Feature/dynamic beta

src/components/Header.css

@@ -115,7 +115,7 @@
   background: rgba(255, 255, 255, 0.1);
 }
 
-@media (max-width: 768px) {
+@media (max-width: 950px) {
   .nav-desktop {
     display: none;
   }

src/pages/HomePage.css

@@ -28,8 +28,10 @@
   font-weight: 700;
   line-height: 1.2;
   margin-bottom: 1rem;
-  padding-right: 4rem;
-  margin-left: 2rem;
+  padding-right: 0rem;
+  margin-left: 0;
+  width: 100%;
+
 }
 
 .hero-subtitle-short {
@@ -39,7 +41,7 @@
   margin-bottom: 1.5rem;
   color: rgba(255, 255, 255, 0.9);
   padding-right: 4rem;
-  margin-left: 2rem;
+  /* margin-left: 2rem; */
   max-width: 400rem;
 }
 
@@ -67,6 +69,7 @@
   padding: 0;
   text-align: left;
   max-width: 500px;
+  width: 100%;
 }
 
 .cta-heading {
@@ -75,6 +78,8 @@
   color: rgba(255, 255, 255, 0.9);
   margin: 0 0 0.5rem 0;
   letter-spacing: -0.01em;
+  width: auto;
+  text-wrap: wrap;
 }
 
 .cta-description {
@@ -86,19 +91,20 @@
 }
 
 .cta-card .btn {
-  background: linear-gradient(135deg, #fa961c 0%, #ffaa00 100%);
+  /* background: linear-gradient(135deg, #fa961c 0%, #ffaa00 100%); */
+  background: rgb(108, 112, 119);
   color: white;
   font-weight: 500;
   padding: 0.5rem 1.25rem;
   font-size: 1.1rem;
-  border: none;
+  border: 2px solid #4d4d4dd6;
   border-radius: 6px;
   transition: all 0.2s ease;
   letter-spacing: 0.01em;
 }
 
 .cta-card .btn:hover {
-  background: linear-gradient(135deg, #ff9012 0%, #ff8809 100%);
+  background:  #555555d6;
   transform: translateY(-1px);
   box-shadow: 0 2px 8px rgba(79, 70, 229, 0.25);
 }
@@ -122,15 +128,15 @@
 }
 
 .btn-primary {
-  background: #2563eb;
+  background: #fa961c;
   color: white;
   font-weight: 600;
   font-size: 1.3rem;
   border: none;
 }
 
 .btn-primary:hover {
-  background: #1d4ed8;
+  background: #dd7e09;
   transform: translateY(-1px);
   box-shadow: 0 4px 12px rgba(37, 99, 235, 0.3);
 }
@@ -178,8 +184,8 @@
   gap: 1.5rem;
   align-items: left;
   justify-content: left;
-  margin-left: 2rem;
-  margin-right: -2rem;
+  /* margin-left: 2rem;
+  margin-right: -2rem; */
 }
 
 .hero-card {

src/pages/LeaderboardPage.css

@@ -172,17 +172,46 @@
   display: flex;
   flex-direction: column;
   gap: 0.35rem;
-  min-width: 200px;
+  min-width: 300px;
 }
 
-.beta-label {
-  display: flex;
-  justify-content: space-between;
-  font-size: 0.9rem;
+.beta-label-link {
+  display: inline-flex;
+  align-items: center;
+  gap: 0.5rem;
+  font-size: 1rem;
   font-weight: 600;
-  color: #1f2937;
+  color: #363a42;
+  background: transparent;
+  border: none;
+  padding: 0;
+  cursor: pointer;
+  position: relative;
 }
 
