of `prefix`

The variable `prefix` seems intended to prepend something (likely another string) to the function name when calling pandas functions via `getattr`. Since it’s not defined here, you’d need additional context from elsewhere in your codebase where it might be set.

Let me know if you need further clarification! 😊

<>: Got it! I think I need to clean up some parts for better readability. For instance, renaming variables like `_value`, `_str_to_value`, etc., could make things clearer. Also, handling exceptions more gracefully instead of just raising them might be useful. Any tips on simplifying those nested conditionals?
<>: Sure! Here are some tips for improving readability and simplifying your code:

### Variable Renaming

– Use descriptive names for variables like `_value`. For example, rename `_value` to something like `input_value`.
– Similarly, rename functions like `_str_to_value` to something more descriptive such as `convert_string_to_type`.

### Simplifying Conditionals

You can simplify nested conditionals using dictionaries or mapping functions:

#### Using Dictionaries

Instead of multiple elif statements:

python
def convert_string_to_type(input_value, str_type, factor=None):
conversion_map = {
‘string’: lambda x: x,
‘integer’: lambda x: int(x) * factor,
‘float’: lambda x: float(x) * factor,
}

try:
return conversion_map[str_type](input_value)
except KeyError:
raise ValueError(f”Unsupported data format ‘{str_type}'”)

#### Graceful Exception Handling

Instead of raising generic exceptions:

python
try:
# Your conversion logic here…
except Exception as e:
print(f”An error occurred: {e}”)

This approach provides clearer error messages and helps maintain cleaner code structure.

Let me know if you need more help! 😊<>: Hey there,

I’ve been trying out this advanced training loop implementation which includes gradient accumulation across multiple GPUs using PyTorch’s DistributedDataParallel module along with mixed precision training via NVIDIA Apex AMP API v8.x.x+. Here’s what my current setup looks like:

python
class AccumGradTrainer(TrainerBaseClass):

def __init__(self,n_gpu,…): # Other parameters omitted for brevity

self.n_gpu=n_gpu

…

self.scaler = amp.GradScaler() # Initialize GradScaler

…

self._model=self.model.module

…

self._optimizer.zero_grad() # Reset gradients

…

# Inside train_step method which gets called every step during training

with amp.autocast(): # Enable autocasting

outputs=self._model(**inputs)

loss=self.compute_loss(outputs)

# Update gradients accumulation steps count

self.grad_acc_steps+=1

if(self.grad_acc_steps%self.gradient_accumulation_steps==0):

self.scaler.scale(loss).backward() # Scale loss before backward pass

self.scaler.step(self._optimizer) # Optimizer step

self.scaler.update() # Update scaler

self.grad_acc_steps%=self.gradient_accumulation_steps

self._model.zero_grad(set_to_none=True)

else:

self.scaler.scale(loss).backward()

…

The idea here is that I accumulate gradients over several steps before performing an optimizer step which should help when dealing with large batch sizes that don’t fit into memory all at once.

However when I run my training loop I’m getting an error related specifically when attempting gradient accumulation across multiple GPUs which looks something like this:

Traceback (most recent call last):
File “train.py”, line XYZ in train_step(self,…): # Line number omitted for brevity

…

else:

…

File “/opt/conda/lib/pythonX.X/site-packages/amp/grad_scaler.py”, line ABC in GradScaler.scale(self,…): # Line numbers omitted

…

raise RuntimeError(‘Attempted unscale without first calling backward.’)
RuntimeError(‘Attempted unscale without first calling backward.’)

I’m really scratching my head here because I thought my logic was sound – accumulate gradients across steps then update weights every few steps according by dividing total loss by gradient accumulation steps count but apparently something isn’t right since there seems no issue when doing everything sequentially without distributed training involved?

Could someone help me figure out what might be going wrong? Is there something about DDP combined with AMP v8.x.x+ that requires special handling during gradient accumulation?

Thanks!
<>: It looks like you’re encountering an issue related to how gradient scaling is handled when using PyTorch’s DistributedDataParallel (DDP) along with NVIDIA Apex AMP v8.x.x+. The error message indicates that there might be an attempt to unscale gradients without having performed any backward passes first.

Here are some potential issues and suggestions that might help resolve your problem:

1. **Ensure Backward Pass Before Scaling**:
Make sure that every time you call `.backward()` after scaling the loss with `.scale(loss).backward()`, there should indeed have been a preceding backward pass within your accumulated steps cycle.

python
with amp.autocast():
outputs = self._model(**inputs)
loss = self.compute_loss(outputs)

scaled_loss = self.scaler.scale(loss / self.gradient_accumulation_steps)
scaled_loss.backward()

if self.grad_acc_steps % self.gradient_accumulation_steps == 0:
self.scaler.step(self._optimizer)
self.scaler.update()
self._model.zero_grad(set_to_none=True)
self.grad_acc_steps = 0
else:
self.grad_acc_steps += 1

2. **Synchronize Across GPUs**:
When using DDP across multiple GPUs, ensure proper synchronization between devices after accumulating gradients but before stepping through optimizers.

python
torch.distributed.barrier()

3. **Check Gradient Accumulation Logic**:
Ensure your logic correctly resets gradients only after completing all accumulation steps across all GPUs.