+.beta-label-text {
+  position: relative;
+  display: inline-block;
+}
+
+.beta-label-text::after {
+  content: '';
+  position: absolute;
+  bottom: -2px;
+  left: 0;
+  width: 100%;
+  height: 1px;
+  background: rgba(37, 99, 235, 0.3);
+  transform: scaleX(0);
+  transition: transform 0.2s ease;
+  transform-origin: left;
+}
+
+.beta-label-link:hover .beta-label-text::after {
+  transform: scaleX(1);
+}
+
+
 .beta-value {
   font-variant-numeric: tabular-nums;
   color: #2563eb;
@@ -196,8 +225,39 @@
 .beta-hints {
   display: flex;
   justify-content: space-between;
-  font-size: 0.75rem;
-  color: #6b7280;
+  font-size: 0.9rem;
+  color: #363636;
+}
+
+.beta-weights {
+  display: flex;
+  gap: 1rem;
+  align-items: center;
+  flex-wrap: wrap;
+  font-size: 0.9rem;
+  color: #1f2937;
+}
+
+.beta-weight {
+  display: flex;
+  flex-direction: column;
+  background: #eef2ff;
+  border-radius: 8px;
+  padding: 0.5rem 0.75rem;
+}
+
+.beta-weight strong {
+  font-size: 1rem;
+  font-weight: 700;
+}
+
+.beta-weight-pill {
+  background: #dbeafe;
+  border-radius: 999px;
+  padding: 0.5rem 1rem;
+  font-weight: 600;
+  color: #1d4ed8;
+
 }
 
 .filter-group {

src/pages/LeaderboardPage.tsx

@@ -31,14 +31,20 @@ const computeArenaScore = (router: Router, beta: number): number => {
   return (((1 + beta) * accuracy * normalizedCost) / denominator) * 100;
 };
 
+const DEFAULT_BETA = 0.1;
+const defaultCostWeight = DEFAULT_BETA / (1 + DEFAULT_BETA);
+
 const LeaderboardPage: React.FC = () => {
   const [searchTerm, setSearchTerm] = useState('');
   const [filterType, setFilterType] = useState<'all' | 'open-source' | 'closed-source'>('all');
   const [activeMetric, setActiveMetric] = useState<
     'arena' | 'accuracy' | 'cost' | 'optimalSelection' | 'optimalCost' | 'optimalAcc' | 'latency' | 'robustness'
   >('arena');
   const [activeTab, setActiveTab] = useState<'spider' | 'deferral'>('spider');
-  const [beta, setBeta] = useState(0.1);
+  const [costWeight, setCostWeight] = useState(defaultCostWeight);
+
+  const beta = costWeight / (1 - costWeight);
+  const accuracyWeight = 1 - costWeight;
 
   // Deferral curve data
   const openSourcePoints = {
@@ -239,23 +245,38 @@ const LeaderboardPage: React.FC = () => {
           </div>
 
           <div className="beta-control">
-            <div className="beta-label">
-              <span>Arena β</span>
-              <span className="beta-value">{beta.toFixed(2)}</span>
-            </div>
+            <button
+              type="button"
+              className="beta-label-link"
+              onClick={() =>
+                document.getElementById('metrics-explanation')?.scrollIntoView({ behavior: 'smooth' })
+              }
+            >
+              <span className="beta-label-text">Weighted Arena Score</span>
+            </button>
             <input
               type="range"
               id="beta-slider"
-              min={0.01}
-              max={0.1}
-              step={0.001}
-              value={beta}
-              onChange={event => setBeta(parseFloat(event.target.value))}
+              min={0.05}
+              max={0.95}
+              step={0.01}
+              value={costWeight}
+              onChange={event => {
+                const value = parseFloat(event.target.value);
+                const clamped = Math.min(0.95, Math.max(0.05, value));
+                setCostWeight(clamped);
+              }}
               className="beta-slider"
             />
             <div className="beta-hints">
-              <span>Accuracy-first</span>
-              <span>Cost-first</span>
+              <span>{(costWeight * 100).toFixed(0)}% Cost Weight</span>
+              <span> Accuracy Weight {(accuracyWeight * 100).toFixed(0)}%</span>
+            </div>
+            <div className="beta-weights">
+
+              <div className="beta-weight-pill">
+                β = cost weight&nbsp;: accuracy weight&nbsp;= {beta.toFixed(2)}
+              </div>
             </div>
           </div>
         </div>
@@ -447,11 +468,11 @@ const LeaderboardPage: React.FC = () => {
         </div>
 
         {/* Metrics Explanation */}
-        <div className="metrics-explanation">
+        <div className="metrics-explanation" id="metrics-explanation">
           <h2>Evaluation Metrics</h2>
           <div className="metrics-grid">
             {/* 1️⃣ Arena Score */}
-            <div className="metric-card">
+            <div className="metric-card" >
               <div className="metric-summary">
                 <h3>Arena Score</h3>
                 <p>Weighted harmonic mean capturing the trade-off between accuracy and cost.</p>