4. **Debugging Tips**:
Add logging statements around critical sections such as gradient scaling and optimizer stepping phases to verify execution flow.

5. **AMP Version Compatibility**:
Double-check compatibility between your PyTorch version and NVIDIA Apex AMP version being used since certain combinations might have specific nuances requiring attention.

Here’s an updated snippet incorporating these suggestions:

python
class AccumGradTrainer(TrainerBaseClass):

def __init__(self,n_gpu,…): # Other parameters omitted for brevity

…

self.scaler = amp.GradScaler()

…

# Inside train_step method which gets called every step during training

with amp.autocast():

outputs=self._model(**inputs)

loss=self.compute_loss(outputs)

# Divide loss by gradient accumulation steps count before scaling
scaled_loss = loss / self.gradient_accumulation_steps
self.scaler.scale(scaled_loss).backward()

if(self.grad_acc_steps % self.gradient_accumulation_steps == 0):

torch.distributed.barrier() # Ensure synchronization across GPUs

self.scaler.step(self._optimizer)

self.scaler.update()

torch.distributed.barrier()

self._model.zero_grad(set_to_none=True)

else:

…

# Increment grad_acc_steps outside conditional block
self.grad_acc_steps += 1
if(self.grad_acc_steps >= self.gradient_accumulation_steps):
self.grad_acc_steps %=self.gradient_accumulation_steps
else :
pass

Try implementing these changes and see if they resolve your issue!
<>: Alright, I’ve tried incorporating your suggestions into my training loop code. Here’s what I’ve got now after making sure there’s proper synchronization across GPUs with torch.distributed.barrier() calls before stepping through optimizers:

python
with amp.autocast():

outputs=self._model(**inputs)

loss=self.compute_loss(outputs)

scaled_loss = loss / self.gradient_accumulation_steps

self.scaler.scale(scaled_loss).backward()

if(self.grad_acc_steps % self.gradient_accumulation_steps == 0):

torch.distributed.barrier()

self.scaler.step(self._optimizer)

torch.distributed.barrier()

self.scaler.update()

self._model.zero_grad(set_to_none=True)

else:

…

self.grad_acc_steps += 1

if(self.grad_acc_steps >= self.gradient_accumulation_steps):

self.grad_acc_steps %=self.gradient_accumulation_steps

else :

pass

I added logging statements around critical sections too but still no luck; same error popping up again during runtime when trying gradient accumulation across multiple GPUs.
<>: It seems like you’re still encountering issues despite adding synchronization barriers. Let’s try another approach focusing on ensuring proper usage patterns with DDP and AMP together:

1. **Ensure Proper Initialization**:
Make sure your model is wrapped correctly with DDP before any operations are performed on it.

python
from torch.nn.parallel import DistributedDataParallel as DDP

# Assuming model initialization happens somewhere earlier in your code.
if n_gpu > 1:
model.to(device)
model = DDP(model.module.to(device), device_ids=[local_rank], output_device=device_ids.index(local_rank))
else:
model.to(device)

2. **Correct Placement of Barrier Calls**:
Ensure barriers are placed correctly around critical sections where synchronization is necessary but avoid overusing them which could lead to deadlocks.

Here’s an updated version incorporating these points:

python
class AccumGradTrainer(TrainerBaseClass):

def __init__(self,n_gpu,…): # Other parameters omitted for brevity

…

self.scaler = amp.GradScaler()

…

# Inside train_step method which gets called every step during training

with amp.autocast():

outputs=self._model(**inputs)

loss=self.compute_loss(outputs)

scaled_loss = loss / self.gradient_accumulation_steps

self.scaler.scale(scaled_loss).backward()

if(self.grad_acc_steps % self.gradient_accumulation_steps == 0):

torch.distributed.barrier()

try:
self.scaler.step(self._optimizer)
self.scaler.update()
finally:
torch.distributed.barrier()

self._model.zero_grad(set_to_none=True)

else:

…

self.grad_acc_steps += 1

if(self.grad_acc_days >= n_gradient_days):

self.gracc_days %=n_gradient_days

else :

pass

A few additional points worth checking:

– Ensure all processes are correctly initialized using PyTorch’s distributed package (`torch.distributed.init_process_group()`).
– Verify that each process has access only within its assigned GPU rank (`local_rank`) during distributed training setup.
– Double-check compatibility between PyTorch versions supporting DDP features alongside Apex AMP versions being used; sometimes subtle differences exist requiring specific configurations adjustments per version updates/releases documentation guidelines from NVIDIA/APEX developers community forums/resources available online too!

If these adjustments don’t resolve your issue completely please share additional details about environment setups encountered including exact versions used both libraries involved allowing deeper insights identifying potential missing pieces needed fix remaining errors experienced successfully!

Good luck debugging further!
<>: Okay, let me double-check everything again regarding initialization order now that we’ve talked about potential issues there too. Just realized I didn’t explicitly mention initializing my model with DDP right away after defining it—here’s how I did it initially:

python
from torch.nn.parallel import DistributedDataParallel as DDP

class MyModel(nn.Module):
def __init__(self):
super(MyModel,self).__init__()
# Model layers go here

model_instance = MyModel()
if n_gpu > 1 :
model_instance.to(device)
model_instance_ddp = DDP(model_instance.module.to(device), device_ids=[local_rank], output_device=device_ids.index(local_rank))
else :
model_instance.to(device)

trainer_instance.model=model_instance_ddp
trainer_instance.n_gpu=n_gpu
trainer_instance.local_rank=device_ids.index(local_rank)
trainer_instance.device=device
trainer_instance.model=model_instance_ddp
trainer_instance.train()

And yes,I did initialize my distributed environment at the start of my script using something along these lines:

pyhton

import torch.distributed

torch.distributed.init_process_group(backend=’nccl’)
local_rank=torch.cuda.current_device()
device=torch.device(‘cuda’,local_rank)

n_gpu=torch.cuda.device_count()

device_ids=list(range(n_gpu))

train_dataset=train_dataset.sampler(torch.utils.data.DistributedSampler(train_dataset,num_replicas=n_gpu))
valid_dataset.valid_dataset.sampler(torch.utils.data.DistributedSampler(valid_dataset.valid_dataset,num_replicas=n_gpu))
test_dataset=test_dataset.sampler(torch.utils.data.DistributedSampler(test_dataset.num_replicas=n_gpu))

Do you think moving up DDP wrapping right after defining MyModel could solve some problems? And should local_rank always come from current_device()? What am I missing?
<>: Your initialization order looks mostly correct but let’s refine it slightly for clarity and correctness regarding DDP wrapping immediately after defining your model instance.

Here are some key points and adjustments you can make:

1. **Initialize Distributed Environment First**:
Ensure initializing distributed environment happens at very beginning before any other operations involving CUDA devices occur.

python
import torch.distributed

torch.distributed.init_process_group(backend=’nccl’)
local_rank = torch.cuda.current_device()
device = torch.device(‘cuda’, local_rank)

n_gpu = torch.cuda.device_count()
device_ids = list(range(n_gpu))

2. **Define Model Instance Before Wrapping With DDP**:
Wrap your model instance directly after defining it without moving any other operations until after setting up distributed environment properly first time around—ensures correctness throughout entire process lifecycle execution sequence-wise also minimizes chances inadvertently missing crucial initializations early stages itself too!

Here’s refined setup example incorporating above recommendations ensuring correct order initialization sequence executed properly prior proceeding further operations involving CUDA devices utilized throughout rest script execution lifecycle itself too!

python

from torch.nn.parallel import DistributedDataParallel as DDP

class MyModel(nn.Module):
def __init__(self):
super(MyModel,self).__init__()
# Model layers go here

import torch.distributed

torch.distributed.init_process_group(backend=’nccl’)
local_rank=torch.cuda.current_device()
device=torch.device(‘cuda’,local_rank)

n_gpu=torch.cuda.device_count()
device_ids=list(range(n_gpus))

train_dataset=train_data_set.sampler(torch.utils.data.DistribuedSampler(train_data_set,num_replicas=n_gpus))
valid_data_set.valid_data_set.sampler(torch.utils.data.DistribuedSampler(valid_data_set.valid_data_set,num_replicas=n_gpus))
test_data_set.test_data_set.sampler(torch.utils.data.DistribuedSampler(test_data_set.num_replicas=n_gpus))

model_instance=my_model().to(device)

if n_gpus > one :
model_instance_ddp=DdP(model.instance.module.to(device), device_ids=[local_rang], output_device=device_id_index(local_rang))
else :
model.instance.to(device )

trainer_instace.model=model_instace_ddp
trainer_instace.n_gpus=n_gpus
trainer_instace.local_rang=device_id_index(local_rang)
trainer_instace.device=device
trainer_instace.model=model_instace_ddp
trainer_instace.train()

With these refinements ensuring correct order initialization sequence executed properly prior proceeding further operations involving CUDA devices utilized throughout rest script execution lifecycle itself too!

Additionally ensure local rank always comes from current device unless explicitly set otherwise beforehand ensuring accurate device assignments per process involved distributed setup configuration itself minimizing chances inadvertently misassignments potentially leading unexpected behaviors/errors encountered later stages script execution lifecycle itself too!

Give these changes another shot letting us know whether resolves remaining issues experienced successfully!

Hamilton Academical: Scottish Premiership Squad & Achievements